COIN-OR::LEMON - Graph Library

Changeset 418:ad483acf1654 in lemon-1.2


Ignore:
Timestamp:
12/02/08 16:33:22 (11 years ago)
Author:
Alpar Juttner <alpar@…>
Branch:
default
Children:
419:9afe81e4c543, 420:6a2a33ad261b, 430:09e416d35896, 446:d369e885d196, 490:7f8560cb9d65
Parents:
413:d8b87e9b90c3 (diff), 417:6ff53afe98b5 (diff)
Note: this is a merge changeset, the changes displayed below correspond to the merge itself.
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public
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Merge

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6 edited

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  • doc/groups.dox

    r406 r418  
    6060
    6161<b>See also:</b> \ref graph_concepts "Graph Structure Concepts".
     62*/
     63
     64/**
     65@defgroup graph_adaptors Adaptor Classes for graphs
     66@ingroup graphs
     67\brief This group contains several adaptor classes for digraphs and graphs
     68
     69The main parts of LEMON are the different graph structures, generic
     70graph algorithms, graph concepts which couple these, and graph
     71adaptors. While the previous notions are more or less clear, the
     72latter one needs further explanation. Graph adaptors are graph classes
     73which serve for considering graph structures in different ways.
     74
     75A short example makes this much clearer.  Suppose that we have an
     76instance \c g of a directed graph type say ListDigraph and an algorithm
     77\code
     78template <typename Digraph>
     79int algorithm(const Digraph&);
     80\endcode
     81is needed to run on the reverse oriented graph.  It may be expensive
     82(in time or in memory usage) to copy \c g with the reversed
     83arcs.  In this case, an adaptor class is used, which (according
     84to LEMON digraph concepts) works as a digraph.  The adaptor uses the
     85original digraph structure and digraph operations when methods of the
     86reversed oriented graph are called.  This means that the adaptor have
     87minor memory usage, and do not perform sophisticated algorithmic
     88actions.  The purpose of it is to give a tool for the cases when a
     89graph have to be used in a specific alteration.  If this alteration is
     90obtained by a usual construction like filtering the arc-set or
     91considering a new orientation, then an adaptor is worthwhile to use.
     92To come back to the reverse oriented graph, in this situation
     93\code
     94template<typename Digraph> class ReverseDigraph;
     95\endcode
     96template class can be used. The code looks as follows
     97\code
     98ListDigraph g;
     99ReverseDigraph<ListGraph> rg(g);
     100int result = algorithm(rg);
     101\endcode
     102After running the algorithm, the original graph \c g is untouched.
     103This techniques gives rise to an elegant code, and based on stable
     104graph adaptors, complex algorithms can be implemented easily.
     105
     106In flow, circulation and bipartite matching problems, the residual
     107graph is of particular importance. Combining an adaptor implementing
     108this, shortest path algorithms and minimum mean cycle algorithms,
     109a range of weighted and cardinality optimization algorithms can be
     110obtained. For other examples, the interested user is referred to the
     111detailed documentation of particular adaptors.
     112
     113The behavior of graph adaptors can be very different. Some of them keep
     114capabilities of the original graph while in other cases this would be
     115meaningless. This means that the concepts that they are models of depend
     116on the graph adaptor, and the wrapped graph(s).
     117If an arc of \c rg is deleted, this is carried out by deleting the
     118corresponding arc of \c g, thus the adaptor modifies the original graph.
     119
     120But for a residual graph, this operation has no sense.
     121Let us stand one more example here to simplify your work.
     122RevGraphAdaptor has constructor
     123\code
     124ReverseDigraph(Digraph& digraph);
     125\endcode
     126This means that in a situation, when a <tt>const ListDigraph&</tt>
     127reference to a graph is given, then it have to be instantiated with
     128<tt>Digraph=const ListDigraph</tt>.
     129\code
     130int algorithm1(const ListDigraph& g) {
     131  RevGraphAdaptor<const ListDigraph> rg(g);
     132  return algorithm2(rg);
     133}
     134\endcode
    62135*/
    63136
  • doc/groups.dox

    r416 r418  
    1616 *
    1717 */
     18
     19namespace lemon {
    1820
    1921/**
     
