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showpage |
| ... | ... |
@@ -152,24 +152,46 @@ |
| 152 | 152 |
Disable SoPlex support. |
| 153 | 153 |
|
| 154 | 154 |
--with-coin[=PREFIX] |
| 155 | 155 |
|
| 156 | 156 |
Enable support for COIN-OR solvers (CLP and CBC). You should |
| 157 | 157 |
specify the prefix too. (by default, COIN-OR tools install |
| 158 | 158 |
themselves to the source code directory). This command enables the |
| 159 | 159 |
solvers that are actually found. |
| 160 | 160 |
|
| 161 | 161 |
--with-coin-includedir=DIR |
| 162 | 162 |
|
| 163 | 163 |
The directory where the COIN-OR header files are located. This is |
| 164 | 164 |
only useful when the COIN-OR headers and libraries are not under |
| 165 | 165 |
the same prefix (which is unlikely). |
| 166 | 166 |
|
| 167 | 167 |
--with-coin-libdir=DIR |
| 168 | 168 |
|
| 169 | 169 |
The directory where the COIN-OR libraries are located. This is only |
| 170 | 170 |
useful when the COIN-OR headers and libraries are not under the |
| 171 | 171 |
same prefix (which is unlikely). |
| 172 | 172 |
|
| 173 | 173 |
--without-coin |
| 174 | 174 |
|
| 175 | 175 |
Disable COIN-OR support. |
| 176 |
|
|
| 177 |
|
|
| 178 |
Makefile Variables |
|
| 179 |
================== |
|
| 180 |
|
|
| 181 |
Some Makefile variables are reserved by the GNU Coding Standards for |
|
| 182 |
the use of the "user" - the person building the package. For instance, |
|
| 183 |
CXX and CXXFLAGS are such variables, and have the same meaning as |
|
| 184 |
explained in the previous section. These variables can be set on the |
|
| 185 |
command line when invoking `make' like this: |
|
| 186 |
`make [VARIABLE=VALUE]...' |
|
| 187 |
|
|
| 188 |
WARNINGCXXFLAGS is a non-standard Makefile variable introduced by us |
|
| 189 |
to hold several compiler flags related to warnings. Its default value |
|
| 190 |
can be overridden when invoking `make'. For example to disable all |
|
| 191 |
warning flags use `make WARNINGCXXFLAGS='. |
|
| 192 |
|
|
| 193 |
In order to turn off a single flag from the default set of warning |
|
| 194 |
flags, you can use the CXXFLAGS variable, since this is passed after |
|
| 195 |
WARNINGCXXFLAGS. For example to turn off `-Wold-style-cast' (which is |
|
| 196 |
used by default when g++ is detected) you can use |
|
| 197 |
`make CXXFLAGS="-g -O2 -Wno-old-style-cast"'. |
| ... | ... |
@@ -5,48 +5,49 @@ |
| 5 | 5 |
|
| 6 | 6 |
CONFIGURE_FILE( |
| 7 | 7 |
${PROJECT_SOURCE_DIR}/doc/Doxyfile.in
|
| 8 | 8 |
${PROJECT_BINARY_DIR}/doc/Doxyfile
|
| 9 | 9 |
@ONLY |
| 10 | 10 |
) |
| 11 | 11 |
|
| 12 | 12 |
IF(DOXYGEN_EXECUTABLE AND PYTHONINTERP_FOUND AND GHOSTSCRIPT_EXECUTABLE) |
| 13 | 13 |
FILE(MAKE_DIRECTORY ${CMAKE_CURRENT_BINARY_DIR}/html/)
|
| 14 | 14 |
SET(GHOSTSCRIPT_OPTIONS -dNOPAUSE -dBATCH -q -dEPSCrop -dTextAlphaBits=4 -dGraphicsAlphaBits=4 -sDEVICE=pngalpha) |
| 15 | 15 |
ADD_CUSTOM_TARGET(html |
| 16 | 16 |
COMMAND ${CMAKE_COMMAND} -E remove_directory gen-images
|
| 17 | 17 |
COMMAND ${CMAKE_COMMAND} -E make_directory gen-images
|
| 18 | 18 |
COMMAND ${GHOSTSCRIPT_EXECUTABLE} ${GHOSTSCRIPT_OPTIONS} -r18 -sOutputFile=gen-images/bipartite_matching.png ${CMAKE_CURRENT_SOURCE_DIR}/images/bipartite_matching.eps
|
| 19 | 19 |
COMMAND ${GHOSTSCRIPT_EXECUTABLE} ${GHOSTSCRIPT_OPTIONS} -r18 -sOutputFile=gen-images/bipartite_partitions.png ${CMAKE_CURRENT_SOURCE_DIR}/images/bipartite_partitions.eps
|
| 20 | 20 |
COMMAND ${GHOSTSCRIPT_EXECUTABLE} ${GHOSTSCRIPT_OPTIONS} -r18 -sOutputFile=gen-images/connected_components.png ${CMAKE_CURRENT_SOURCE_DIR}/images/connected_components.eps
|
| 21 | 21 |
COMMAND ${GHOSTSCRIPT_EXECUTABLE} ${GHOSTSCRIPT_OPTIONS} -r18 -sOutputFile=gen-images/edge_biconnected_components.png ${CMAKE_CURRENT_SOURCE_DIR}/images/edge_biconnected_components.eps
|
| 22 | 22 |
COMMAND ${GHOSTSCRIPT_EXECUTABLE} ${GHOSTSCRIPT_OPTIONS} -r18 -sOutputFile=gen-images/grid_graph.png ${CMAKE_CURRENT_SOURCE_DIR}/images/grid_graph.eps
|
| 23 | 23 |
COMMAND ${GHOSTSCRIPT_EXECUTABLE} ${GHOSTSCRIPT_OPTIONS} -r18 -sOutputFile=gen-images/node_biconnected_components.png ${CMAKE_CURRENT_SOURCE_DIR}/images/node_biconnected_components.eps
|
| 24 | 24 |
COMMAND ${GHOSTSCRIPT_EXECUTABLE} ${GHOSTSCRIPT_OPTIONS} -r18 -sOutputFile=gen-images/nodeshape_0.png ${CMAKE_CURRENT_SOURCE_DIR}/images/nodeshape_0.eps
|
| 25 | 25 |
COMMAND ${GHOSTSCRIPT_EXECUTABLE} ${GHOSTSCRIPT_OPTIONS} -r18 -sOutputFile=gen-images/nodeshape_1.png ${CMAKE_CURRENT_SOURCE_DIR}/images/nodeshape_1.eps
|
| 26 | 26 |
COMMAND ${GHOSTSCRIPT_EXECUTABLE} ${GHOSTSCRIPT_OPTIONS} -r18 -sOutputFile=gen-images/nodeshape_2.png ${CMAKE_CURRENT_SOURCE_DIR}/images/nodeshape_2.eps
|
| 27 | 27 |
COMMAND ${GHOSTSCRIPT_EXECUTABLE} ${GHOSTSCRIPT_OPTIONS} -r18 -sOutputFile=gen-images/nodeshape_3.png ${CMAKE_CURRENT_SOURCE_DIR}/images/nodeshape_3.eps
|
| 28 | 28 |
COMMAND ${GHOSTSCRIPT_EXECUTABLE} ${GHOSTSCRIPT_OPTIONS} -r18 -sOutputFile=gen-images/nodeshape_4.png ${CMAKE_CURRENT_SOURCE_DIR}/images/nodeshape_4.eps
|
| 29 |
COMMAND ${GHOSTSCRIPT_EXECUTABLE} ${GHOSTSCRIPT_OPTIONS} -r18 -sOutputFile=gen-images/planar.png ${CMAKE_CURRENT_SOURCE_DIR}/images/planar.eps
|
|
| 29 | 30 |
COMMAND ${GHOSTSCRIPT_EXECUTABLE} ${GHOSTSCRIPT_OPTIONS} -r18 -sOutputFile=gen-images/strongly_connected_components.png ${CMAKE_CURRENT_SOURCE_DIR}/images/strongly_connected_components.eps
|
| 30 | 31 |
COMMAND ${CMAKE_COMMAND} -E remove_directory html
|
| 31 | 32 |
COMMAND ${PYTHON_EXECUTABLE} ${PROJECT_SOURCE_DIR}/scripts/bib2dox.py ${CMAKE_CURRENT_SOURCE_DIR}/references.bib >references.dox
|
| 32 | 33 |
COMMAND ${DOXYGEN_EXECUTABLE} Doxyfile
|
| 33 | 34 |
WORKING_DIRECTORY ${CMAKE_CURRENT_BINARY_DIR}
|
| 34 | 35 |
) |
| 35 | 36 |
|
| 36 | 37 |
SET_TARGET_PROPERTIES(html PROPERTIES PROJECT_LABEL BUILD_DOC) |
| 37 | 38 |
|
| 38 | 39 |
IF(UNIX) |
| 39 | 40 |
INSTALL( |
| 40 | 41 |
DIRECTORY ${CMAKE_CURRENT_BINARY_DIR}/html/
|
| 41 | 42 |
DESTINATION share/doc/lemon/html |
| 42 | 43 |
COMPONENT html_documentation |
| 43 | 44 |
) |
| 44 | 45 |
ELSEIF(WIN32) |
| 45 | 46 |
INSTALL( |
| 46 | 47 |
DIRECTORY ${CMAKE_CURRENT_BINARY_DIR}/html/
|
| 47 | 48 |
DESTINATION doc |
| 48 | 49 |
COMPONENT html_documentation |
| 49 | 50 |
) |
| 50 | 51 |
ENDIF() |
| 51 | 52 |
|
| 52 | 53 |
ENDIF() |
| ... | ... |
@@ -7,48 +7,49 @@ |
| 7 | 7 |
doc/lgf.dox \ |
| 8 | 8 |
doc/license.dox \ |
| 9 | 9 |
doc/mainpage.dox \ |
| 10 | 10 |
doc/migration.dox \ |
| 11 | 11 |
doc/min_cost_flow.dox \ |
| 12 | 12 |
doc/named-param.dox \ |
| 13 | 13 |
doc/namespaces.dox \ |
| 14 | 14 |
doc/html \ |
| 15 | 15 |
doc/CMakeLists.txt |
| 16 | 16 |
|
| 17 | 17 |
DOC_EPS_IMAGES18 = \ |
| 18 | 18 |
grid_graph.eps \ |
| 19 | 19 |
nodeshape_0.eps \ |
| 20 | 20 |
nodeshape_1.eps \ |
| 21 | 21 |
nodeshape_2.eps \ |
| 22 | 22 |
nodeshape_3.eps \ |
| 23 | 23 |
nodeshape_4.eps |
| 24 | 24 |
|
| 25 | 25 |
DOC_EPS_IMAGES27 = \ |
| 26 | 26 |
bipartite_matching.eps \ |
| 27 | 27 |
bipartite_partitions.eps \ |
| 28 | 28 |
connected_components.eps \ |
| 29 | 29 |
edge_biconnected_components.eps \ |
| 30 | 30 |
node_biconnected_components.eps \ |
| 31 |
planar.eps \ |
|
| 31 | 32 |
strongly_connected_components.eps |
| 32 | 33 |
|
| 33 | 34 |
DOC_EPS_IMAGES = \ |
| 34 | 35 |
$(DOC_EPS_IMAGES18) \ |
| 35 | 36 |
$(DOC_EPS_IMAGES27) |
| 36 | 37 |
|
| 37 | 38 |
DOC_PNG_IMAGES = \ |
| 38 | 39 |
$(DOC_EPS_IMAGES:%.eps=doc/gen-images/%.png) |
| 39 | 40 |
|
| 40 | 41 |
EXTRA_DIST += $(DOC_EPS_IMAGES:%=doc/images/%) |
| 41 | 42 |
|
| 42 | 43 |
doc/html: |
| 43 | 44 |
$(MAKE) $(AM_MAKEFLAGS) html |
| 44 | 45 |
|
| 45 | 46 |
GS_COMMAND=gs -dNOPAUSE -dBATCH -q -dEPSCrop -dTextAlphaBits=4 -dGraphicsAlphaBits=4 |
| 46 | 47 |
|
| 47 | 48 |
$(DOC_EPS_IMAGES18:%.eps=doc/gen-images/%.png): doc/gen-images/%.png: doc/images/%.eps |
| 48 | 49 |
-mkdir doc/gen-images |
| 49 | 50 |
if test ${gs_found} = yes; then \
|
| 50 | 51 |
$(GS_COMMAND) -sDEVICE=pngalpha -r18 -sOutputFile=$@ $<; \ |
| 51 | 52 |
else \ |
| 52 | 53 |
echo; \ |
| 53 | 54 |
echo "Ghostscript not found."; \ |
| 54 | 55 |
echo; \ |
| ... | ... |
@@ -150,48 +150,53 @@ |
| 150 | 150 |
/// This class provides an efficient implementation of the Bellman-Ford |
| 151 | 151 |
/// algorithm. The maximum time complexity of the algorithm is |
| 152 | 152 |
/// <tt>O(ne)</tt>. |
| 153 | 153 |
/// |
| 154 | 154 |
/// The Bellman-Ford algorithm solves the single-source shortest path |
| 155 | 155 |
/// problem when the arcs can have negative lengths, but the digraph |
| 156 | 156 |
/// should not contain directed cycles with negative total length. |
| 157 | 157 |
/// If all arc costs are non-negative, consider to use the Dijkstra |
| 158 | 158 |
/// algorithm instead, since it is more efficient. |
| 159 | 159 |
/// |
| 160 | 160 |
/// The arc lengths are passed to the algorithm using a |
| 161 | 161 |
/// \ref concepts::ReadMap "ReadMap", so it is easy to change it to any |
| 162 | 162 |
/// kind of length. The type of the length values is determined by the |
| 163 | 163 |
/// \ref concepts::ReadMap::Value "Value" type of the length map. |
| 164 | 164 |
/// |
| 165 | 165 |
/// There is also a \ref bellmanFord() "function-type interface" for the |
| 166 | 166 |
/// Bellman-Ford algorithm, which is convenient in the simplier cases and |
| 167 | 167 |
/// it can be used easier. |
| 168 | 168 |
/// |
| 169 | 169 |
/// \tparam GR The type of the digraph the algorithm runs on. |
| 170 | 170 |
/// The default type is \ref ListDigraph. |
| 171 | 171 |
/// \tparam LEN A \ref concepts::ReadMap "readable" arc map that specifies |
| 172 | 172 |
/// the lengths of the arcs. The default map type is |
| 173 | 173 |
/// \ref concepts::Digraph::ArcMap "GR::ArcMap<int>". |
| 174 |
/// \tparam TR The traits class that defines various types used by the |
|
| 175 |
/// algorithm. By default, it is \ref BellmanFordDefaultTraits |
|
| 176 |
/// "BellmanFordDefaultTraits<GR, LEN>". |
|
| 177 |
/// In most cases, this parameter should not be set directly, |
|
| 178 |
/// consider to use the named template parameters instead. |
|
| 174 | 179 |
#ifdef DOXYGEN |
| 175 | 180 |
template <typename GR, typename LEN, typename TR> |
| 176 | 181 |
#else |
| 177 | 182 |
template <typename GR=ListDigraph, |
| 178 | 183 |
typename LEN=typename GR::template ArcMap<int>, |
| 179 | 184 |
typename TR=BellmanFordDefaultTraits<GR,LEN> > |
| 180 | 185 |
#endif |
| 181 | 186 |
class BellmanFord {
|
| 182 | 187 |
public: |
| 183 | 188 |
|
| 184 | 189 |
///The type of the underlying digraph. |
| 185 | 190 |
typedef typename TR::Digraph Digraph; |
| 186 | 191 |
|
| 187 | 192 |
/// \brief The type of the arc lengths. |
| 188 | 193 |
typedef typename TR::LengthMap::Value Value; |
| 189 | 194 |
/// \brief The type of the map that stores the arc lengths. |
| 190 | 195 |
typedef typename TR::LengthMap LengthMap; |
| 191 | 196 |
/// \brief The type of the map that stores the last |
| 192 | 197 |
/// arcs of the shortest paths. |
| 193 | 198 |
typedef typename TR::PredMap PredMap; |
| 194 | 199 |
/// \brief The type of the map that stores the distances of the nodes. |
| 195 | 200 |
typedef typename TR::DistMap DistMap; |
| 196 | 201 |
/// The type of the paths. |
| 197 | 202 |
typedef PredMapPath<Digraph, PredMap> Path; |
| ... | ... |
@@ -912,48 +917,51 @@ |
| 912 | 917 |
|
| 913 | 918 |
/// This constructor requires two parameters, |
| 914 | 919 |
/// others are initiated to \c 0. |
| 915 | 920 |
/// \param gr The digraph the algorithm runs on. |
| 916 | 921 |
/// \param len The length map. |
| 917 | 922 |
BellmanFordWizardBase(const GR& gr, |
| 918 | 923 |
const LEN& len) : |
| 919 | 924 |
_graph(reinterpret_cast<void*>(const_cast<GR*>(&gr))), |
| 920 | 925 |
_length(reinterpret_cast<void*>(const_cast<LEN*>(&len))), |
| 921 | 926 |
_pred(0), _dist(0), _path(0), _di(0) {}
|
| 922 | 927 |
|
| 923 | 928 |
}; |
| 924 | 929 |
|
| 925 | 930 |
/// \brief Auxiliary class for the function-type interface of the |
| 926 | 931 |
/// \ref BellmanFord "Bellman-Ford" algorithm. |
| 927 | 932 |
/// |
