1.1 --- a/lemon/suurballe.h Sat Apr 25 18:25:59 2009 +0200
1.2 +++ b/lemon/suurballe.h Sat Apr 25 02:12:41 2009 +0200
1.3 @@ -25,6 +25,7 @@
1.4 /// nodes having minimum total length.
1.5
1.6 #include <vector>
1.7 +#include <limits>
1.8 #include <lemon/bin_heap.h>
1.9 #include <lemon/path.h>
1.10 #include <lemon/list_graph.h>
1.11 @@ -42,22 +43,26 @@
1.12 /// finding arc-disjoint paths having minimum total length (cost)
1.13 /// from a given source node to a given target node in a digraph.
1.14 ///
1.15 - /// In fact, this implementation is the specialization of the
1.16 - /// \ref CapacityScaling "successive shortest path" algorithm.
1.17 + /// Note that this problem is a special case of the \ref min_cost_flow
1.18 + /// "minimum cost flow problem". This implementation is actually an
1.19 + /// efficient specialized version of the \ref CapacityScaling
1.20 + /// "Successive Shortest Path" algorithm directly for this problem.
1.21 + /// Therefore this class provides query functions for flow values and
1.22 + /// node potentials (the dual solution) just like the minimum cost flow
1.23 + /// algorithms.
1.24 ///
1.25 /// \tparam GR The digraph type the algorithm runs on.
1.26 - /// The default value is \c ListDigraph.
1.27 - /// \tparam LEN The type of the length (cost) map.
1.28 - /// The default value is <tt>Digraph::ArcMap<int></tt>.
1.29 + /// \tparam LEN The type of the length map.
1.30 + /// The default value is <tt>GR::ArcMap<int></tt>.
1.31 ///
1.32 /// \warning Length values should be \e non-negative \e integers.
1.33 ///
1.34 /// \note For finding node-disjoint paths this algorithm can be used
1.35 - /// with \ref SplitNodes.
1.36 + /// along with the \ref SplitNodes adaptor.
1.37 #ifdef DOXYGEN
1.38 template <typename GR, typename LEN>
1.39 #else
1.40 - template < typename GR = ListDigraph,
1.41 + template < typename GR,
1.42 typename LEN = typename GR::template ArcMap<int> >
1.43 #endif
1.44 class Suurballe
1.45 @@ -75,23 +80,28 @@
1.46 typedef LEN LengthMap;
1.47 /// The type of the lengths.
1.48 typedef typename LengthMap::Value Length;
1.49 +#ifdef DOXYGEN
1.50 + /// The type of the flow map.
1.51 + typedef GR::ArcMap<int> FlowMap;
1.52 + /// The type of the potential map.
1.53 + typedef GR::NodeMap<Length> PotentialMap;
1.54 +#else
1.55 /// The type of the flow map.
1.56 typedef typename Digraph::template ArcMap<int> FlowMap;
1.57 /// The type of the potential map.
1.58 typedef typename Digraph::template NodeMap<Length> PotentialMap;
1.59 +#endif
1.60 +
1.61 /// The type of the path structures.
1.62 - typedef SimplePath<Digraph> Path;
1.63 + typedef SimplePath<GR> Path;
1.64
1.65 private:
1.66
1.67 - /// \brief Special implementation of the Dijkstra algorithm
1.68 - /// for finding shortest paths in the residual network.
1.69 - ///
1.70 - /// \ref ResidualDijkstra is a special implementation of the
1.71 - /// \ref Dijkstra algorithm for finding shortest paths in the
1.72 - /// residual network of the digraph with respect to the reduced arc
1.73 - /// lengths and modifying the node potentials according to the
1.74 - /// distance of the nodes.
1.75 + // ResidualDijkstra is a special implementation of the
1.76 + // Dijkstra algorithm for finding shortest paths in the
1.77 + // residual network with respect to the reduced arc lengths
1.78 + // and modifying the node potentials according to the
1.79 + // distance of the nodes.
1.80 class ResidualDijkstra
1.81 {
1.82 typedef typename Digraph::template NodeMap<int> HeapCrossRef;
1.83 @@ -120,14 +130,14 @@
1.84 public:
1.85
1.86 /// Constructor.
1.87 - ResidualDijkstra( const Digraph &digraph,
1.88 + ResidualDijkstra( const Digraph &graph,
1.89 const FlowMap &flow,
1.90 const LengthMap &length,
1.91 PotentialMap &potential,
1.92 PredMap &pred,
1.93 Node s, Node t ) :
1.94 - _graph(digraph), _flow(flow), _length(length), _potential(potential),
1.95 - _dist(digraph), _pred(pred), _s(s), _t(t) {}
1.96 + _graph(graph), _flow(flow), _length(length), _potential(potential),
1.97 + _dist(graph), _pred(pred), _s(s), _t(t) {}
1.98
1.99 /// \brief Run the algorithm. It returns \c true if a path is found
1.100 /// from the source node to the target node.
1.101 @@ -236,16 +246,16 @@
1.102 ///
1.103 /// Constructor.
1.104 ///
1.105 - /// \param digraph The digraph the algorithm runs on.