    162164
    163165This group describes maps that are specifically designed to assign
    164 values to the nodes and arcs of graphs.
     166values to the nodes and arcs/edges of graphs.
     167
     168If you are looking for the standard graph maps (\c NodeMap, \c ArcMap,
     169\c EdgeMap), see the \ref graph_concepts "Graph Structure Concepts".
    165170*/
    166171
     
    173178maps from other maps.
    174179
    175 Most of them are \ref lemon::concepts::ReadMap "read-only maps".
     180Most of them are \ref concepts::ReadMap "read-only maps".
    176181They can make arithmetic and logical operations between one or two maps
    177182(negation, shifting, addition, multiplication, logical 'and', 'or',
     
    275280\brief Common graph search algorithms.
    276281
    277 This group describes the common graph search algorithms like
    278 Breadth-First Search (BFS) and Depth-First Search (DFS).
     282This group describes the common graph search algorithms, namely
     283\e breadth-first \e search (BFS) and \e depth-first \e search (DFS).
    279284*/
    280285
     
    284289\brief Algorithms for finding shortest paths.
    285290
    286 This group describes the algorithms for finding shortest paths in graphs.
     291This group describes the algorithms for finding shortest paths in digraphs.
     292
     293 - \ref Dijkstra algorithm for finding shortest paths from a source node
     294   when all arc lengths are non-negative.
     295 - \ref BellmanFord "Bellman-Ford" algorithm for finding shortest paths
     296   from a source node when arc lenghts can be either positive or negative,
     297   but the digraph should not contain directed cycles with negative total
     298   length.
     299 - \ref FloydWarshall "Floyd-Warshall" and \ref Johnson "Johnson" algorithms
     300   for solving the \e all-pairs \e shortest \e paths \e problem when arc
     301   lenghts can be either positive or negative, but the digraph should
     302   not contain directed cycles with negative total length.
     303 - \ref Suurballe A successive shortest path algorithm for finding
     304   arc-disjoint paths between two nodes having minimum total length.
    287305*/
    288306
     
    295313feasible circulations.
    296314
    297 The maximum flow problem is to find a flow between a single source and
    298 a single target that is maximum. Formally, there is a \f$G=(V,A)\f$
    299 directed graph, an \f$c_a:A\rightarrow\mathbf{R}^+_0\f$ capacity
    300 function and given \f$s, t \in V\f$ source and target node. The
    301 maximum flow is the \f$f_a\f$ solution of the next optimization problem:
    302 
    303 \f[ 0 \le f_a \le c_a \f]
    304 \f[ \sum_{v\in\delta^{-}(u)}f_{vu}=\sum_{v\in\delta^{+}(u)}f_{uv}
    305 \qquad \forall u \in V \setminus \{s,t\}\f]
    306 \f[ \max \sum_{v\in\delta^{+}(s)}f_{uv} - \sum_{v\in\delta^{-}(s)}f_{vu}\f]
     315The \e maximum \e flow \e problem is to find a flow of maximum value between
     316a single source and a single target. Formally, there is a \f$G=(V,A)\f$
     317digraph, a \f$cap:A\rightarrow\mathbf{R}^+_0\f$ capacity function and
     318\f$s, t \in V\f$ source and target nodes.
     319A maximum flow is an \f$f:A\rightarrow\mathbf{R}^+_0\f$ solution of the
     320following optimization problem.
     321
     322\f[ \max\sum_{a\in\delta_{out}(s)}f(a) - \sum_{a\in\delta_{in}(s)}f(a) \f]
     323\f[ \sum_{a\in\delta_{out}(v)} f(a) = \sum_{a\in\delta_{in}(v)} f(a)
     324    \qquad \forall v\in V\setminus\{s,t\} \f]
     325\f[ 0 \leq f(a) \leq cap(a) \qquad \forall a\in A \f]
    307326
    308327LEMON contains several algorithms for solving maximum flow problems:
    309 - \ref lemon::EdmondsKarp "Edmonds-Karp"
    310 - \ref lemon::Preflow "Goldberg's Preflow algorithm"
    311 - \ref lemon::DinitzSleatorTarjan "Dinitz's blocking flow algorithm with dynamic trees"
    312 - \ref lemon::GoldbergTarjan "Preflow algorithm with dynamic trees"
    313 
    314 In most cases the \ref lemon::Preflow "Preflow" algorithm provides the
    315 fastest method to compute the maximum flow. All impelementations
    316 provides functions to query the minimum cut, which is the dual linear
    317 programming problem of the maximum flow.
     328- \ref EdmondsKarp Edmonds-Karp algorithm.
     329- \ref Preflow Goldberg-Tarjan's preflow push-relabel algorithm.
     330- \ref DinitzSleatorTarjan Dinitz's blocking flow algorithm with dynamic trees.
     331- \ref GoldbergTarjan Preflow push-relabel algorithm with dynamic trees.
     332
     333In most cases the \ref Preflow "Preflow" algorithm provides the
     334fastest method for computing a maximum flow. All implementations
     335provides functions to also query the minimum cut, which is the dual
     336problem of the maximum flow.
    318337*/
    319338
     