| 928 | 933 |
/// This auxiliary class is created to implement the |
| 929 | 934 |
/// \ref bellmanFord() "function-type interface" of the |
| 930 | 935 |
/// \ref BellmanFord "Bellman-Ford" algorithm. |
| 931 | 936 |
/// It does not have own \ref run() method, it uses the |
| 932 | 937 |
/// functions and features of the plain \ref BellmanFord. |
| 933 | 938 |
/// |
| 934 | 939 |
/// This class should only be used through the \ref bellmanFord() |
| 935 | 940 |
/// function, which makes it easier to use the algorithm. |
| 941 |
/// |
|
| 942 |
/// \tparam TR The traits class that defines various types used by the |
|
| 943 |
/// algorithm. |
|
| 936 | 944 |
template<class TR> |
| 937 | 945 |
class BellmanFordWizard : public TR {
|
| 938 | 946 |
typedef TR Base; |
| 939 | 947 |
|
| 940 | 948 |
typedef typename TR::Digraph Digraph; |
| 941 | 949 |
|
| 942 | 950 |
typedef typename Digraph::Node Node; |
| 943 | 951 |
typedef typename Digraph::NodeIt NodeIt; |
| 944 | 952 |
typedef typename Digraph::Arc Arc; |
| 945 | 953 |
typedef typename Digraph::OutArcIt ArcIt; |
| 946 | 954 |
|
| 947 | 955 |
typedef typename TR::LengthMap LengthMap; |
| 948 | 956 |
typedef typename LengthMap::Value Value; |
| 949 | 957 |
typedef typename TR::PredMap PredMap; |
| 950 | 958 |
typedef typename TR::DistMap DistMap; |
| 951 | 959 |
typedef typename TR::Path Path; |
| 952 | 960 |
|
| 953 | 961 |
public: |
| 954 | 962 |
/// Constructor. |
| 955 | 963 |
BellmanFordWizard() : TR() {}
|
| 956 | 964 |
|
| 957 | 965 |
/// \brief Constructor that requires parameters. |
| 958 | 966 |
/// |
| 959 | 967 |
/// Constructor that requires parameters. |
| ... | ... |
@@ -100,48 +100,53 @@ |
| 100 | 100 |
///It must conform to the \ref concepts::WriteMap "WriteMap" concept. |
| 101 | 101 |
typedef typename Digraph::template NodeMap<int> DistMap; |
| 102 | 102 |
///Instantiates a \c DistMap. |
| 103 | 103 |
|
| 104 | 104 |
///This function instantiates a \ref DistMap. |
| 105 | 105 |
///\param g is the digraph, to which we would like to define the |
| 106 | 106 |
///\ref DistMap. |
| 107 | 107 |
static DistMap *createDistMap(const Digraph &g) |
| 108 | 108 |
{
|
| 109 | 109 |
return new DistMap(g); |
| 110 | 110 |
} |
| 111 | 111 |
}; |
| 112 | 112 |
|
| 113 | 113 |
///%BFS algorithm class. |
| 114 | 114 |
|
| 115 | 115 |
///\ingroup search |
| 116 | 116 |
///This class provides an efficient implementation of the %BFS algorithm. |
| 117 | 117 |
/// |
| 118 | 118 |
///There is also a \ref bfs() "function-type interface" for the BFS |
| 119 | 119 |
///algorithm, which is convenient in the simplier cases and it can be |
| 120 | 120 |
///used easier. |
| 121 | 121 |
/// |
| 122 | 122 |
///\tparam GR The type of the digraph the algorithm runs on. |
| 123 | 123 |
///The default type is \ref ListDigraph. |
| 124 |
///\tparam TR The traits class that defines various types used by the |
|
| 125 |
///algorithm. By default, it is \ref BfsDefaultTraits |
|
| 126 |
///"BfsDefaultTraits<GR>". |
|
| 127 |
///In most cases, this parameter should not be set directly, |
|
| 128 |
///consider to use the named template parameters instead. |
|
| 124 | 129 |
#ifdef DOXYGEN |
| 125 | 130 |
template <typename GR, |
| 126 | 131 |
typename TR> |
| 127 | 132 |
#else |
| 128 | 133 |
template <typename GR=ListDigraph, |
| 129 | 134 |
typename TR=BfsDefaultTraits<GR> > |
| 130 | 135 |
#endif |
| 131 | 136 |
class Bfs {
|
| 132 | 137 |
public: |
| 133 | 138 |
|
| 134 | 139 |
///The type of the digraph the algorithm runs on. |
| 135 | 140 |
typedef typename TR::Digraph Digraph; |
| 136 | 141 |
|
| 137 | 142 |
///\brief The type of the map that stores the predecessor arcs of the |
| 138 | 143 |
///shortest paths. |
| 139 | 144 |
typedef typename TR::PredMap PredMap; |
| 140 | 145 |
///The type of the map that stores the distances of the nodes. |
| 141 | 146 |
typedef typename TR::DistMap DistMap; |
| 142 | 147 |
///The type of the map that indicates which nodes are reached. |
| 143 | 148 |
typedef typename TR::ReachedMap ReachedMap; |
| 144 | 149 |
///The type of the map that indicates which nodes are processed. |
| 145 | 150 |
typedef typename TR::ProcessedMap ProcessedMap; |
| 146 | 151 |
///The type of the paths. |
| 147 | 152 |
typedef PredMapPath<Digraph, PredMap> Path; |
| ... | ... |
@@ -936,48 +941,51 @@ |
| 936 | 941 |
/// all of the attributes to \c 0. |
| 937 | 942 |
BfsWizardBase() : _g(0), _reached(0), _processed(0), _pred(0), |
| 938 | 943 |
_dist(0), _path(0), _di(0) {}
|
| 939 | 944 |
|
| 940 | 945 |
/// Constructor. |
| 941 | 946 |
|
| 942 | 947 |
/// This constructor requires one parameter, |
| 943 | 948 |
/// others are initiated to \c 0. |
| 944 | 949 |
/// \param g The digraph the algorithm runs on. |
| 945 | 950 |
BfsWizardBase(const GR &g) : |
| 946 | 951 |
_g(reinterpret_cast<void*>(const_cast<GR*>(&g))), |
| 947 | 952 |
_reached(0), _processed(0), _pred(0), _dist(0), _path(0), _di(0) {}
|
| 948 | 953 |
|
| 949 | 954 |
}; |
| 950 | 955 |
|
| 951 | 956 |
/// Auxiliary class for the function-type interface of BFS algorithm. |
| 952 | 957 |
|
| 953 | 958 |
/// This auxiliary class is created to implement the |
| 954 | 959 |
/// \ref bfs() "function-type interface" of \ref Bfs algorithm. |
| 955 | 960 |
/// It does not have own \ref run(Node) "run()" method, it uses the |
| 956 | 961 |
/// functions and features of the plain \ref Bfs. |
| 957 | 962 |
/// |
| 958 | 963 |
/// This class should only be used through the \ref bfs() function, |
| 959 | 964 |
/// which makes it easier to use the algorithm. |
| 965 |
/// |
|
| 966 |
/// \tparam TR The traits class that defines various types used by the |
|
| 967 |
/// algorithm. |
|
| 960 | 968 |
template<class TR> |
| 961 | 969 |
class BfsWizard : public TR |
| 962 | 970 |
{
|
| 963 | 971 |
typedef TR Base; |
| 964 | 972 |
|
| 965 | 973 |
typedef typename TR::Digraph Digraph; |
| 966 | 974 |
|
| 967 | 975 |
typedef typename Digraph::Node Node; |
| 968 | 976 |
typedef typename Digraph::NodeIt NodeIt; |
| 969 | 977 |
typedef typename Digraph::Arc Arc; |
| 970 | 978 |
typedef typename Digraph::OutArcIt OutArcIt; |
| 971 | 979 |
|
| 972 | 980 |
typedef typename TR::PredMap PredMap; |
| 973 | 981 |
typedef typename TR::DistMap DistMap; |
| 974 | 982 |
typedef typename TR::ReachedMap ReachedMap; |
| 975 | 983 |
typedef typename TR::ProcessedMap ProcessedMap; |
| 976 | 984 |
typedef typename TR::Path Path; |
| 977 | 985 |
|
| 978 | 986 |
public: |
| 979 | 987 |
|
| 980 | 988 |
/// Constructor. |
| 981 | 989 |
BfsWizard() : TR() {}
|
| 982 | 990 |
|
| 983 | 991 |
/// Constructor that requires parameters. |
| ... | ... |
@@ -1274,53 +1282,53 @@ |
| 1274 | 1282 |
/// \ingroup search |
| 1275 | 1283 |
/// |
| 1276 | 1284 |
/// \brief BFS algorithm class with visitor interface. |
| 1277 | 1285 |
/// |
| 1278 | 1286 |
/// This class provides an efficient implementation of the BFS algorithm |
| 1279 | 1287 |
/// with visitor interface. |
| 1280 | 1288 |
/// |
| 1281 | 1289 |
/// The BfsVisit class provides an alternative interface to the Bfs |
| 1282 | 1290 |
/// class. It works with callback mechanism, the BfsVisit object calls |
| 1283 | 1291 |
/// the member functions of the \c Visitor class on every BFS event. |
| 1284 | 1292 |
/// |
| 1285 | 1293 |
/// This interface of the BFS algorithm should be used in special cases |
| 1286 | 1294 |
/// when extra actions have to be performed in connection with certain |
| 1287 | 1295 |
/// events of the BFS algorithm. Otherwise consider to use Bfs or bfs() |
| 1288 | 1296 |
/// instead. |
| 1289 | 1297 |
/// |
| 1290 | 1298 |
/// \tparam GR The type of the digraph the algorithm runs on. |
| 1291 | 1299 |
/// The default type is \ref ListDigraph. |
| 1292 | 1300 |
/// The value of GR is not used directly by \ref BfsVisit, |
| 1293 | 1301 |
/// it is only passed to \ref BfsVisitDefaultTraits. |
| 1294 | 1302 |
/// \tparam VS The Visitor type that is used by the algorithm. |
| 1295 | 1303 |
/// \ref BfsVisitor "BfsVisitor<GR>" is an empty visitor, which |
| 1296 | 1304 |
/// does not observe the BFS events. If you want to observe the BFS |
| 1297 | 1305 |
/// events, you should implement your own visitor class. |
| 1298 |
/// \tparam TR Traits class to set various data types used by the |
|
| 1299 |
/// algorithm. The default traits class is |
|
| 1300 |
/// \ref BfsVisitDefaultTraits "BfsVisitDefaultTraits<GR>". |
|
| 1301 |
/// See \ref BfsVisitDefaultTraits for the documentation of |
|
| 1302 |
/// |
|
| 1306 |
/// \tparam TR The traits class that defines various types used by the |
|
| 1307 |
/// algorithm. By default, it is \ref BfsVisitDefaultTraits |
|
| 1308 |
/// "BfsVisitDefaultTraits<GR>". |
|
| 1309 |
/// In most cases, this parameter should not be set directly, |
|
| 1310 |
/// consider to use the named template parameters instead. |
|
| 1303 | 1311 |
#ifdef DOXYGEN |
| 1304 | 1312 |
template <typename GR, typename VS, typename TR> |
| 1305 | 1313 |
#else |
| 1306 | 1314 |
template <typename GR = ListDigraph, |
| 1307 | 1315 |
typename VS = BfsVisitor<GR>, |
| 1308 | 1316 |
typename TR = BfsVisitDefaultTraits<GR> > |
| 1309 | 1317 |
#endif |
| 1310 | 1318 |
class BfsVisit {
|
| 1311 | 1319 |
public: |
| 1312 | 1320 |
|
| 1313 | 1321 |
///The traits class. |
| 1314 | 1322 |
typedef TR Traits; |
| 1315 | 1323 |
|
| 1316 | 1324 |
///The type of the digraph the algorithm runs on. |
| 1317 | 1325 |
typedef typename Traits::Digraph Digraph; |
| 1318 | 1326 |
|
| 1319 | 1327 |
///The visitor type used by the algorithm. |
| 1320 | 1328 |
typedef VS Visitor; |
| 1321 | 1329 |
|
| 1322 | 1330 |
///The type of the map that indicates which nodes are reached. |
| 1323 | 1331 |
typedef typename Traits::ReachedMap ReachedMap; |
| 1324 | 1332 |
|
| 1325 | 1333 |
private: |
| 1326 | 1334 |
| ... | ... |
@@ -56,51 +56,56 @@ |
| 56 | 56 |
/// its priority type must be \c Cost and its cross reference type |
| 57 | 57 |
/// must be \ref RangeMap "RangeMap<int>". |
| 58 | 58 |
typedef BinHeap<Cost, RangeMap<int> > Heap; |
| 59 | 59 |
}; |
| 60 | 60 |
|
| 61 | 61 |
/// \addtogroup min_cost_flow_algs |
| 62 | 62 |
/// @{
|
| 63 | 63 |
|
| 64 | 64 |
/// \brief Implementation of the Capacity Scaling algorithm for |
| 65 | 65 |
/// finding a \ref min_cost_flow "minimum cost flow". |
| 66 | 66 |
/// |
| 67 | 67 |
/// \ref CapacityScaling implements the capacity scaling version |
| 68 | 68 |
/// of the successive shortest path algorithm for finding a |
| 69 | 69 |
/// \ref min_cost_flow "minimum cost flow" \ref amo93networkflows, |
| 70 | 70 |
/// \ref edmondskarp72theoretical. It is an efficient dual |
| 71 | 71 |
/// solution method. |
| 72 | 72 |
/// |
| 73 | 73 |
/// Most of the parameters of the problem (except for the digraph) |
| 74 | 74 |
/// can be given using separate functions, and the algorithm can be |
| 75 | 75 |
/// executed using the \ref run() function. If some parameters are not |
| 76 | 76 |
/// specified, then default values will be used. |
| 77 | 77 |
/// |
| 78 | 78 |
/// \tparam GR The digraph type the algorithm runs on. |
| 79 | 79 |
/// \tparam V The number type used for flow amounts, capacity bounds |
| 80 |
/// and supply values in the algorithm. By default it is \c int. |
|
| 80 |
/// and supply values in the algorithm. By default, it is \c int. |
|
| 81 | 81 |
/// \tparam C The number type used for costs and potentials in the |
| 82 |
/// algorithm. By default it is the same as \c V. |
|
| 82 |
/// algorithm. By default, it is the same as \c V. |
|
| 83 |
/// \tparam TR The traits class that defines various types used by the |
|
| 84 |
/// algorithm. By default, it is \ref CapacityScalingDefaultTraits |
|
| 85 |
/// "CapacityScalingDefaultTraits<GR, V, C>". |
|
| 86 |
/// In most cases, this parameter should not be set directly, |
|
| 87 |
/// consider to use the named template parameters instead. |
|
| 83 | 88 |
/// |
| 84 | 89 |
/// \warning Both number types must be signed and all input data must |
| 85 | 90 |
/// be integer. |