1.106 + /// \param graph The digraph the algorithm runs on.
1.107 /// \param length The length (cost) values of the arcs.
1.108 - /// \param s The source node.
1.109 - /// \param t The target node.
1.110 - Suurballe( const Digraph &digraph,
1.111 - const LengthMap &length,
1.112 - Node s, Node t ) :
1.113 - _graph(digraph), _length(length), _flow(0), _local_flow(false),
1.114 - _potential(0), _local_potential(false), _source(s), _target(t),
1.115 - _pred(digraph) {}
1.116 + Suurballe( const Digraph &graph,
1.117 + const LengthMap &length ) :
1.118 + _graph(graph), _length(length), _flow(0), _local_flow(false),
1.119 + _potential(0), _local_potential(false), _pred(graph)
1.120 + {
1.121 + LEMON_ASSERT(std::numeric_limits<Length>::is_integer,
1.122 + "The length type of Suurballe must be integer");
1.123 + }
1.124
1.125 /// Destructor.
1.126 ~Suurballe() {
1.127 @@ -257,9 +267,12 @@
1.128 /// \brief Set the flow map.
1.129 ///
1.130 /// This function sets the flow map.
1.131 + /// If it is not used before calling \ref run() or \ref init(),
1.132 + /// an instance will be allocated automatically. The destructor
1.133 + /// deallocates this automatically allocated map, of course.
1.134 ///
1.135 - /// The found flow contains only 0 and 1 values. It is the union of
1.136 - /// the found arc-disjoint paths.
1.137 + /// The found flow contains only 0 and 1 values, since it is the
1.138 + /// union of the found arc-disjoint paths.
1.139 ///
1.140 /// \return <tt>(*this)</tt>
1.141 Suurballe& flowMap(FlowMap &map) {
1.142 @@ -274,9 +287,12 @@
1.143 /// \brief Set the potential map.
1.144 ///
1.145 /// This function sets the potential map.
1.146 + /// If it is not used before calling \ref run() or \ref init(),
1.147 + /// an instance will be allocated automatically. The destructor
1.148 + /// deallocates this automatically allocated map, of course.
1.149 ///
1.150 - /// The potentials provide the dual solution of the underlying
1.151 - /// minimum cost flow problem.
1.152 + /// The node potentials provide the dual solution of the underlying
1.153 + /// \ref min_cost_flow "minimum cost flow problem".
1.154 ///
1.155 /// \return <tt>(*this)</tt>
1.156 Suurballe& potentialMap(PotentialMap &map) {
1.157 @@ -301,22 +317,24 @@
1.158 ///
1.159 /// This function runs the algorithm.
1.160 ///
1.161 + /// \param s The source node.
1.162 + /// \param t The target node.
1.163 /// \param k The number of paths to be found.
1.164 ///
1.165 /// \return \c k if there are at least \c k arc-disjoint paths from
1.166 /// \c s to \c t in the digraph. Otherwise it returns the number of
1.167 /// arc-disjoint paths found.
1.168 ///
1.169 - /// \note Apart from the return value, <tt>s.run(k)</tt> is just a
1.170 - /// shortcut of the following code.
1.171 + /// \note Apart from the return value, <tt>s.run(s, t, k)</tt> is
1.172 + /// just a shortcut of the following code.
1.173 /// \code
1.174 - /// s.init();
1.175 - /// s.findFlow(k);
1.176 + /// s.init(s);
1.177 + /// s.findFlow(t, k);
1.178 /// s.findPaths();
1.179 /// \endcode
1.180 - int run(int k = 2) {
1.181 - init();
1.182 - findFlow(k);
1.183 + int run(const Node& s, const Node& t, int k = 2) {
1.184 + init(s);
1.185 + findFlow(t, k);
1.186 findPaths();
1.187 return _path_num;
1.188 }
1.189 @@ -324,7 +342,11 @@
1.190 /// \brief Initialize the algorithm.
1.191 ///
1.192 /// This function initializes the algorithm.
1.193 - void init() {
1.194 + ///
1.195 + /// \param s The source node.
1.196 + void init(const Node& s) {
1.197 + _source = s;
1.198 +
1.199 // Initialize maps
1.200 if (!_flow) {
1.201 _flow = new FlowMap(_graph);
1.202 @@ -336,25 +358,28 @@
1.203 }
1.204 for (ArcIt e(_graph); e != INVALID; ++e) (*_flow)[e] = 0;
1.205 for (NodeIt n(_graph); n != INVALID; ++n) (*_potential)[n] = 0;
1.206 -
1.207 - _dijkstra = new ResidualDijkstra( _graph, *_flow, _length,
1.208 - *_potential, _pred,
1.209 - _source, _target );
1.210 }
1.211
1.212 - /// \brief Execute the successive shortest path algorithm to find
1.213 - /// an optimal flow.
1.214 + /// \brief Execute the algorithm to find an optimal flow.
1.215 ///
1.216 /// This function executes the successive shortest path algorithm to
1.217 - /// find a minimum cost flow, which is the union of \c k or less
1.218 + /// find a minimum cost flow, which is the union of \c k (or less)
1.219 /// arc-disjoint paths.