    326345This group describes the algorithms for finding minimum cost flows and
    327346circulations.
     347
     348The \e minimum \e cost \e flow \e problem is to find a feasible flow of
     349minimum total cost from a set of supply nodes to a set of demand nodes
     350in a network with capacity constraints and arc costs.
     351Formally, let \f$G=(V,A)\f$ be a digraph,
     352\f$lower, upper: A\rightarrow\mathbf{Z}^+_0\f$ denote the lower and
     353upper bounds for the flow values on the arcs,
     354\f$cost: A\rightarrow\mathbf{Z}^+_0\f$ denotes the cost per unit flow
     355on the arcs, and
     356\f$supply: V\rightarrow\mathbf{Z}\f$ denotes the supply/demand values
     357of the nodes.
     358A minimum cost flow is an \f$f:A\rightarrow\mathbf{R}^+_0\f$ solution of
     359the following optimization problem.
     360
     361\f[ \min\sum_{a\in A} f(a) cost(a) \f]
     362\f[ \sum_{a\in\delta_{out}(v)} f(a) - \sum_{a\in\delta_{in}(v)} f(a) =
     363    supply(v) \qquad \forall v\in V \f]
     364\f[ lower(a) \leq f(a) \leq upper(a) \qquad \forall a\in A \f]
     365
     366LEMON contains several algorithms for solving minimum cost flow problems:
     367 - \ref CycleCanceling Cycle-canceling algorithms.
     368 - \ref CapacityScaling Successive shortest path algorithm with optional
     369   capacity scaling.
     370 - \ref CostScaling Push-relabel and augment-relabel algorithms based on
     371   cost scaling.
     372 - \ref NetworkSimplex Primal network simplex algorithm with various
     373   pivot strategies.
    328374*/
    329375
     