| 86 | 91 |
/// \warning This algorithm does not support negative costs for such |
| 87 | 92 |
/// arcs that have infinite upper bound. |
| 88 | 93 |
#ifdef DOXYGEN |
| 89 | 94 |
template <typename GR, typename V, typename C, typename TR> |
| 90 | 95 |
#else |
| 91 | 96 |
template < typename GR, typename V = int, typename C = V, |
| 92 | 97 |
typename TR = CapacityScalingDefaultTraits<GR, V, C> > |
| 93 | 98 |
#endif |
| 94 | 99 |
class CapacityScaling |
| 95 | 100 |
{
|
| 96 | 101 |
public: |
| 97 | 102 |
|
| 98 | 103 |
/// The type of the digraph |
| 99 | 104 |
typedef typename TR::Digraph Digraph; |
| 100 | 105 |
/// The type of the flow amounts, capacity bounds and supply values |
| 101 | 106 |
typedef typename TR::Value Value; |
| 102 | 107 |
/// The type of the arc costs |
| 103 | 108 |
typedef typename TR::Cost Cost; |
| 104 | 109 |
|
| 105 | 110 |
/// The type of the heap used for internal Dijkstra computations |
| 106 | 111 |
typedef typename TR::Heap Heap; |
| ... | ... |
@@ -152,48 +152,53 @@ |
| 152 | 152 |
constraints have to be satisfied with equality, i.e. all demands |
| 153 | 153 |
have to be satisfied and all supplies have to be used. |
| 154 | 154 |
|
| 155 | 155 |
If you need the opposite inequalities in the supply/demand constraints |
| 156 | 156 |
(i.e. the total demand is less than the total supply and all the demands |
| 157 | 157 |
have to be satisfied while there could be supplies that are not used), |
| 158 | 158 |
then you could easily transform the problem to the above form by reversing |
| 159 | 159 |
the direction of the arcs and taking the negative of the supply values |
| 160 | 160 |
(e.g. using \ref ReverseDigraph and \ref NegMap adaptors). |
| 161 | 161 |
|
| 162 | 162 |
This algorithm either calculates a feasible circulation, or provides |
| 163 | 163 |
a \ref barrier() "barrier", which prooves that a feasible soultion |
| 164 | 164 |
cannot exist. |
| 165 | 165 |
|
| 166 | 166 |
Note that this algorithm also provides a feasible solution for the |
| 167 | 167 |
\ref min_cost_flow "minimum cost flow problem". |
| 168 | 168 |
|
| 169 | 169 |
\tparam GR The type of the digraph the algorithm runs on. |
| 170 | 170 |
\tparam LM The type of the lower bound map. The default |
| 171 | 171 |
map type is \ref concepts::Digraph::ArcMap "GR::ArcMap<int>". |
| 172 | 172 |
\tparam UM The type of the upper bound (capacity) map. |
| 173 | 173 |
The default map type is \c LM. |
| 174 | 174 |
\tparam SM The type of the supply map. The default map type is |
| 175 | 175 |
\ref concepts::Digraph::NodeMap "GR::NodeMap<UM::Value>". |
| 176 |
\tparam TR The traits class that defines various types used by the |
|
| 177 |
algorithm. By default, it is \ref CirculationDefaultTraits |
|
| 178 |
"CirculationDefaultTraits<GR, LM, UM, SM>". |
|
| 179 |
In most cases, this parameter should not be set directly, |
|
| 180 |
consider to use the named template parameters instead. |
|
| 176 | 181 |
*/ |
| 177 | 182 |
#ifdef DOXYGEN |
| 178 | 183 |
template< typename GR, |
| 179 | 184 |
typename LM, |
| 180 | 185 |
typename UM, |
| 181 | 186 |
typename SM, |
| 182 | 187 |
typename TR > |
| 183 | 188 |
#else |
| 184 | 189 |
template< typename GR, |
| 185 | 190 |
typename LM = typename GR::template ArcMap<int>, |
| 186 | 191 |
typename UM = LM, |
| 187 | 192 |
typename SM = typename GR::template NodeMap<typename UM::Value>, |
| 188 | 193 |
typename TR = CirculationDefaultTraits<GR, LM, UM, SM> > |
| 189 | 194 |
#endif |
| 190 | 195 |
class Circulation {
|
| 191 | 196 |
public: |
| 192 | 197 |
|
| 193 | 198 |
///The \ref CirculationDefaultTraits "traits class" of the algorithm. |
| 194 | 199 |
typedef TR Traits; |
| 195 | 200 |
///The type of the digraph the algorithm runs on. |
| 196 | 201 |
typedef typename Traits::Digraph Digraph; |
| 197 | 202 |
///The type of the flow and supply values. |
| 198 | 203 |
typedef typename Traits::Value Value; |
| 199 | 204 |
| ... | ... |
@@ -83,82 +83,86 @@ |
| 83 | 83 |
}; |
| 84 | 84 |
|
| 85 | 85 |
|
| 86 | 86 |
/// \addtogroup min_cost_flow_algs |
| 87 | 87 |
/// @{
|
| 88 | 88 |
|
| 89 | 89 |
/// \brief Implementation of the Cost Scaling algorithm for |
| 90 | 90 |
/// finding a \ref min_cost_flow "minimum cost flow". |
| 91 | 91 |
/// |
| 92 | 92 |
/// \ref CostScaling implements a cost scaling algorithm that performs |
| 93 | 93 |
/// push/augment and relabel operations for finding a \ref min_cost_flow |
| 94 | 94 |
/// "minimum cost flow" \ref amo93networkflows, \ref goldberg90approximation, |
| 95 | 95 |
/// \ref goldberg97efficient, \ref bunnagel98efficient. |
| 96 | 96 |
/// It is a highly efficient primal-dual solution method, which |
| 97 | 97 |
/// can be viewed as the generalization of the \ref Preflow |
| 98 | 98 |
/// "preflow push-relabel" algorithm for the maximum flow problem. |
| 99 | 99 |
/// |
| 100 | 100 |
/// Most of the parameters of the problem (except for the digraph) |
| 101 | 101 |
/// can be given using separate functions, and the algorithm can be |
| 102 | 102 |
/// executed using the \ref run() function. If some parameters are not |
| 103 | 103 |
/// specified, then default values will be used. |
| 104 | 104 |
/// |
| 105 | 105 |
/// \tparam GR The digraph type the algorithm runs on. |
| 106 | 106 |
/// \tparam V The number type used for flow amounts, capacity bounds |
| 107 |
/// and supply values in the algorithm. By default it is \c int. |
|
| 107 |
/// and supply values in the algorithm. By default, it is \c int. |
|
| 108 | 108 |
/// \tparam C The number type used for costs and potentials in the |
| 109 |
/// algorithm. By default it is the same as \c V. |
|
| 109 |
/// algorithm. By default, it is the same as \c V. |
|
| 110 |
/// \tparam TR The traits class that defines various types used by the |
|
| 111 |
/// algorithm. By default, it is \ref CostScalingDefaultTraits |
|
| 112 |
/// "CostScalingDefaultTraits<GR, V, C>". |
|
| 113 |
/// In most cases, this parameter should not be set directly, |
|
| 114 |
/// consider to use the named template parameters instead. |
|
| 110 | 115 |
/// |
| 111 | 116 |
/// \warning Both number types must be signed and all input data must |
| 112 | 117 |
/// be integer. |
| 113 | 118 |
/// \warning This algorithm does not support negative costs for such |
| 114 | 119 |
/// arcs that have infinite upper bound. |
| 115 | 120 |
/// |
| 116 | 121 |
/// \note %CostScaling provides three different internal methods, |
| 117 | 122 |
/// from which the most efficient one is used by default. |
| 118 | 123 |
/// For more information, see \ref Method. |
| 119 | 124 |
#ifdef DOXYGEN |
| 120 | 125 |
template <typename GR, typename V, typename C, typename TR> |
| 121 | 126 |
#else |
| 122 | 127 |
template < typename GR, typename V = int, typename C = V, |
| 123 | 128 |
typename TR = CostScalingDefaultTraits<GR, V, C> > |
| 124 | 129 |
#endif |
| 125 | 130 |
class CostScaling |
| 126 | 131 |
{
|
| 127 | 132 |
public: |
| 128 | 133 |
|
| 129 | 134 |
/// The type of the digraph |
| 130 | 135 |
typedef typename TR::Digraph Digraph; |
| 131 | 136 |
/// The type of the flow amounts, capacity bounds and supply values |
| 132 | 137 |
typedef typename TR::Value Value; |
| 133 | 138 |
/// The type of the arc costs |
| 134 | 139 |
typedef typename TR::Cost Cost; |
| 135 | 140 |
|
| 136 | 141 |
/// \brief The large cost type |
| 137 | 142 |
/// |
| 138 | 143 |
/// The large cost type used for internal computations. |
| 139 |
/// Using the \ref CostScalingDefaultTraits "default traits class", |
|
| 140 |
/// it is \c long \c long if the \c Cost type is integer, |
|
| 144 |
/// By default, it is \c long \c long if the \c Cost type is integer, |
|
| 141 | 145 |
/// otherwise it is \c double. |
| 142 | 146 |
typedef typename TR::LargeCost LargeCost; |
| 143 | 147 |
|
| 144 | 148 |
/// The \ref CostScalingDefaultTraits "traits class" of the algorithm |
| 145 | 149 |
typedef TR Traits; |
| 146 | 150 |
|
| 147 | 151 |
public: |
| 148 | 152 |
|
| 149 | 153 |
/// \brief Problem type constants for the \c run() function. |
| 150 | 154 |
/// |
| 151 | 155 |
/// Enum type containing the problem type constants that can be |
| 152 | 156 |
/// returned by the \ref run() function of the algorithm. |
| 153 | 157 |
enum ProblemType {
|
| 154 | 158 |
/// The problem has no feasible solution (flow). |
| 155 | 159 |
INFEASIBLE, |
| 156 | 160 |
/// The problem has optimal solution (i.e. it is feasible and |
| 157 | 161 |
/// bounded), and the algorithm has found optimal flow and node |
| 158 | 162 |
/// potentials (primal and dual solutions). |
| 159 | 163 |
OPTIMAL, |
| 160 | 164 |
/// The digraph contains an arc of negative cost and infinite |
| 161 | 165 |
/// upper bound. It means that the objective function is unbounded |
| 162 | 166 |
/// on that arc, however, note that it could actually be bounded |
| 163 | 167 |
/// over the feasible flows, but this algroithm cannot handle |
| 164 | 168 |
/// these cases. |
| ... | ... |
@@ -100,48 +100,53 @@ |
| 100 | 100 |
///It must conform to the \ref concepts::WriteMap "WriteMap" concept. |
| 101 | 101 |
typedef typename Digraph::template NodeMap<int> DistMap; |
| 102 | 102 |
///Instantiates a \c DistMap. |
| 103 | 103 |
|
| 104 | 104 |
///This function instantiates a \ref DistMap. |
| 105 | 105 |
///\param g is the digraph, to which we would like to define the |
| 106 | 106 |
///\ref DistMap. |
| 107 | 107 |
static DistMap *createDistMap(const Digraph &g) |
| 108 | 108 |
{
|
| 109 | 109 |
return new DistMap(g); |
| 110 | 110 |
} |
| 111 | 111 |
}; |
| 112 | 112 |
|
| 113 | 113 |
///%DFS algorithm class. |
| 114 | 114 |
|
| 115 | 115 |
///\ingroup search |
| 116 | 116 |
///This class provides an efficient implementation of the %DFS algorithm. |
| 117 | 117 |
/// |
| 118 | 118 |
///There is also a \ref dfs() "function-type interface" for the DFS |
| 119 | 119 |
///algorithm, which is convenient in the simplier cases and it can be |
| 120 | 120 |
///used easier. |
| 121 | 121 |
/// |
| 122 | 122 |
///\tparam GR The type of the digraph the algorithm runs on. |
| 123 | 123 |
///The default type is \ref ListDigraph. |
| 124 |
///\tparam TR The traits class that defines various types used by the |
|
| 125 |
///algorithm. By default, it is \ref DfsDefaultTraits |
|
| 126 |
///"DfsDefaultTraits<GR>". |
|
| 127 |
///In most cases, this parameter should not be set directly, |
|
| 128 |
///consider to use the named template parameters instead. |
|
| 124 | 129 |
#ifdef DOXYGEN |
| 125 | 130 |
template <typename GR, |
| 126 | 131 |
typename TR> |
| 127 | 132 |
#else |
| 128 | 133 |
template <typename GR=ListDigraph, |
| 129 | 134 |
typename TR=DfsDefaultTraits<GR> > |
| 130 | 135 |
#endif |
| 131 | 136 |
class Dfs {
|
| 132 | 137 |
public: |
| 133 | 138 |
|
| 134 | 139 |
///The type of the digraph the algorithm runs on. |
| 135 | 140 |
typedef typename TR::Digraph Digraph; |
| 136 | 141 |
|
| 137 | 142 |
///\brief The type of the map that stores the predecessor arcs of the |
| 138 | 143 |
///DFS paths. |
| 139 | 144 |
typedef typename TR::PredMap PredMap; |
| 140 | 145 |
///The type of the map that stores the distances of the nodes. |
| 141 | 146 |
typedef typename TR::DistMap DistMap; |
| 142 | 147 |
///The type of the map that indicates which nodes are reached. |
| 143 | 148 |
typedef typename TR::ReachedMap ReachedMap; |
| 144 | 149 |
///The type of the map that indicates which nodes are processed. |
| 145 | 150 |
typedef typename TR::ProcessedMap ProcessedMap; |
| 146 | 151 |
///The type of the paths. |
| 147 | 152 |
typedef PredMapPath<Digraph, PredMap> Path; |
| ... | ... |
@@ -866,48 +871,51 @@ |
| 866 | 871 |
/// all of the attributes to \c 0. |
| 867 | 872 |
DfsWizardBase() : _g(0), _reached(0), _processed(0), _pred(0), |
| 868 | 873 |
_dist(0), _path(0), _di(0) {}
|
| 869 | 874 |
|
| 870 | 875 |
/// Constructor. |
| 871 | 876 |
|
| 872 | 877 |
/// This constructor requires one parameter, |
| 873 | 878 |
/// others are initiated to \c 0. |
| 874 | 879 |
/// \param g The digraph the algorithm runs on. |
| 875 | 880 |
DfsWizardBase(const GR &g) : |
| 876 | 881 |
_g(reinterpret_cast<void*>(const_cast<GR*>(&g))), |
| 877 | 882 |
_reached(0), _processed(0), _pred(0), _dist(0), _path(0), _di(0) {}
|
| 878 | 883 |
|
| 879 | 884 |
}; |
| 880 | 885 |
|
| 881 | 886 |
/// Auxiliary class for the function-type interface of DFS algorithm. |
| 882 | 887 |
|
| 883 | 888 |
/// This auxiliary class is created to implement the |
| 884 | 889 |
/// \ref dfs() "function-type interface" of \ref Dfs algorithm. |
| 885 | 890 |
/// It does not have own \ref run(Node) "run()" method, it uses the |
| 886 | 891 |
/// functions and features of the plain \ref Dfs. |
| 887 | 892 |
/// |
| 888 | 893 |
/// This class should only be used through the \ref dfs() function, |
| 889 | 894 |
/// which makes it easier to use the algorithm. |
| 895 |
/// |
|
| 896 |
/// \tparam TR The traits class that defines various types used by the |
|
| 897 |
/// algorithm. |
|
| 890 | 898 |
template<class TR> |
| 891 | 899 |
class DfsWizard : public TR |
| 892 | 900 |
{
|
| 893 | 901 |
typedef TR Base; |
| 894 | 902 |
|
| 895 | 903 |
typedef typename TR::Digraph Digraph; |
| 896 | 904 |
|
| 897 | 905 |
typedef typename Digraph::Node Node; |
| 898 | 906 |
typedef typename Digraph::NodeIt NodeIt; |
| 899 | 907 |
typedef typename Digraph::Arc Arc; |
| 900 | 908 |
typedef typename Digraph::OutArcIt OutArcIt; |
| 901 | 909 |
|
| 902 | 910 |
typedef typename TR::PredMap PredMap; |
| 903 | 911 |
typedef typename TR::DistMap DistMap; |
| 904 | 912 |
typedef typename TR::ReachedMap ReachedMap; |
| 905 | 913 |
typedef typename TR::ProcessedMap ProcessedMap; |
| 906 | 914 |
typedef typename TR::Path Path; |
| 907 | 915 |
|
| 908 | 916 |
public: |
| 909 | 917 |
|
| 910 | 918 |
/// Constructor. |
| 911 | 919 |
DfsWizard() : TR() {}
|
| 912 | 920 |
|
| 913 | 921 |
/// Constructor that requires parameters. |
| ... | ... |
@@ -1216,53 +1224,53 @@ |
| 1216 | 1224 |
/// \ingroup search |
| 1217 | 1225 |
/// |
| 1218 | 1226 |
/// \brief DFS algorithm class with visitor interface. |
| 1219 | 1227 |
/// |
| 1220 | 1228 |
/// This class provides an efficient implementation of the DFS algorithm |
| 1221 | 1229 |
/// with visitor interface. |
| 1222 | 1230 |
/// |
| 1223 | 1231 |
/// The DfsVisit class provides an alternative interface to the Dfs |
| 1224 | 1232 |
/// class. It works with callback mechanism, the DfsVisit object calls |
| 1225 | 1233 |
/// the member functions of the \c Visitor class on every DFS event. |
| 1226 | 1234 |
/// |
| 1227 | 1235 |
/// This interface of the DFS algorithm should be used in special cases |
| 1228 | 1236 |
/// when extra actions have to be performed in connection with certain |
| 1229 | 1237 |
/// events of the DFS algorithm. Otherwise consider to use Dfs or dfs() |
| 1230 | 1238 |
/// instead. |
| 1231 | 1239 |
/// |
| 1232 | 1240 |
/// \tparam GR The type of the digraph the algorithm runs on. |
| 1233 | 1241 |
/// The default type is \ref ListDigraph. |
| 1234 | 1242 |
/// The value of GR is not used directly by \ref DfsVisit, |
| 1235 | 1243 |
/// it is only passed to \ref DfsVisitDefaultTraits. |
| 1236 | 1244 |
/// \tparam VS The Visitor type that is used by the algorithm. |
| 1237 | 1245 |
/// \ref DfsVisitor "DfsVisitor<GR>" is an empty visitor, which |
| 1238 | 1246 |
/// does not observe the DFS events. If you want to observe the DFS |
| 1239 | 1247 |
/// events, you should implement your own visitor class. |
| 1240 |
/// \tparam TR Traits class to set various data types used by the |
|
| 1241 |
/// algorithm. The default traits class is |
|
| 1242 |
/// \ref DfsVisitDefaultTraits "DfsVisitDefaultTraits<GR>". |
|
| 1243 |
/// See \ref DfsVisitDefaultTraits for the documentation of |
|
| 1244 |
/// |
|
| 1248 |
/// \tparam TR The traits class that defines various types used by the |
|
| 1249 |
/// algorithm. By default, it is \ref DfsVisitDefaultTraits |
|
| 1250 |
/// "DfsVisitDefaultTraits<GR>". |
|
| 1251 |
/// In most cases, this parameter should not be set directly, |
|
| 1252 |
/// consider to use the named template parameters instead. |
|
| 1245 | 1253 |
#ifdef DOXYGEN |
| 1246 | 1254 |
template <typename GR, typename VS, typename TR> |
| 1247 | 1255 |
#else |
| 1248 | 1256 |
template <typename GR = ListDigraph, |
| 1249 | 1257 |
typename VS = DfsVisitor<GR>, |
| 1250 | 1258 |
typename TR = DfsVisitDefaultTraits<GR> > |
| 1251 | 1259 |
#endif |
| 1252 | 1260 |
class DfsVisit {
|
| 1253 | 1261 |
public: |
| 1254 | 1262 |
|
| 1255 | 1263 |
///The traits class. |
| 1256 | 1264 |
typedef TR Traits; |
| 1257 | 1265 |
|
| 1258 | 1266 |
///The type of the digraph the algorithm runs on. |
| 1259 | 1267 |
typedef typename Traits::Digraph Digraph; |
| 1260 | 1268 |
|
| 1261 | 1269 |
///The visitor type used by the algorithm. |
| 1262 | 1270 |
typedef VS Visitor; |
| 1263 | 1271 |
|
| 1264 | 1272 |
///The type of the map that indicates which nodes are reached. |
| 1265 | 1273 |
typedef typename Traits::ReachedMap ReachedMap; |
| 1266 | 1274 |
|
| 1267 | 1275 |
private: |
| 1268 | 1276 |
| ... | ... |
@@ -171,48 +171,53 @@ |
| 171 | 171 |
/// |
| 172 | 172 |
///The %Dijkstra algorithm solves the single-source shortest path problem |
| 173 | 173 |
///when all arc lengths are non-negative. If there are negative lengths, |
| 174 | 174 |
///the BellmanFord algorithm should be used instead. |
| 175 | 175 |
/// |
| 176 | 176 |
///The arc lengths are passed to the algorithm using a |
| 177 | 177 |
///\ref concepts::ReadMap "ReadMap", |
| 178 | 178 |
///so it is easy to change it to any kind of length. |
| 179 | 179 |
///The type of the length is determined by the |
| 180 | 180 |
///\ref concepts::ReadMap::Value "Value" of the length map. |
| 181 | 181 |
///It is also possible to change the underlying priority heap. |
| 182 | 182 |
/// |
| 183 | 183 |
///There is also a \ref dijkstra() "function-type interface" for the |
| 184 | 184 |
///%Dijkstra algorithm, which is convenient in the simplier cases and |
| 185 | 185 |
///it can be used easier. |
| 186 | 186 |
/// |
| 187 | 187 |
///\tparam GR The type of the digraph the algorithm runs on. |
| 188 | 188 |
///The default type is \ref ListDigraph. |
| 189 | 189 |
///\tparam LEN A \ref concepts::ReadMap "readable" arc map that specifies |
| 190 | 190 |
///the lengths of the arcs. |
| 191 | 191 |
///It is read once for each arc, so the map may involve in |
| 192 | 192 |
///relatively time consuming process to compute the arc lengths if |
| 193 | 193 |
///it is necessary. The default map type is \ref |
| 194 | 194 |
///concepts::Digraph::ArcMap "GR::ArcMap<int>". |
| 195 |
///\tparam TR The traits class that defines various types used by the |
|
| 196 |
///algorithm. By default, it is \ref DijkstraDefaultTraits |
|
| 197 |
///"DijkstraDefaultTraits<GR, LEN>". |
|
| 198 |
///In most cases, this parameter should not be set directly, |
|
| 199 |
///consider to use the named template parameters instead. |
|
| 195 | 200 |
#ifdef DOXYGEN |
| 196 | 201 |
template <typename GR, typename LEN, typename TR> |
| 197 | 202 |
#else |
| 198 | 203 |
template <typename GR=ListDigraph, |
| 199 | 204 |
typename LEN=typename GR::template ArcMap<int>, |
| 200 | 205 |
typename TR=DijkstraDefaultTraits<GR,LEN> > |
| 201 | 206 |
#endif |
| 202 | 207 |
class Dijkstra {
|
| 203 | 208 |
public: |
| 204 | 209 |
|
| 205 | 210 |
///The type of the digraph the algorithm runs on. |
| 206 | 211 |
typedef typename TR::Digraph Digraph; |
| 207 | 212 |
|
| 208 | 213 |
///The type of the arc lengths. |
| 209 | 214 |
typedef typename TR::Value Value; |
| 210 | 215 |
///The type of the map that stores the arc lengths. |
| 211 | 216 |
typedef typename TR::LengthMap LengthMap; |
| 212 | 217 |
///\brief The type of the map that stores the predecessor arcs of the |
| 213 | 218 |
///shortest paths. |
| 214 | 219 |
typedef typename TR::PredMap PredMap; |
| 215 | 220 |
///The type of the map that stores the distances of the nodes. |
| 216 | 221 |
typedef typename TR::DistMap DistMap; |
| 217 | 222 |
///The type of the map that indicates which nodes are processed. |
| 218 | 223 |
typedef typename TR::ProcessedMap ProcessedMap; |
| ... | ... |
@@ -1071,48 +1076,51 @@ |
| 1071 | 1076 |
_dist(0), _path(0), _di(0) {}
|
| 1072 | 1077 |
|
| 1073 | 1078 |
/// Constructor. |
| 1074 | 1079 |
|
| 1075 | 1080 |
/// This constructor requires two parameters, |
| 1076 | 1081 |
/// others are initiated to \c 0. |
| 1077 | 1082 |
/// \param g The digraph the algorithm runs on. |
| 1078 | 1083 |
/// \param l The length map. |
| 1079 | 1084 |
DijkstraWizardBase(const GR &g,const LEN &l) : |
| 1080 | 1085 |
_g(reinterpret_cast<void*>(const_cast<GR*>(&g))), |
| 1081 | 1086 |
_length(reinterpret_cast<void*>(const_cast<LEN*>(&l))), |
| 1082 | 1087 |
_processed(0), _pred(0), _dist(0), _path(0), _di(0) {}
|
| 1083 | 1088 |
|
| 1084 | 1089 |
}; |
| 1085 | 1090 |
|
| 1086 | 1091 |
/// Auxiliary class for the function-type interface of Dijkstra algorithm. |
| 1087 | 1092 |
|
| 1088 | 1093 |
/// This auxiliary class is created to implement the |
| 1089 | 1094 |
/// \ref dijkstra() "function-type interface" of \ref Dijkstra algorithm. |
| 1090 | 1095 |
/// It does not have own \ref run(Node) "run()" method, it uses the |
| 1091 | 1096 |
/// functions and features of the plain \ref Dijkstra. |
| 1092 | 1097 |
/// |
| 1093 | 1098 |
/// This class should only be used through the \ref dijkstra() function, |
| 1094 | 1099 |
/// which makes it easier to use the algorithm. |
| 1100 |
/// |
|
| 1101 |
/// \tparam TR The traits class that defines various types used by the |
|
| 1102 |
/// algorithm. |
|
| 1095 | 1103 |
template<class TR> |
| 1096 | 1104 |
class DijkstraWizard : public TR |
| 1097 | 1105 |
{
|
| 1098 | 1106 |
typedef TR Base; |
| 1099 | 1107 |
|
| 1100 | 1108 |
typedef typename TR::Digraph Digraph; |
| 1101 | 1109 |
|
| 1102 | 1110 |
typedef typename Digraph::Node Node; |
| 1103 | 1111 |
typedef typename Digraph::NodeIt NodeIt; |
| 1104 | 1112 |
typedef typename Digraph::Arc Arc; |
| 1105 | 1113 |
typedef typename Digraph::OutArcIt OutArcIt; |
| 1106 | 1114 |
|
| 1107 | 1115 |
typedef typename TR::LengthMap LengthMap; |
| 1108 | 1116 |
typedef typename LengthMap::Value Value; |
| 1109 | 1117 |
typedef typename TR::PredMap PredMap; |
| 1110 | 1118 |
typedef typename TR::DistMap DistMap; |
| 1111 | 1119 |
typedef typename TR::ProcessedMap ProcessedMap; |
| 1112 | 1120 |
typedef typename TR::Path Path; |
| 1113 | 1121 |
typedef typename TR::Heap Heap; |
| 1114 | 1122 |
|
| 1115 | 1123 |
public: |
| 1116 | 1124 |
|
| 1117 | 1125 |
/// Constructor. |
| 1118 | 1126 |
DijkstraWizard() : TR() {}
|
| ... | ... |
@@ -85,71 +85,75 @@ |
| 85 | 85 |
#else |
| 86 | 86 |
typedef long LargeValue; |
| 87 | 87 |
#endif |
| 88 | 88 |
typedef lemon::Tolerance<LargeValue> Tolerance; |
| 89 | 89 |
typedef lemon::Path<Digraph> Path; |
| 90 | 90 |
}; |
| 91 | 91 |
|
| 92 | 92 |
|
| 93 | 93 |
/// \addtogroup min_mean_cycle |
| 94 | 94 |
/// @{
|
| 95 | 95 |
|
| 96 | 96 |
/// \brief Implementation of the Hartmann-Orlin algorithm for finding |
| 97 | 97 |
/// a minimum mean cycle. |
| 98 | 98 |
/// |
| 99 | 99 |
/// This class implements the Hartmann-Orlin algorithm for finding |
| 100 | 100 |
/// a directed cycle of minimum mean length (cost) in a digraph |
| 101 | 101 |
/// \ref amo93networkflows, \ref dasdan98minmeancycle. |
| 102 | 102 |
/// It is an improved version of \ref Karp "Karp"'s original algorithm, |
| 103 | 103 |
/// it applies an efficient early termination scheme. |
| 104 | 104 |
/// It runs in time O(ne) and uses space O(n<sup>2</sup>+e). |
| 105 | 105 |
/// |
| 106 | 106 |
/// \tparam GR The type of the digraph the algorithm runs on. |
| 107 | 107 |
/// \tparam LEN The type of the length map. The default |
| 108 | 108 |
/// map type is \ref concepts::Digraph::ArcMap "GR::ArcMap<int>". |
| 109 |
/// \tparam TR The traits class that defines various types used by the |
|
| 110 |
/// algorithm. By default, it is \ref HartmannOrlinDefaultTraits |