    336382This group describes the algorithms for finding minimum cut in graphs.
    337383
    338 The minimum cut problem is to find a non-empty and non-complete
    339 \f$X\f$ subset of the vertices with minimum overall capacity on
    340 outgoing arcs. Formally, there is \f$G=(V,A)\f$ directed graph, an
    341 \f$c_a:A\rightarrow\mathbf{R}^+_0\f$ capacity function. The minimum
     384The \e minimum \e cut \e problem is to find a non-empty and non-complete
     385\f$X\f$ subset of the nodes with minimum overall capacity on
     386outgoing arcs. Formally, there is a \f$G=(V,A)\f$ digraph, a
     387\f$cap: A\rightarrow\mathbf{R}^+_0\f$ capacity function. The minimum
    342388cut is the \f$X\f$ solution of the next optimization problem:
    343389
    344390\f[ \min_{X \subset V, X\not\in \{\emptyset, V\}}
    345 \sum_{uv\in A, u\in X, v\not\in X}c_{uv}\f]
     391    \sum_{uv\in A, u\in X, v\not\in X}cap(uv) \f]
    346392
    347393LEMON contains several algorithms related to minimum cut problems:
    348394
    349 - \ref lemon::HaoOrlin "Hao-Orlin algorithm" to calculate minimum cut
    350   in directed graphs
    351 - \ref lemon::NagamochiIbaraki "Nagamochi-Ibaraki algorithm" to
    352   calculate minimum cut in undirected graphs
    353 - \ref lemon::GomoryHuTree "Gomory-Hu tree computation" to calculate all
    354   pairs minimum cut in undirected graphs
     395- \ref HaoOrlin "Hao-Orlin algorithm" for calculating minimum cut
     396  in directed graphs.
     397- \ref NagamochiIbaraki "Nagamochi-Ibaraki algorithm" for
     398  calculating minimum cut in undirected graphs.
     399- \ref GomoryHuTree "Gomory-Hu tree computation" for calculating
     400  all-pairs minimum cut in undirected graphs.
    355401
    356402If you want to find minimum cut just between two distinict nodes,
    357 please see the \ref max_flow "Maximum Flow page".
     403see the \ref max_flow "maximum flow problem".
    358404*/
    359405
     
    394440graphs.  The matching problems in bipartite graphs are generally
    395441easier than in general graphs. The goal of the matching optimization
    396 can be the finding maximum cardinality, maximum weight or minimum cost
     442can be finding maximum cardinality, maximum weight or minimum cost
    397443matching. The search can be constrained to find perfect or
    398444maximum cardinality matching.
    399445
    400 LEMON contains the next algorithms:
    401 - \ref lemon::MaxBipartiteMatching "MaxBipartiteMatching" Hopcroft-Karp
    402   augmenting path algorithm for calculate maximum cardinality matching in
    403   bipartite graphs
    404 - \ref lemon::PrBipartiteMatching "PrBipartiteMatching" Push-Relabel
    405   algorithm for calculate maximum cardinality matching in bipartite graphs
    406 - \ref lemon::MaxWeightedBipartiteMatching "MaxWeightedBipartiteMatching"
    407   Successive shortest path algorithm for calculate maximum weighted matching
    408   and maximum weighted bipartite matching in bipartite graph
    409 - \ref lemon::MinCostMaxBipartiteMatching "MinCostMaxBipartiteMatching"
    410   Successive shortest path algorithm for calculate minimum cost maximum
    411   matching in bipartite graph
    412 - \ref lemon::MaxMatching "MaxMatching" Edmond's blossom shrinking algorithm
    413   for calculate maximum cardinality matching in general graph
    414 - \ref lemon::MaxWeightedMatching "MaxWeightedMatching" Edmond's blossom
    415   shrinking algorithm for calculate maximum weighted matching in general
    416   graph
    417 - \ref lemon::MaxWeightedPerfectMatching "MaxWeightedPerfectMatching"
    418   Edmond's blossom shrinking algorithm for calculate maximum weighted
    419   perfect matching in general graph
     446The matching algorithms implemented in LEMON:
     447- \ref MaxBipartiteMatching Hopcroft-Karp augmenting path algorithm
     448  for calculating maximum cardinality matching in bipartite graphs.
     449- \ref PrBipartiteMatching Push-relabel algorithm
     450  for calculating maximum cardinality matching in bipartite graphs.
     451- \ref MaxWeightedBipartiteMatching
     452  Successive shortest path algorithm for calculating maximum weighted
     453  matching and maximum weighted bipartite matching in bipartite graphs.
     454- \ref MinCostMaxBipartiteMatching
     455  Successive shortest path algorithm for calculating minimum cost maximum
     456  matching in bipartite graphs.
     457- \ref MaxMatching Edmond's blossom shrinking algorithm for calculating
     458  maximum cardinality matching in general graphs.
     459- \ref MaxWeightedMatching Edmond's blossom shrinking algorithm for calculating
     460  maximum weighted matching in general graphs.
     461- \ref MaxWeightedPerfectMatching
     462  Edmond's blossom shrinking algorithm for calculating maximum weighted
     463  perfect matching in general graphs.
    420464
    421465\image html bipartite_matching.png
     