|
| 111 |
/// "HartmannOrlinDefaultTraits<GR, LEN>". |
|
| 112 |
/// In most cases, this parameter should not be set directly, |
|
| 113 |
/// consider to use the named template parameters instead. |
|
| 109 | 114 |
#ifdef DOXYGEN |
| 110 | 115 |
template <typename GR, typename LEN, typename TR> |
| 111 | 116 |
#else |
| 112 | 117 |
template < typename GR, |
| 113 | 118 |
typename LEN = typename GR::template ArcMap<int>, |
| 114 | 119 |
typename TR = HartmannOrlinDefaultTraits<GR, LEN> > |
| 115 | 120 |
#endif |
| 116 | 121 |
class HartmannOrlin |
| 117 | 122 |
{
|
| 118 | 123 |
public: |
| 119 | 124 |
|
| 120 | 125 |
/// The type of the digraph |
| 121 | 126 |
typedef typename TR::Digraph Digraph; |
| 122 | 127 |
/// The type of the length map |
| 123 | 128 |
typedef typename TR::LengthMap LengthMap; |
| 124 | 129 |
/// The type of the arc lengths |
| 125 | 130 |
typedef typename TR::Value Value; |
| 126 | 131 |
|
| 127 | 132 |
/// \brief The large value type |
| 128 | 133 |
/// |
| 129 | 134 |
/// The large value type used for internal computations. |
| 130 |
/// Using the \ref HartmannOrlinDefaultTraits "default traits class", |
|
| 131 |
/// it is \c long \c long if the \c Value type is integer, |
|
| 135 |
/// By default, it is \c long \c long if the \c Value type is integer, |
|
| 132 | 136 |
/// otherwise it is \c double. |
| 133 | 137 |
typedef typename TR::LargeValue LargeValue; |
| 134 | 138 |
|
| 135 | 139 |
/// The tolerance type |
| 136 | 140 |
typedef typename TR::Tolerance Tolerance; |
| 137 | 141 |
|
| 138 | 142 |
/// \brief The path type of the found cycles |
| 139 | 143 |
/// |
| 140 | 144 |
/// The path type of the found cycles. |
| 141 | 145 |
/// Using the \ref HartmannOrlinDefaultTraits "default traits class", |
| 142 | 146 |
/// it is \ref lemon::Path "Path<Digraph>". |
| 143 | 147 |
typedef typename TR::Path Path; |
| 144 | 148 |
|
| 145 | 149 |
/// The \ref HartmannOrlinDefaultTraits "traits class" of the algorithm |
| 146 | 150 |
typedef TR Traits; |
| 147 | 151 |
|
| 148 | 152 |
private: |
| 149 | 153 |
|
| 150 | 154 |
TEMPLATE_DIGRAPH_TYPEDEFS(Digraph); |
| 151 | 155 |
|
| 152 | 156 |
// Data sturcture for path data |
| 153 | 157 |
struct PathData |
| 154 | 158 |
{
|
| 155 | 159 |
LargeValue dist; |
| ... | ... |
@@ -85,71 +85,75 @@ |
| 85 | 85 |
#else |
| 86 | 86 |
typedef long LargeValue; |
| 87 | 87 |
#endif |
| 88 | 88 |
typedef lemon::Tolerance<LargeValue> Tolerance; |
| 89 | 89 |
typedef lemon::Path<Digraph> Path; |
| 90 | 90 |
}; |
| 91 | 91 |
|
| 92 | 92 |
|
| 93 | 93 |
/// \addtogroup min_mean_cycle |
| 94 | 94 |
/// @{
|
| 95 | 95 |
|
| 96 | 96 |
/// \brief Implementation of Howard's algorithm for finding a minimum |
| 97 | 97 |
/// mean cycle. |
| 98 | 98 |
/// |
| 99 | 99 |
/// This class implements Howard's policy iteration algorithm for finding |
| 100 | 100 |
/// a directed cycle of minimum mean length (cost) in a digraph |
| 101 | 101 |
/// \ref amo93networkflows, \ref dasdan98minmeancycle. |
| 102 | 102 |
/// This class provides the most efficient algorithm for the |
| 103 | 103 |
/// minimum mean cycle problem, though the best known theoretical |
| 104 | 104 |
/// bound on its running time is exponential. |
| 105 | 105 |
/// |
| 106 | 106 |
/// \tparam GR The type of the digraph the algorithm runs on. |
| 107 | 107 |
/// \tparam LEN The type of the length map. The default |
| 108 | 108 |
/// map type is \ref concepts::Digraph::ArcMap "GR::ArcMap<int>". |
| 109 |
/// \tparam TR The traits class that defines various types used by the |
|
| 110 |
/// algorithm. By default, it is \ref HowardDefaultTraits |
|
| 111 |
/// "HowardDefaultTraits<GR, LEN>". |
|
| 112 |
/// In most cases, this parameter should not be set directly, |
|
| 113 |
/// consider to use the named template parameters instead. |
|
| 109 | 114 |
#ifdef DOXYGEN |
| 110 | 115 |
template <typename GR, typename LEN, typename TR> |
| 111 | 116 |
#else |
| 112 | 117 |
template < typename GR, |
| 113 | 118 |
typename LEN = typename GR::template ArcMap<int>, |
| 114 | 119 |
typename TR = HowardDefaultTraits<GR, LEN> > |
| 115 | 120 |
#endif |
| 116 | 121 |
class Howard |
| 117 | 122 |
{
|
| 118 | 123 |
public: |
| 119 | 124 |
|
| 120 | 125 |
/// The type of the digraph |
| 121 | 126 |
typedef typename TR::Digraph Digraph; |
| 122 | 127 |
/// The type of the length map |
| 123 | 128 |
typedef typename TR::LengthMap LengthMap; |
| 124 | 129 |
/// The type of the arc lengths |
| 125 | 130 |
typedef typename TR::Value Value; |
| 126 | 131 |
|
| 127 | 132 |
/// \brief The large value type |
| 128 | 133 |
/// |
| 129 | 134 |
/// The large value type used for internal computations. |
| 130 |
/// Using the \ref HowardDefaultTraits "default traits class", |
|
| 131 |
/// it is \c long \c long if the \c Value type is integer, |
|
| 135 |
/// By default, it is \c long \c long if the \c Value type is integer, |
|
| 132 | 136 |
/// otherwise it is \c double. |
| 133 | 137 |
typedef typename TR::LargeValue LargeValue; |
| 134 | 138 |
|
| 135 | 139 |
/// The tolerance type |
| 136 | 140 |
typedef typename TR::Tolerance Tolerance; |
| 137 | 141 |
|
| 138 | 142 |
/// \brief The path type of the found cycles |
| 139 | 143 |
/// |
| 140 | 144 |
/// The path type of the found cycles. |
| 141 | 145 |
/// Using the \ref HowardDefaultTraits "default traits class", |
| 142 | 146 |
/// it is \ref lemon::Path "Path<Digraph>". |
| 143 | 147 |
typedef typename TR::Path Path; |
| 144 | 148 |
|
| 145 | 149 |
/// The \ref HowardDefaultTraits "traits class" of the algorithm |
| 146 | 150 |
typedef TR Traits; |
| 147 | 151 |
|
| 148 | 152 |
private: |
| 149 | 153 |
|
| 150 | 154 |
TEMPLATE_DIGRAPH_TYPEDEFS(Digraph); |
| 151 | 155 |
|
| 152 | 156 |
// The digraph the algorithm runs on |
| 153 | 157 |
const Digraph &_gr; |
| 154 | 158 |
// The length of the arcs |
| 155 | 159 |
const LengthMap &_length; |
| ... | ... |
@@ -83,71 +83,75 @@ |
| 83 | 83 |
#ifdef LEMON_HAVE_LONG_LONG |
| 84 | 84 |
typedef long long LargeValue; |
| 85 | 85 |
#else |
| 86 | 86 |
typedef long LargeValue; |
| 87 | 87 |
#endif |
| 88 | 88 |
typedef lemon::Tolerance<LargeValue> Tolerance; |
| 89 | 89 |
typedef lemon::Path<Digraph> Path; |
| 90 | 90 |
}; |
| 91 | 91 |
|
| 92 | 92 |
|
| 93 | 93 |
/// \addtogroup min_mean_cycle |
| 94 | 94 |
/// @{
|
| 95 | 95 |
|
| 96 | 96 |
/// \brief Implementation of Karp's algorithm for finding a minimum |
| 97 | 97 |
/// mean cycle. |
| 98 | 98 |
/// |
| 99 | 99 |
/// This class implements Karp's algorithm for finding a directed |
| 100 | 100 |
/// cycle of minimum mean length (cost) in a digraph |
| 101 | 101 |
/// \ref amo93networkflows, \ref dasdan98minmeancycle. |
| 102 | 102 |
/// It runs in time O(ne) and uses space O(n<sup>2</sup>+e). |
| 103 | 103 |
/// |
| 104 | 104 |
/// \tparam GR The type of the digraph the algorithm runs on. |
| 105 | 105 |
/// \tparam LEN The type of the length map. The default |
| 106 | 106 |
/// map type is \ref concepts::Digraph::ArcMap "GR::ArcMap<int>". |
| 107 |
/// \tparam TR The traits class that defines various types used by the |
|
| 108 |
/// algorithm. By default, it is \ref KarpDefaultTraits |
|
| 109 |
/// "KarpDefaultTraits<GR, LEN>". |
|
| 110 |
/// In most cases, this parameter should not be set directly, |
|
| 111 |
/// consider to use the named template parameters instead. |
|
| 107 | 112 |
#ifdef DOXYGEN |
| 108 | 113 |
template <typename GR, typename LEN, typename TR> |
| 109 | 114 |
#else |
| 110 | 115 |
template < typename GR, |
| 111 | 116 |
typename LEN = typename GR::template ArcMap<int>, |
| 112 | 117 |
typename TR = KarpDefaultTraits<GR, LEN> > |
| 113 | 118 |
#endif |
| 114 | 119 |
class Karp |
| 115 | 120 |
{
|
| 116 | 121 |
public: |
| 117 | 122 |
|
| 118 | 123 |
/// The type of the digraph |
| 119 | 124 |
typedef typename TR::Digraph Digraph; |
| 120 | 125 |
/// The type of the length map |
| 121 | 126 |
typedef typename TR::LengthMap LengthMap; |
| 122 | 127 |
/// The type of the arc lengths |
| 123 | 128 |
typedef typename TR::Value Value; |
| 124 | 129 |
|
| 125 | 130 |
/// \brief The large value type |
| 126 | 131 |
/// |
| 127 | 132 |
/// The large value type used for internal computations. |
| 128 |
/// Using the \ref KarpDefaultTraits "default traits class", |
|
| 129 |
/// it is \c long \c long if the \c Value type is integer, |
|
| 133 |
/// By default, it is \c long \c long if the \c Value type is integer, |
|
| 130 | 134 |
/// otherwise it is \c double. |
| 131 | 135 |
typedef typename TR::LargeValue LargeValue; |
| 132 | 136 |
|
| 133 | 137 |
/// The tolerance type |
| 134 | 138 |
typedef typename TR::Tolerance Tolerance; |
| 135 | 139 |
|
| 136 | 140 |
/// \brief The path type of the found cycles |
| 137 | 141 |
/// |
| 138 | 142 |
/// The path type of the found cycles. |
| 139 | 143 |
/// Using the \ref KarpDefaultTraits "default traits class", |
| 140 | 144 |
/// it is \ref lemon::Path "Path<Digraph>". |
| 141 | 145 |
typedef typename TR::Path Path; |
| 142 | 146 |
|
| 143 | 147 |
/// The \ref KarpDefaultTraits "traits class" of the algorithm |
| 144 | 148 |
typedef TR Traits; |
| 145 | 149 |
|
| 146 | 150 |
private: |
| 147 | 151 |
|
| 148 | 152 |
TEMPLATE_DIGRAPH_TYPEDEFS(Digraph); |
| 149 | 153 |
|
| 150 | 154 |
// Data sturcture for path data |
| 151 | 155 |
struct PathData |
| 152 | 156 |
{
|
| 153 | 157 |
LargeValue dist; |
| ... | ... |
@@ -91,59 +91,60 @@ |
| 91 | 91 |
|
| 92 | 92 |
}; |
| 93 | 93 |
|
| 94 | 94 |
/// \ingroup spantree |
| 95 | 95 |
/// |
| 96 | 96 |
/// \brief Minimum Cost Arborescence algorithm class. |
| 97 | 97 |
/// |
| 98 | 98 |
/// This class provides an efficient implementation of the |
| 99 | 99 |
/// Minimum Cost Arborescence algorithm. The arborescence is a tree |
| 100 | 100 |
/// which is directed from a given source node of the digraph. One or |
| 101 | 101 |
/// more sources should be given to the algorithm and it will calculate |
| 102 | 102 |
/// the minimum cost subgraph that is the union of arborescences with the |
| 103 | 103 |
/// given sources and spans all the nodes which are reachable from the |
| 104 | 104 |
/// sources. The time complexity of the algorithm is O(n<sup>2</sup>+e). |
| 105 | 105 |
/// |
| 106 | 106 |
/// The algorithm also provides an optimal dual solution, therefore |
| 107 | 107 |
/// the optimality of the solution can be checked. |
| 108 | 108 |
/// |
| 109 | 109 |
/// \param GR The digraph type the algorithm runs on. |
| 110 | 110 |
/// \param CM A read-only arc map storing the costs of the |
| 111 | 111 |
/// arcs. It is read once for each arc, so the map may involve in |
| 112 | 112 |
/// relatively time consuming process to compute the arc costs if |
| 113 | 113 |
/// it is necessary. The default map type is \ref |
| 114 | 114 |
/// concepts::Digraph::ArcMap "Digraph::ArcMap<int>". |
| 115 |
/// \param TR Traits class to set various data types used |
|
| 116 |
/// by the algorithm. The default traits class is |
|
| 117 |
/// \ |
|
| 115 |
/// \tparam TR The traits class that defines various types used by the |
|
| 116 |
/// algorithm. By default, it is \ref MinCostArborescenceDefaultTraits |
|
| 118 | 117 |
/// "MinCostArborescenceDefaultTraits<GR, CM>". |
| 118 |
/// In most cases, this parameter should not be set directly, |
|
| 119 |
/// consider to use the named template parameters instead. |
|
| 119 | 120 |
#ifndef DOXYGEN |
| 120 | 121 |
template <typename GR, |
| 121 | 122 |
typename CM = typename GR::template ArcMap<int>, |
| 122 | 123 |
typename TR = |
| 123 | 124 |
MinCostArborescenceDefaultTraits<GR, CM> > |
| 124 | 125 |
#else |
| 125 |
template <typename GR, typename CM, |
|
| 126 |
template <typename GR, typename CM, typename TR> |
|
| 126 | 127 |
#endif |
| 127 | 128 |
class MinCostArborescence {
|
| 128 | 129 |
public: |
| 129 | 130 |
|
| 130 | 131 |
/// \brief The \ref MinCostArborescenceDefaultTraits "traits class" |
| 131 | 132 |
/// of the algorithm. |
| 132 | 133 |
typedef TR Traits; |
| 133 | 134 |
/// The type of the underlying digraph. |
| 134 | 135 |
typedef typename Traits::Digraph Digraph; |
| 135 | 136 |
/// The type of the map that stores the arc costs. |
| 136 | 137 |
typedef typename Traits::CostMap CostMap; |
| 137 | 138 |
///The type of the costs of the arcs. |
| 138 | 139 |
typedef typename Traits::Value Value; |
| 139 | 140 |
///The type of the predecessor map. |
| 140 | 141 |
typedef typename Traits::PredMap PredMap; |
| 141 | 142 |
///The type of the map that stores which arcs are in the arborescence. |
| 142 | 143 |
typedef typename Traits::ArborescenceMap ArborescenceMap; |
| 143 | 144 |
|
| 144 | 145 |
typedef MinCostArborescence Create; |
| 145 | 146 |
|
| 146 | 147 |
private: |
| 147 | 148 |
|
| 148 | 149 |
TEMPLATE_DIGRAPH_TYPEDEFS(Digraph); |
| 149 | 150 |
| ... | ... |
@@ -497,72 +497,73 @@ |
| 497 | 497 |
|
| 498 | 498 |
if (child != INVALID) {
|
| 499 | 499 |
if (low_map[child] < rorder) return true; |
| 500 | 500 |
} |
| 501 | 501 |
|
| 502 | 502 |
if (ancestor_map[node] < rorder) return true; |
| 503 | 503 |
|
| 504 | 504 |
return false; |
| 505 | 505 |
} |
| 506 | 506 |
|
| 507 | 507 |
bool pertinent(const Node& node, const EmbedArc& embed_arc, |
| 508 | 508 |
const MergeRoots& merge_roots) {
|
| 509 | 509 |
return !merge_roots[node].empty() || embed_arc[node]; |
| 510 | 510 |
} |
| 511 | 511 |
|
| 512 | 512 |
}; |
| 513 | 513 |
|
| 514 | 514 |
} |
| 515 | 515 |
|
| 516 | 516 |
/// \ingroup planar |
| 517 | 517 |
/// |
| 518 | 518 |
/// \brief Planarity checking of an undirected simple graph |
| 519 | 519 |
/// |
| 520 | 520 |
/// This function implements the Boyer-Myrvold algorithm for |
| 521 |
/// planarity checking of an undirected graph. It is a simplified |
|
| 521 |
/// planarity checking of an undirected simple graph. It is a simplified |
|
| 522 | 522 |
/// version of the PlanarEmbedding algorithm class because neither |
| 523 |
/// the embedding nor the |
|
| 523 |
/// the embedding nor the Kuratowski subdivisons are computed. |
|
| 524 | 524 |
template <typename GR> |
| 525 | 525 |
bool checkPlanarity(const GR& graph) {
|
| 526 | 526 |
_planarity_bits::PlanarityChecking<GR> pc(graph); |
| 527 | 527 |
return pc.run(); |
| 528 | 528 |
} |
| 529 | 529 |
|
| 530 | 530 |
/// \ingroup planar |
| 531 | 531 |
/// |
| 532 | 532 |
/// \brief Planar embedding of an undirected simple graph |
| 533 | 533 |
/// |
| 534 | 534 |
/// This class implements the Boyer-Myrvold algorithm for planar |
| 535 |
/// embedding of an undirected graph. The planar embedding is an |
|
| 535 |
/// embedding of an undirected simple graph. The planar embedding is an |
|
| 536 | 536 |
/// ordering of the outgoing edges of the nodes, which is a possible |
| 537 | 537 |
/// configuration to draw the graph in the plane. If there is not |
| 538 |
/// such ordering then the graph contains a \f$ K_5 \f$ (full graph |
|
| 539 |
/// with 5 nodes) or a \f$ K_{3,3} \f$ (complete bipartite graph on
|
|
| 540 |
/// |
|
| 538 |
/// such ordering then the graph contains a K<sub>5</sub> (full graph |
|
| 539 |
/// with 5 nodes) or a K<sub>3,3</sub> (complete bipartite graph on |
|
| 540 |
/// 3 Red and 3 Blue nodes) subdivision. |
|
| 541 | 541 |
/// |
| 542 | 542 |
/// The current implementation calculates either an embedding or a |
| 543 |
/// Kuratowski subdivision. The running time of the algorithm is |
|
| 544 |
/// \f$ O(n) \f$. |
|
| 543 |
/// Kuratowski subdivision. The running time of the algorithm is O(n). |
|
| 544 |
/// |
|
| 545 |
/// \see PlanarDrawing, checkPlanarity() |
|
| 545 | 546 |
template <typename Graph> |
| 546 | 547 |
class PlanarEmbedding {
|
| 547 | 548 |
private: |
| 548 | 549 |
|
| 549 | 550 |
TEMPLATE_GRAPH_TYPEDEFS(Graph); |
| 550 | 551 |
|
| 551 | 552 |
const Graph& _graph; |
| 552 | 553 |
typename Graph::template ArcMap<Arc> _embedding; |
| 553 | 554 |
|
| 554 | 555 |
typename Graph::template EdgeMap<bool> _kuratowski; |
| 555 | 556 |
|
| 556 | 557 |
private: |
| 557 | 558 |
|
| 558 | 559 |
typedef typename Graph::template NodeMap<Arc> PredMap; |
| 559 | 560 |
|
| 560 | 561 |
typedef typename Graph::template EdgeMap<bool> TreeMap; |
| 561 | 562 |
|
| 562 | 563 |
typedef typename Graph::template NodeMap<int> OrderMap; |
| 563 | 564 |
typedef std::vector<Node> OrderList; |
| 564 | 565 |
|
| 565 | 566 |
typedef typename Graph::template NodeMap<int> LowMap; |
| 566 | 567 |
typedef typename Graph::template NodeMap<int> AncestorMap; |
| 567 | 568 |
|
| 568 | 569 |
typedef _planarity_bits::NodeDataNode<Graph> NodeDataNode; |
| ... | ... |
@@ -570,64 +571,68 @@ |
| 570 | 571 |
|
| 571 | 572 |
typedef _planarity_bits::ChildListNode<Graph> ChildListNode; |
| 572 | 573 |
typedef typename Graph::template NodeMap<ChildListNode> ChildLists; |
| 573 | 574 |
|
| 574 | 575 |
typedef typename Graph::template NodeMap<std::list<int> > MergeRoots; |
| 575 | 576 |
|
| 576 | 577 |
typedef typename Graph::template NodeMap<Arc> EmbedArc; |
| 577 | 578 |
|
| 578 | 579 |
typedef _planarity_bits::ArcListNode<Graph> ArcListNode; |
| 579 | 580 |
typedef typename Graph::template ArcMap<ArcListNode> ArcLists; |
| 580 | 581 |
|
| 581 | 582 |
typedef typename Graph::template NodeMap<bool> FlipMap; |
| 582 | 583 |
|
| 583 | 584 |
typedef typename Graph::template NodeMap<int> TypeMap; |
| 584 | 585 |
|
| 585 | 586 |
enum IsolatorNodeType {
|
| 586 | 587 |
HIGHX = 6, LOWX = 7, |
| 587 | 588 |
HIGHY = 8, LOWY = 9, |
| 588 | 589 |
ROOT = 10, PERTINENT = 11, |
| 589 | 590 |
INTERNAL = 12 |
| 590 | 591 |
}; |
| 591 | 592 |
|
| 592 | 593 |
public: |
| 593 | 594 |
|
| 594 |
/// \brief The map for |
|
| 595 |
/// \brief The map type for storing the embedding |
|
| 596 |
/// |
|
| 597 |
/// The map type for storing the embedding. |
|
| 598 |
/// \see embeddingMap() |
|
| 595 | 599 |
typedef typename Graph::template ArcMap<Arc> EmbeddingMap; |
| 596 | 600 |
|
| 597 | 601 |
/// \brief Constructor |
| 598 | 602 |
/// |
| 599 |
/// \note The graph should be simple, i.e. parallel and loop arc |
|
| 600 |
/// free. |
|
| 603 |
/// Constructor. |
|
| 604 |
/// \pre The graph must be simple, i.e. it should not |
|
| 605 |
/// contain parallel or loop arcs. |
|
| 601 | 606 |
PlanarEmbedding(const Graph& graph) |
| 602 | 607 |
: _graph(graph), _embedding(_graph), _kuratowski(graph, false) {}
|
| 603 | 608 |
|
| 604 |
/// \brief |
|
| 609 |
/// \brief Run the algorithm. |
|
| 605 | 610 |
/// |
| 606 |
/// Runs the algorithm. |
|
| 607 |
/// \param kuratowski If the parameter is false, then the |
|
| 611 |
/// This function runs the algorithm. |
|
| 612 |
/// \param kuratowski If this parameter is set to \c false, then the |
|
| 608 | 613 |
/// algorithm does not compute a Kuratowski subdivision. |
| 609 |
///\return |
|
| 614 |
/// \return \c true if the graph is planar. |
|
| 610 | 615 |
bool run(bool kuratowski = true) {
|
| 611 | 616 |
typedef _planarity_bits::PlanarityVisitor<Graph> Visitor; |
| 612 | 617 |
|
| 613 | 618 |
PredMap pred_map(_graph, INVALID); |
| 614 | 619 |
TreeMap tree_map(_graph, false); |
| 615 | 620 |
|
| 616 | 621 |
OrderMap order_map(_graph, -1); |
| 617 | 622 |
OrderList order_list; |
| 618 | 623 |
|
| 619 | 624 |
AncestorMap ancestor_map(_graph, -1); |
| 620 | 625 |
LowMap low_map(_graph, -1); |
| 621 | 626 |
|
| 622 | 627 |
Visitor visitor(_graph, pred_map, tree_map, |
| 623 | 628 |
order_map, order_list, ancestor_map, low_map); |
| 624 | 629 |
DfsVisit<Graph, Visitor> visit(_graph, visitor); |
| 625 | 630 |
visit.run(); |
| 626 | 631 |
|
| 627 | 632 |
ChildLists child_lists(_graph); |
| 628 | 633 |
createChildLists(tree_map, order_map, low_map, child_lists); |
| 629 | 634 |
|
| 630 | 635 |
NodeData node_data(2 * order_list.size()); |
| 631 | 636 |
|
| 632 | 637 |
EmbedArc embed_arc(_graph, INVALID); |
| 633 | 638 |
|
| ... | ... |
@@ -678,72 +683,74 @@ |
| 678 | 683 |
if (embed_arc[target] != INVALID) {
|
| 679 | 684 |
if (kuratowski) {
|
| 680 | 685 |
isolateKuratowski(e, node_data, arc_lists, flip_map, |
| 681 | 686 |
order_map, order_list, pred_map, child_lists, |
| 682 | 687 |
ancestor_map, low_map, |
| 683 | 688 |
embed_arc, merge_roots); |
| 684 | 689 |
} |
| 685 | 690 |
return false; |
| 686 | 691 |
} |
| 687 | 692 |
} |
| 688 | 693 |
} |
| 689 | 694 |
} |
| 690 | 695 |
|
| 691 | 696 |
for (int i = 0; i < int(order_list.size()); ++i) {
|
| 692 | 697 |
|
| 693 | 698 |
mergeRemainingFaces(order_list[i], node_data, order_list, order_map, |
| 694 | 699 |
child_lists, arc_lists); |
| 695 | 700 |
storeEmbedding(order_list[i], node_data, order_map, pred_map, |
| 696 | 701 |
arc_lists, flip_map); |
| 697 | 702 |
} |
| 698 | 703 |
|
| 699 | 704 |
return true; |
| 700 | 705 |
} |
| 701 | 706 |
|
| 702 |
/// \brief |
|
| 707 |
/// \brief Give back the successor of an arc |
|
| 703 | 708 |
/// |
| 704 |
/// |
|
| 709 |
/// This function gives back the successor of an arc. It makes |
|
| 705 | 710 |
/// possible to query the cyclic order of the outgoing arcs from |
| 706 | 711 |
/// a node. |
| 707 | 712 |
Arc next(const Arc& arc) const {
|
| 708 | 713 |
return _embedding[arc]; |
| 709 | 714 |
} |
| 710 | 715 |
|
| 711 |
/// \brief |
|
| 716 |
/// \brief Give back the calculated embedding map |
|
| 712 | 717 |
/// |
| 713 |
/// The returned map contains the successor of each arc in the |
|
| 714 |
/// graph. |
|
| 718 |
/// This function gives back the calculated embedding map, which |
|
| 719 |
/// contains the successor of each arc in the cyclic order of the |
|
| 720 |
/// outgoing arcs of its source node. |
|
| 715 | 721 |
const EmbeddingMap& embeddingMap() const {
|
| 716 | 722 |
return _embedding; |
| 717 | 723 |
} |
| 718 | 724 |
|
| 719 |
/// \brief Gives back true if the undirected arc is in the |
|
| 720 |
/// kuratowski subdivision |
|
| 725 |
/// \brief Give back \c true if the given edge is in the Kuratowski |
|
| 726 |
/// subdivision |
|
| 721 | 727 |
/// |
| 722 |
/// Gives back true if the undirected arc is in the kuratowski |
|
| 723 |
/// subdivision |
|
| 724 |
/// \note The \c run() had to be called with true value. |
|
| 725 |
bool kuratowski(const Edge& edge) {
|
|
| 728 |
/// This function gives back \c true if the given edge is in the found |
|
| 729 |
/// Kuratowski subdivision. |
|
| 730 |
/// \pre The \c run() function must be called with \c true parameter |
|
| 731 |
/// before using this function. |
|
| 732 |
bool kuratowski(const Edge& edge) const {
|
|
| 726 | 733 |
return _kuratowski[edge]; |
| 727 | 734 |
} |
| 728 | 735 |
|
| 729 | 736 |
private: |
| 730 | 737 |
|
| 731 | 738 |
void createChildLists(const TreeMap& tree_map, const OrderMap& order_map, |
| 732 | 739 |
const LowMap& low_map, ChildLists& child_lists) {
|
| 733 | 740 |
|
| 734 | 741 |
for (NodeIt n(_graph); n != INVALID; ++n) {
|
| 735 | 742 |
Node source = n; |
| 736 | 743 |
|
| 737 | 744 |
std::vector<Node> targets; |
| 738 | 745 |
for (OutArcIt e(_graph, n); e != INVALID; ++e) {
|
| 739 | 746 |
Node target = _graph.target(e); |
| 740 | 747 |
|
| 741 | 748 |
if (order_map[source] < order_map[target] && tree_map[e]) {
|
| 742 | 749 |
targets.push_back(target); |
| 743 | 750 |
} |
| 744 | 751 |
} |
| 745 | 752 |
|
| 746 | 753 |
if (targets.size() == 0) {
|
| 747 | 754 |
child_lists[source].first = INVALID; |
| 748 | 755 |
} else if (targets.size() == 1) {
|
| 749 | 756 |
child_lists[source].first = targets[0]; |
| ... | ... |
@@ -2038,71 +2045,74 @@ |
| 2038 | 2045 |
graph.direct(graph.addEdge(t, graph.source(e)), true); |
| 2039 | 2046 |
|
| 2040 | 2047 |
embedding[n] = pn; |
| 2041 | 2048 |
embedding[graph.oppositeArc(n)] = e; |
| 2042 | 2049 |
embedding[graph.oppositeArc(p)] = graph.oppositeArc(n); |
| 2043 | 2050 |
|
| 2044 | 2051 |
pn = n; |
| 2045 | 2052 |
|
| 2046 | 2053 |
p = e; |
| 2047 | 2054 |
e = embedding[graph.oppositeArc(e)]; |
| 2048 | 2055 |
|
| 2049 | 2056 |
} |
| 2050 | 2057 |
embedding[graph.oppositeArc(e)] = pn; |
| 2051 | 2058 |
} |
| 2052 | 2059 |
} |
| 2053 | 2060 |
} |
| 2054 | 2061 |
|
| 2055 | 2062 |
} |
| 2056 | 2063 |
|
| 2057 | 2064 |
/// \ingroup planar |