    429473
    430474This group describes the algorithms for finding a minimum cost spanning
    431 tree in a graph
     475tree in a graph.
    432476*/
    433477
     
    620664\anchor demoprograms
    621665
    622 @defgroup demos Demo programs
     666@defgroup demos Demo Programs
    623667
    624668Some demo programs are listed here. Their full source codes can be found in
     
    630674
    631675/**
    632 @defgroup tools Standalone utility applications
     676@defgroup tools Standalone Utility Applications
    633677
    634678Some utility applications are listed here.
     
    638682*/
    639683
     684}
  • lemon/Makefile.am

    r409 r418  
    1717
    1818lemon_HEADERS += \
     19        lemon/adaptors.h \
    1920        lemon/arg_parser.h \
    2021        lemon/assert.h \
     
    6162        lemon/bits/default_map.h \
    6263        lemon/bits/enable_if.h \
     64        lemon/bits/graph_adaptor_extender.h \
    6365        lemon/bits/graph_extender.h \
    6466        lemon/bits/map_extender.h \
    6567        lemon/bits/path_dump.h \
    6668        lemon/bits/traits.h \
     69        lemon/bits/variant.h \
    6770        lemon/bits/vector_map.h
    6871
  • lemon/Makefile.am

    r416 r418  
    2222        lemon/bfs.h \
    2323        lemon/bin_heap.h \
     24        lemon/circulation.h \
    2425        lemon/color.h \
    2526        lemon/concept_check.h \
     
    3738        lemon/hypercube_graph.h \
    3839        lemon/kruskal.h \
     40        lemon/hao_orlin.h \
    3941        lemon/lgf_reader.h \
    4042        lemon/lgf_writer.h \
  • test/Makefile.am

    r410 r418  
    1717        test/dim_test \
    1818        test/error_test \
     19        test/graph_adaptor_test \
    1920        test/graph_copy_test \
    2021        test/graph_test \
     
    4546test_dim_test_SOURCES = test/dim_test.cc
    4647test_error_test_SOURCES = test/error_test.cc
     48test_graph_adaptor_test_SOURCES = test/graph_adaptor_test.cc
    4749test_graph_copy_test_SOURCES = test/graph_copy_test.cc
    4850test_graph_test_SOURCES = test/graph_test.cc
  • test/Makefile.am

    r414 r418  
    1010check_PROGRAMS += \
    1111        test/bfs_test \
     12        test/circulation_test \
    1213        test/counter_test \
    1314        test/dfs_test \
     
    2223        test/heap_test \
    2324        test/kruskal_test \
     25        test/hao_orlin_test \
    2426        test/maps_test \
    2527        test/max_matching_test \
     
    3739
    3840test_bfs_test_SOURCES = test/bfs_test.cc
     41test_circulation_test_SOURCES = test/circulation_test.cc
    3942test_counter_test_SOURCES = test/counter_test.cc
    4043test_dfs_test_SOURCES = test/dfs_test.cc
     
    4952test_heap_test_SOURCES = test/heap_test.cc
    5053test_kruskal_test_SOURCES = test/kruskal_test.cc
     54test_hao_orlin_test_SOURCES = test/hao_orlin_test.cc
    5155test_maps_test_SOURCES = test/maps_test.cc
    5256test_max_matching_test_SOURCES = test/max_matching_test.cc
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