| 2058 | 2065 |
/// |
| 2059 | 2066 |
/// \brief Schnyder's planar drawing algorithm |
| 2060 | 2067 |
/// |
| 2061 | 2068 |
/// The planar drawing algorithm calculates positions for the nodes |
| 2062 |
/// in the plane which coordinates satisfy that if the arcs are |
|
| 2063 |
/// represented with straight lines then they will not intersect |
|
| 2069 |
/// in the plane. These coordinates satisfy that if the edges are |
|
| 2070 |
/// represented with straight lines, then they will not intersect |
|
| 2064 | 2071 |
/// each other. |
| 2065 | 2072 |
/// |
| 2066 |
/// Scnyder's algorithm embeds the graph on \c (n-2,n-2) size grid, |
|
| 2067 |
/// i.e. each node will be located in the \c [0,n-2]x[0,n-2] square. |
|
| 2073 |
/// Scnyder's algorithm embeds the graph on an \c (n-2)x(n-2) size grid, |
|
| 2074 |
/// i.e. each node will be located in the \c [0..n-2]x[0..n-2] square. |
|
| 2068 | 2075 |
/// The time complexity of the algorithm is O(n). |
| 2076 |
/// |
|
| 2077 |
/// \see PlanarEmbedding |
|
| 2069 | 2078 |
template <typename Graph> |
| 2070 | 2079 |
class PlanarDrawing {
|
| 2071 | 2080 |
public: |
| 2072 | 2081 |
|
| 2073 | 2082 |
TEMPLATE_GRAPH_TYPEDEFS(Graph); |
| 2074 | 2083 |
|
| 2075 |
/// \brief The point type for |
|
| 2084 |
/// \brief The point type for storing coordinates |
|
| 2076 | 2085 |
typedef dim2::Point<int> Point; |
| 2077 |
/// \brief The map type for |
|
| 2086 |
/// \brief The map type for storing the coordinates of the nodes |
|
| 2078 | 2087 |
typedef typename Graph::template NodeMap<Point> PointMap; |
| 2079 | 2088 |
|
| 2080 | 2089 |
|
| 2081 | 2090 |
/// \brief Constructor |
| 2082 | 2091 |
/// |
| 2083 | 2092 |
/// Constructor |
| 2084 |
/// \pre The graph |
|
| 2093 |
/// \pre The graph must be simple, i.e. it should not |
|
| 2094 |
/// contain parallel or loop arcs. |
|
| 2085 | 2095 |
PlanarDrawing(const Graph& graph) |
| 2086 | 2096 |
: _graph(graph), _point_map(graph) {}
|
| 2087 | 2097 |
|
| 2088 | 2098 |
private: |
| 2089 | 2099 |
|
| 2090 | 2100 |
template <typename AuxGraph, typename AuxEmbeddingMap> |
| 2091 | 2101 |
void drawing(const AuxGraph& graph, |
| 2092 | 2102 |
const AuxEmbeddingMap& next, |
| 2093 | 2103 |
PointMap& point_map) {
|
| 2094 | 2104 |
TEMPLATE_GRAPH_TYPEDEFS(AuxGraph); |
| 2095 | 2105 |
|
| 2096 | 2106 |
typename AuxGraph::template ArcMap<Arc> prev(graph); |
| 2097 | 2107 |
|
| 2098 | 2108 |
for (NodeIt n(graph); n != INVALID; ++n) {
|
| 2099 | 2109 |
Arc e = OutArcIt(graph, n); |
| 2100 | 2110 |
|
| 2101 | 2111 |
Arc p = e, l = e; |
| 2102 | 2112 |
|
| 2103 | 2113 |
e = next[e]; |
| 2104 | 2114 |
while (e != l) {
|
| 2105 | 2115 |
prev[e] = p; |
| 2106 | 2116 |
p = e; |
| 2107 | 2117 |
e = next[e]; |
| 2108 | 2118 |
} |
| ... | ... |
@@ -2345,241 +2355,246 @@ |
| 2345 | 2355 |
cpath[anode] = cpath[bnode] = 1; |
| 2346 | 2356 |
typename AuxGraph::template NodeMap<int> cpath_atree(graph, 0); |
| 2347 | 2357 |
cpath_atree[anode] = atree[anode]; |
| 2348 | 2358 |
typename AuxGraph::template NodeMap<int> cpath_btree(graph, 0); |
| 2349 | 2359 |
cpath_btree[bnode] = btree[bnode]; |
| 2350 | 2360 |
for (int i = 1; i < int(corder.size()); ++i) {
|
| 2351 | 2361 |
Node n = corder[i]; |
| 2352 | 2362 |
cpath[n] = cpath[cpred[n]] + 1; |
| 2353 | 2363 |
cpath_atree[n] = atree[n] + cpath_atree[cpred[n]]; |
| 2354 | 2364 |
cpath_btree[n] = btree[n] + cpath_btree[cpred[n]]; |
| 2355 | 2365 |
} |
| 2356 | 2366 |
|
| 2357 | 2367 |
typename AuxGraph::template NodeMap<int> third(graph); |
| 2358 | 2368 |
for (NodeIt n(graph); n != INVALID; ++n) {
|
| 2359 | 2369 |
point_map[n].x = |
| 2360 | 2370 |
bpath_atree[n] + cpath_atree[n] - atree[n] - cpath[n] + 1; |
| 2361 | 2371 |
point_map[n].y = |
| 2362 | 2372 |
cpath_btree[n] + apath_btree[n] - btree[n] - apath[n] + 1; |
| 2363 | 2373 |
} |
| 2364 | 2374 |
|
| 2365 | 2375 |
} |
| 2366 | 2376 |
|
| 2367 | 2377 |
public: |
| 2368 | 2378 |
|
| 2369 |
/// \brief |
|
| 2379 |
/// \brief Calculate the node positions |
|
| 2370 | 2380 |
/// |
| 2371 |
/// This function calculates the node positions. |
|
| 2372 |
/// \return %True if the graph is planar. |
|
| 2381 |
/// This function calculates the node positions on the plane. |
|
| 2382 |
/// \return \c true if the graph is planar. |
|
| 2373 | 2383 |
bool run() {
|
| 2374 | 2384 |
PlanarEmbedding<Graph> pe(_graph); |
| 2375 | 2385 |
if (!pe.run()) return false; |
| 2376 | 2386 |
|
| 2377 | 2387 |
run(pe); |
| 2378 | 2388 |
return true; |
| 2379 | 2389 |
} |
| 2380 | 2390 |
|
| 2381 |
/// \brief |
|
| 2391 |
/// \brief Calculate the node positions according to a |
|
| 2382 | 2392 |
/// combinatorical embedding |
| 2383 | 2393 |
/// |
| 2384 |
/// This function calculates the node locations. The \c embedding |
|
| 2385 |
/// parameter should contain a valid combinatorical embedding, i.e. |
|
| 2386 |
/// |
|
| 2394 |
/// This function calculates the node positions on the plane. |
|
| 2395 |
/// The given \c embedding map should contain a valid combinatorical |
|
| 2396 |
/// embedding, i.e. a valid cyclic order of the arcs. |
|
| 2397 |
/// It can be computed using PlanarEmbedding. |
|
| 2387 | 2398 |
template <typename EmbeddingMap> |
| 2388 | 2399 |
void run(const EmbeddingMap& embedding) {
|
| 2389 | 2400 |
typedef SmartEdgeSet<Graph> AuxGraph; |
| 2390 | 2401 |
|
| 2391 | 2402 |
if (3 * countNodes(_graph) - 6 == countEdges(_graph)) {
|
| 2392 | 2403 |
drawing(_graph, embedding, _point_map); |
| 2393 | 2404 |
return; |
| 2394 | 2405 |
} |
| 2395 | 2406 |
|
| 2396 | 2407 |
AuxGraph aux_graph(_graph); |
| 2397 | 2408 |
typename AuxGraph::template ArcMap<typename AuxGraph::Arc> |
| 2398 | 2409 |
aux_embedding(aux_graph); |
| 2399 | 2410 |
|
| 2400 | 2411 |
{
|
| 2401 | 2412 |
|
| 2402 | 2413 |
typename Graph::template EdgeMap<typename AuxGraph::Edge> |
| 2403 | 2414 |
ref(_graph); |
| 2404 | 2415 |
|
| 2405 | 2416 |
for (EdgeIt e(_graph); e != INVALID; ++e) {
|
| 2406 | 2417 |
ref[e] = aux_graph.addEdge(_graph.u(e), _graph.v(e)); |
| 2407 | 2418 |
} |
| 2408 | 2419 |
|
| 2409 | 2420 |
for (EdgeIt e(_graph); e != INVALID; ++e) {
|
| 2410 | 2421 |
Arc ee = embedding[_graph.direct(e, true)]; |
| 2411 | 2422 |
aux_embedding[aux_graph.direct(ref[e], true)] = |
| 2412 | 2423 |
aux_graph.direct(ref[ee], _graph.direction(ee)); |
| 2413 | 2424 |
ee = embedding[_graph.direct(e, false)]; |
| 2414 | 2425 |
aux_embedding[aux_graph.direct(ref[e], false)] = |
| 2415 | 2426 |
aux_graph.direct(ref[ee], _graph.direction(ee)); |
| 2416 | 2427 |
} |
| 2417 | 2428 |
} |
| 2418 | 2429 |
_planarity_bits::makeConnected(aux_graph, aux_embedding); |
| 2419 | 2430 |
_planarity_bits::makeBiNodeConnected(aux_graph, aux_embedding); |
| 2420 | 2431 |
_planarity_bits::makeMaxPlanar(aux_graph, aux_embedding); |
| 2421 | 2432 |
drawing(aux_graph, aux_embedding, _point_map); |
| 2422 | 2433 |
} |
| 2423 | 2434 |
|
| 2424 | 2435 |
/// \brief The coordinate of the given node |
| 2425 | 2436 |
/// |
| 2426 |
/// |
|
| 2437 |
/// This function returns the coordinate of the given node. |
|
| 2427 | 2438 |
Point operator[](const Node& node) const {
|
| 2428 | 2439 |
return _point_map[node]; |
| 2429 | 2440 |
} |
| 2430 | 2441 |
|
| 2431 |
/// \brief |
|
| 2442 |
/// \brief Return the grid embedding in a node map |
|
| 2432 | 2443 |
/// |
| 2433 |
/// |
|
| 2444 |
/// This function returns the grid embedding in a node map of |
|
| 2445 |
/// \c dim2::Point<int> coordinates. |
|
| 2434 | 2446 |
const PointMap& coords() const {
|
| 2435 | 2447 |
return _point_map; |
| 2436 | 2448 |
} |
| 2437 | 2449 |
|
| 2438 | 2450 |
private: |
| 2439 | 2451 |
|
| 2440 | 2452 |
const Graph& _graph; |
| 2441 | 2453 |
PointMap _point_map; |
| 2442 | 2454 |
|
| 2443 | 2455 |
}; |
| 2444 | 2456 |
|
| 2445 | 2457 |
namespace _planarity_bits {
|
| 2446 | 2458 |
|
| 2447 | 2459 |
template <typename ColorMap> |
| 2448 | 2460 |
class KempeFilter {
|
| 2449 | 2461 |
public: |
| 2450 | 2462 |
typedef typename ColorMap::Key Key; |
| 2451 | 2463 |
typedef bool Value; |
| 2452 | 2464 |
|
| 2453 | 2465 |
KempeFilter(const ColorMap& color_map, |
| 2454 | 2466 |
const typename ColorMap::Value& first, |
| 2455 | 2467 |
const typename ColorMap::Value& second) |
| 2456 | 2468 |
: _color_map(color_map), _first(first), _second(second) {}
|
| 2457 | 2469 |
|
| 2458 | 2470 |
Value operator[](const Key& key) const {
|
| 2459 | 2471 |
return _color_map[key] == _first || _color_map[key] == _second; |
| 2460 | 2472 |
} |
| 2461 | 2473 |
|
| 2462 | 2474 |
private: |
| 2463 | 2475 |
const ColorMap& _color_map; |
| 2464 | 2476 |
typename ColorMap::Value _first, _second; |
| 2465 | 2477 |
}; |
| 2466 | 2478 |
} |
| 2467 | 2479 |
|
| 2468 | 2480 |
/// \ingroup planar |
| 2469 | 2481 |
/// |
| 2470 | 2482 |
/// \brief Coloring planar graphs |
| 2471 | 2483 |
/// |
| 2472 | 2484 |
/// The graph coloring problem is the coloring of the graph nodes |
| 2473 |
/// that there are not adjacent nodes with the same color. The |
|
| 2474 |
/// planar graphs can be always colored with four colors, it is |
|
| 2475 |
/// |
|
| 2485 |
/// so that there are no adjacent nodes with the same color. The |
|
| 2486 |
/// planar graphs can always be colored with four colors, which is |
|
| 2487 |
/// proved by Appel and Haken. Their proofs provide a quadratic |
|
| 2476 | 2488 |
/// time algorithm for four coloring, but it could not be used to |
| 2477 |
/// implement efficient algorithm. The five and six coloring can be |
|
| 2478 |
/// made in linear time, but in this class the five coloring has |
|
| 2489 |
/// implement an efficient algorithm. The five and six coloring can be |
|
| 2490 |
/// made in linear time, but in this class, the five coloring has |
|
| 2479 | 2491 |
/// quadratic worst case time complexity. The two coloring (if |
| 2480 | 2492 |
/// possible) is solvable with a graph search algorithm and it is |
| 2481 | 2493 |
/// implemented in \ref bipartitePartitions() function in LEMON. To |
| 2482 |
/// decide whether the planar graph is three colorable is |
|
| 2483 |
/// NP-complete. |
|
| 2494 |
/// decide whether a planar graph is three colorable is NP-complete. |
|
| 2484 | 2495 |
/// |
| 2485 | 2496 |
/// This class contains member functions for calculate colorings |
| 2486 | 2497 |
/// with five and six colors. The six coloring algorithm is a simple |
| 2487 | 2498 |
/// greedy coloring on the backward minimum outgoing order of nodes. |
| 2488 |
/// This order can be computed as in each phase the node with least |
|
| 2489 |
/// outgoing arcs to unprocessed nodes is chosen. This order |
|
| 2499 |
/// This order can be computed by selecting the node with least |
|
| 2500 |
/// outgoing arcs to unprocessed nodes in each phase. This order |
|
| 2490 | 2501 |
/// guarantees that when a node is chosen for coloring it has at |
| 2491 | 2502 |
/// most five already colored adjacents. The five coloring algorithm |
| 2492 | 2503 |
/// use the same method, but if the greedy approach fails to color |
| 2493 | 2504 |
/// with five colors, i.e. the node has five already different |
| 2494 | 2505 |
/// colored neighbours, it swaps the colors in one of the connected |
| 2495 | 2506 |
/// two colored sets with the Kempe recoloring method. |
| 2496 | 2507 |
template <typename Graph> |
| 2497 | 2508 |
class PlanarColoring {
|
| 2498 | 2509 |
public: |
| 2499 | 2510 |
|
| 2500 | 2511 |
TEMPLATE_GRAPH_TYPEDEFS(Graph); |
| 2501 | 2512 |
|
| 2502 |
/// \brief The map type for |
|
| 2513 |
/// \brief The map type for storing color indices |
|
| 2503 | 2514 |
typedef typename Graph::template NodeMap<int> IndexMap; |
| 2504 |
/// \brief The map type for |
|
| 2515 |
/// \brief The map type for storing colors |
|
| 2516 |
/// |
|
| 2517 |
/// The map type for storing colors. |
|
| 2518 |
/// \see Palette, Color |
|
| 2505 | 2519 |
typedef ComposeMap<Palette, IndexMap> ColorMap; |
| 2506 | 2520 |
|
| 2507 | 2521 |
/// \brief Constructor |
| 2508 | 2522 |
/// |
| 2509 |
/// Constructor |
|
| 2510 |
/// \pre The graph should be simple, i.e. loop and parallel arc free. |
|
| 2523 |
/// Constructor. |
|
| 2524 |
/// \pre The graph must be simple, i.e. it should not |
|
| 2525 |
/// contain parallel or loop arcs. |
|
| 2511 | 2526 |
PlanarColoring(const Graph& graph) |
| 2512 | 2527 |
: _graph(graph), _color_map(graph), _palette(0) {
|
| 2513 | 2528 |
_palette.add(Color(1,0,0)); |
| 2514 | 2529 |
_palette.add(Color(0,1,0)); |
| 2515 | 2530 |
_palette.add(Color(0,0,1)); |
| 2516 | 2531 |
_palette.add(Color(1,1,0)); |
| 2517 | 2532 |
_palette.add(Color(1,0,1)); |
| 2518 | 2533 |
_palette.add(Color(0,1,1)); |
| 2519 | 2534 |
} |
| 2520 | 2535 |
|
| 2521 |
/// \brief |
|
| 2536 |
/// \brief Return the node map of color indices |
|
| 2522 | 2537 |
/// |
| 2523 |
/// Returns the \e NodeMap of color indexes. The values are in the |
|
| 2524 |
/// range \c [0..4] or \c [0..5] according to the coloring method. |
|
| 2538 |
/// This function returns the node map of color indices. The values are |
|
| 2539 |
/// in the range \c [0..4] or \c [0..5] according to the coloring method. |
|
| 2525 | 2540 |
IndexMap colorIndexMap() const {
|
| 2526 | 2541 |
return _color_map; |
| 2527 | 2542 |
} |
| 2528 | 2543 |
|
| 2529 |
/// \brief |
|
| 2544 |
/// \brief Return the node map of colors |
|
| 2530 | 2545 |
/// |
| 2531 |
/// Returns the \e NodeMap of colors. The values are five or six |
|
| 2532 |
/// distinct \ref lemon::Color "colors". |
|
| 2546 |
/// This function returns the node map of colors. The values are among |
|
| 2547 |
/// five or six distinct \ref lemon::Color "colors". |
|
| 2533 | 2548 |
ColorMap colorMap() const {
|
| 2534 | 2549 |
return composeMap(_palette, _color_map); |
| 2535 | 2550 |
} |
| 2536 | 2551 |
|
| 2537 |
/// \brief |
|
| 2552 |
/// \brief Return the color index of the node |
|
| 2538 | 2553 |
/// |
| 2539 |
/// Returns the color index of the node. The values are in the |
|
| 2540 |
/// range \c [0..4] or \c [0..5] according to the coloring method. |
|
| 2554 |
/// This function returns the color index of the given node. The value is |
|
| 2555 |
/// in the range \c [0..4] or \c [0..5] according to the coloring method. |
|
| 2541 | 2556 |
int colorIndex(const Node& node) const {
|
| 2542 | 2557 |
return _color_map[node]; |
| 2543 | 2558 |
} |
| 2544 | 2559 |
|
| 2545 |
/// \brief |
|
| 2560 |
/// \brief Return the color of the node |
|
| 2546 | 2561 |
/// |
| 2547 |
/// Returns the color of the node. The values are five or six |
|
| 2548 |
/// distinct \ref lemon::Color "colors". |
|
| 2562 |
/// This function returns the color of the given node. The value is among |
|
| 2563 |
/// five or six distinct \ref lemon::Color "colors". |
|
| 2549 | 2564 |
Color color(const Node& node) const {
|
| 2550 | 2565 |
return _palette[_color_map[node]]; |
| 2551 | 2566 |
} |
| 2552 | 2567 |
|
| 2553 | 2568 |
|
| 2554 |
/// \brief |
|
| 2569 |
/// \brief Calculate a coloring with at most six colors |
|
| 2555 | 2570 |
/// |
| 2556 | 2571 |
/// This function calculates a coloring with at most six colors. The time |
| 2557 | 2572 |
/// complexity of this variant is linear in the size of the graph. |
| 2558 |
/// \return %True when the algorithm could color the graph with six color. |
|
| 2559 |
/// If the algorithm fails, then the graph could not be planar. |
|
| 2560 |
/// \note This function can return true if the graph is not |
|
| 2561 |
/// planar but it can be colored with 6 colors. |
|
| 2573 |
/// \return \c true if the algorithm could color the graph with six colors. |
|
| 2574 |
/// If the algorithm fails, then the graph is not planar. |
|
| 2575 |
/// \note This function can return \c true if the graph is not |
|
| 2576 |
/// planar, but it can be colored with at most six colors. |
|
| 2562 | 2577 |
bool runSixColoring() {
|
| 2563 | 2578 |
|
| 2564 | 2579 |
typename Graph::template NodeMap<int> heap_index(_graph, -1); |
| 2565 | 2580 |
BucketHeap<typename Graph::template NodeMap<int> > heap(heap_index); |
| 2566 | 2581 |
|
| 2567 | 2582 |
for (NodeIt n(_graph); n != INVALID; ++n) {
|
| 2568 | 2583 |
_color_map[n] = -2; |
| 2569 | 2584 |
heap.push(n, countOutArcs(_graph, n)); |
| 2570 | 2585 |
} |
| 2571 | 2586 |
|
| 2572 | 2587 |
std::vector<Node> order; |
| 2573 | 2588 |
|
| 2574 | 2589 |
while (!heap.empty()) {
|
| 2575 | 2590 |
Node n = heap.top(); |
| 2576 | 2591 |
heap.pop(); |
| 2577 | 2592 |
_color_map[n] = -1; |
| 2578 | 2593 |
order.push_back(n); |
| 2579 | 2594 |
for (OutArcIt e(_graph, n); e != INVALID; ++e) {
|
| 2580 | 2595 |
Node t = _graph.runningNode(e); |
| 2581 | 2596 |
if (_color_map[t] == -2) {
|
| 2582 | 2597 |
heap.decrease(t, heap[t] - 1); |
| 2583 | 2598 |
} |
| 2584 | 2599 |
} |
| 2585 | 2600 |
} |
| ... | ... |
@@ -2639,99 +2654,102 @@ |
| 2639 | 2654 |
void kempeRecoloring(const Node& node, const EmbeddingMap& embedding) {
|
| 2640 | 2655 |
std::vector<Node> nodes; |
| 2641 | 2656 |
nodes.reserve(4); |
| 2642 | 2657 |
|
| 2643 | 2658 |
for (Arc e = OutArcIt(_graph, node); e != INVALID; e = embedding[e]) {
|
| 2644 | 2659 |
Node t = _graph.target(e); |
| 2645 | 2660 |
if (_color_map[t] != -1) {
|
| 2646 | 2661 |
nodes.push_back(t); |
| 2647 | 2662 |
if (nodes.size() == 4) break; |
| 2648 | 2663 |
} |
| 2649 | 2664 |
} |
| 2650 | 2665 |
|
| 2651 | 2666 |
int color = _color_map[nodes[0]]; |
| 2652 | 2667 |
if (recolor(nodes[0], nodes[2])) {
|
| 2653 | 2668 |
_color_map[node] = color; |
| 2654 | 2669 |
} else {
|
| 2655 | 2670 |
color = _color_map[nodes[1]]; |
| 2656 | 2671 |
recolor(nodes[1], nodes[3]); |
| 2657 | 2672 |
_color_map[node] = color; |
| 2658 | 2673 |
} |
| 2659 | 2674 |
} |
| 2660 | 2675 |
|
| 2661 | 2676 |
public: |
| 2662 | 2677 |
|
| 2663 |
/// \brief |
|
| 2678 |
/// \brief Calculate a coloring with at most five colors |
|
| 2664 | 2679 |
/// |
| 2665 | 2680 |
/// This function calculates a coloring with at most five |
| 2666 | 2681 |
/// colors. The worst case time complexity of this variant is |
| 2667 | 2682 |
/// quadratic in the size of the graph. |
| 2683 |
/// \param embedding This map should contain a valid combinatorical |
|
| 2684 |
/// embedding, i.e. a valid cyclic order of the arcs. |
|
| 2685 |
/// It can be computed using PlanarEmbedding. |
|
| 2668 | 2686 |
template <typename EmbeddingMap> |
| 2669 | 2687 |
void runFiveColoring(const EmbeddingMap& embedding) {
|
| 2670 | 2688 |
|
| 2671 | 2689 |
typename Graph::template NodeMap<int> heap_index(_graph, -1); |
| 2672 | 2690 |
BucketHeap<typename Graph::template NodeMap<int> > heap(heap_index); |
| 2673 | 2691 |
|
| 2674 | 2692 |
for (NodeIt n(_graph); n != INVALID; ++n) {
|
| 2675 | 2693 |
_color_map[n] = -2; |
| 2676 | 2694 |
heap.push(n, countOutArcs(_graph, n)); |
| 2677 | 2695 |
} |
| 2678 | 2696 |
|
| 2679 | 2697 |
std::vector<Node> order; |
| 2680 | 2698 |
|
| 2681 | 2699 |
while (!heap.empty()) {
|
| 2682 | 2700 |
Node n = heap.top(); |
| 2683 | 2701 |
heap.pop(); |
| 2684 | 2702 |
_color_map[n] = -1; |
| 2685 | 2703 |
order.push_back(n); |
| 2686 | 2704 |
for (OutArcIt e(_graph, n); e != INVALID; ++e) {
|
| 2687 | 2705 |
Node t = _graph.runningNode(e); |
| 2688 | 2706 |
if (_color_map[t] == -2) {
|
| 2689 | 2707 |
heap.decrease(t, heap[t] - 1); |
| 2690 | 2708 |
} |
| 2691 | 2709 |
} |
| 2692 | 2710 |
} |
| 2693 | 2711 |
|
| 2694 | 2712 |
for (int i = order.size() - 1; i >= 0; --i) {
|
| 2695 | 2713 |
std::vector<bool> forbidden(5, false); |
| 2696 | 2714 |
for (OutArcIt e(_graph, order[i]); e != INVALID; ++e) {
|
| 2697 | 2715 |
Node t = _graph.runningNode(e); |
| 2698 | 2716 |
if (_color_map[t] != -1) {
|
| 2699 | 2717 |
forbidden[_color_map[t]] = true; |
| 2700 | 2718 |
} |
| 2701 | 2719 |
} |
| 2702 | 2720 |
for (int k = 0; k < 5; ++k) {
|
| 2703 | 2721 |
if (!forbidden[k]) {
|
| 2704 | 2722 |
_color_map[order[i]] = k; |
| 2705 | 2723 |
break; |
| 2706 | 2724 |
} |
| 2707 | 2725 |
} |
| 2708 | 2726 |
if (_color_map[order[i]] == -1) {
|
| 2709 | 2727 |
kempeRecoloring(order[i], embedding); |
| 2710 | 2728 |
} |
| 2711 | 2729 |
} |
| 2712 | 2730 |
} |
| 2713 | 2731 |
|
| 2714 |
/// \brief |
|
| 2732 |
/// \brief Calculate a coloring with at most five colors |
|
| 2715 | 2733 |
/// |
| 2716 | 2734 |
/// This function calculates a coloring with at most five |
| 2717 | 2735 |
/// colors. The worst case time complexity of this variant is |
| 2718 | 2736 |
/// quadratic in the size of the graph. |
| 2719 |
/// \return |
|
| 2737 |
/// \return \c true if the graph is planar. |
|
| 2720 | 2738 |
bool runFiveColoring() {
|
| 2721 | 2739 |
PlanarEmbedding<Graph> pe(_graph); |
| 2722 | 2740 |
if (!pe.run()) return false; |
| 2723 | 2741 |
|
| 2724 | 2742 |
runFiveColoring(pe.embeddingMap()); |
| 2725 | 2743 |
return true; |
| 2726 | 2744 |
} |
| 2727 | 2745 |
|
| 2728 | 2746 |
private: |
| 2729 | 2747 |
|
| 2730 | 2748 |
const Graph& _graph; |
| 2731 | 2749 |
IndexMap _color_map; |
| 2732 | 2750 |
Palette _palette; |
| 2733 | 2751 |
}; |
| 2734 | 2752 |
|
| 2735 | 2753 |
} |
| 2736 | 2754 |
|
| 2737 | 2755 |
#endif |
| ... | ... |
@@ -98,48 +98,53 @@ |
| 98 | 98 |
|
| 99 | 99 |
/// \ingroup max_flow |
| 100 | 100 |
/// |
| 101 | 101 |
/// \brief %Preflow algorithm class. |
| 102 | 102 |
/// |
| 103 | 103 |
/// This class provides an implementation of Goldberg-Tarjan's \e preflow |
| 104 | 104 |
/// \e push-relabel algorithm producing a \ref max_flow |
| 105 | 105 |
/// "flow of maximum value" in a digraph \ref clrs01algorithms, |
| 106 | 106 |
/// \ref amo93networkflows, \ref goldberg88newapproach. |
| 107 | 107 |
/// The preflow algorithms are the fastest known maximum |
| 108 | 108 |
/// flow algorithms. The current implementation uses a mixture of the |
| 109 | 109 |
/// \e "highest label" and the \e "bound decrease" heuristics. |
| 110 | 110 |
/// The worst case time complexity of the algorithm is \f$O(n^2\sqrt{e})\f$.
|
| 111 | 111 |
/// |
| 112 | 112 |
/// The algorithm consists of two phases. After the first phase |
| 113 | 113 |
/// the maximum flow value and the minimum cut is obtained. The |
| 114 | 114 |
/// second phase constructs a feasible maximum flow on each arc. |
| 115 | 115 |
/// |
| 116 | 116 |
/// \warning This implementation cannot handle infinite or very large |
| 117 | 117 |
/// capacities (e.g. the maximum value of \c CAP::Value). |
| 118 | 118 |
/// |
| 119 | 119 |
/// \tparam GR The type of the digraph the algorithm runs on. |
| 120 | 120 |
/// \tparam CAP The type of the capacity map. The default map |
| 121 | 121 |
/// type is \ref concepts::Digraph::ArcMap "GR::ArcMap<int>". |
| 122 |
/// \tparam TR The traits class that defines various types used by the |
|
| 123 |
/// algorithm. By default, it is \ref PreflowDefaultTraits |
|
| 124 |
/// "PreflowDefaultTraits<GR, CAP>". |
|
| 125 |
/// In most cases, this parameter should not be set directly, |
|
| 126 |
/// consider to use the named template parameters instead. |
|
| 122 | 127 |
#ifdef DOXYGEN |
| 123 | 128 |
template <typename GR, typename CAP, typename TR> |
| 124 | 129 |
#else |
| 125 | 130 |
template <typename GR, |
| 126 | 131 |
typename CAP = typename GR::template ArcMap<int>, |
| 127 | 132 |
typename TR = PreflowDefaultTraits<GR, CAP> > |
| 128 | 133 |
#endif |
| 129 | 134 |
class Preflow {
|
| 130 | 135 |
public: |
| 131 | 136 |
|
| 132 | 137 |
///The \ref PreflowDefaultTraits "traits class" of the algorithm. |
| 133 | 138 |
typedef TR Traits; |
| 134 | 139 |
///The type of the digraph the algorithm runs on. |
| 135 | 140 |
typedef typename Traits::Digraph Digraph; |
| 136 | 141 |
///The type of the capacity map. |
| 137 | 142 |
typedef typename Traits::CapacityMap CapacityMap; |
| 138 | 143 |
///The type of the flow values. |
| 139 | 144 |
typedef typename Traits::Value Value; |
| 140 | 145 |
|
| 141 | 146 |
///The type of the flow map. |
| 142 | 147 |
typedef typename Traits::FlowMap FlowMap; |
| 143 | 148 |
///The type of the elevator. |
| 144 | 149 |
typedef typename Traits::Elevator Elevator; |
| 145 | 150 |
///The type of the tolerance. |
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