1.220 ///
1.221 + /// \param t The target node.
1.222 + /// \param k The number of paths to be found.
1.223 + ///
1.224 /// \return \c k if there are at least \c k arc-disjoint paths from
1.225 - /// \c s to \c t in the digraph. Otherwise it returns the number of
1.226 - /// arc-disjoint paths found.
1.227 + /// the source node to the given node \c t in the digraph.
1.228 + /// Otherwise it returns the number of arc-disjoint paths found.
1.229 ///
1.230 /// \pre \ref init() must be called before using this function.
1.231 - int findFlow(int k = 2) {
1.232 + int findFlow(const Node& t, int k = 2) {
1.233 + _target = t;
1.234 + _dijkstra =
1.235 + new ResidualDijkstra( _graph, *_flow, _length, *_potential, _pred,
1.236 + _source, _target );
1.237 +
1.238 // Find shortest paths
1.239 _path_num = 0;
1.240 while (_path_num < k) {
1.241 @@ -380,13 +405,12 @@
1.242
1.243 /// \brief Compute the paths from the flow.
1.244 ///
1.245 - /// This function computes the paths from the flow.
1.246 + /// This function computes the paths from the found minimum cost flow,
1.247 + /// which is the union of some arc-disjoint paths.
1.248 ///
1.249 /// \pre \ref init() and \ref findFlow() must be called before using
1.250 /// this function.
1.251 void findPaths() {
1.252 - // Create the residual flow map (the union of the paths not found
1.253 - // so far)
1.254 FlowMap res_flow(_graph);
1.255 for(ArcIt a(_graph); a != INVALID; ++a) res_flow[a] = (*_flow)[a];
1.256
1.257 @@ -413,10 +437,37 @@
1.258
1.259 /// @{
1.260
1.261 - /// \brief Return a const reference to the arc map storing the
1.262 + /// \brief Return the total length of the found paths.
1.263 + ///
1.264 + /// This function returns the total length of the found paths, i.e.
1.265 + /// the total cost of the found flow.
1.266 + /// The complexity of the function is O(e).
1.267 + ///
1.268 + /// \pre \ref run() or \ref findFlow() must be called before using
1.269 + /// this function.
1.270 + Length totalLength() const {
1.271 + Length c = 0;
1.272 + for (ArcIt e(_graph); e != INVALID; ++e)
1.273 + c += (*_flow)[e] * _length[e];
1.274 + return c;
1.275 + }
1.276 +
1.277 + /// \brief Return the flow value on the given arc.
1.278 + ///
1.279 + /// This function returns the flow value on the given arc.
1.280 + /// It is \c 1 if the arc is involved in one of the found arc-disjoint
1.281 + /// paths, otherwise it is \c 0.
1.282 + ///
1.283 + /// \pre \ref run() or \ref findFlow() must be called before using
1.284 + /// this function.
1.285 + int flow(const Arc& arc) const {
1.286 + return (*_flow)[arc];
1.287 + }
1.288 +
1.289 + /// \brief Return a const reference to an arc map storing the
1.290 /// found flow.
1.291 ///
1.292 - /// This function returns a const reference to the arc map storing
1.293 + /// This function returns a const reference to an arc map storing
1.294 /// the flow that is the union of the found arc-disjoint paths.
1.295 ///
1.296 /// \pre \ref run() or \ref findFlow() must be called before using
1.297 @@ -425,34 +476,11 @@
1.298 return *_flow;
1.299 }
1.300
1.301 - /// \brief Return a const reference to the node map storing the
1.302 - /// found potentials (the dual solution).
1.303 - ///
1.304 - /// This function returns a const reference to the node map storing
1.305 - /// the found potentials that provide the dual solution of the
1.306 - /// underlying minimum cost flow problem.
1.307 - ///
1.308 - /// \pre \ref run() or \ref findFlow() must be called before using
1.309 - /// this function.
1.310 - const PotentialMap& potentialMap() const {
1.311 - return *_potential;
1.312 - }
1.313 -
1.314 - /// \brief Return the flow on the given arc.
1.315 - ///
1.316 - /// This function returns the flow on the given arc.
1.317 - /// It is \c 1 if the arc is involved in one of the found paths,
1.318 - /// otherwise it is \c 0.
1.319 - ///
1.320 - /// \pre \ref run() or \ref findFlow() must be called before using
1.321 - /// this function.
1.322 - int flow(const Arc& arc) const {
1.323 - return (*_flow)[arc];
1.324 - }
1.325 -
1.326 /// \brief Return the potential of the given node.
1.327 ///
1.328 /// This function returns the potential of the given node.
1.329 + /// The node potentials provide the dual solution of the
1.330 + /// underlying \ref min_cost_flow "minimum cost flow problem".
1.331 ///
1.332 /// \pre \ref run() or \ref findFlow() must be called before using
1.333 /// this function.
1.334 @@ -460,18 +488,17 @@
1.335 return (*_potential)[node];
1.336 }
1.337
1.338 - /// \brief Return the total length (cost) of the found paths (flow).
1.339 + /// \brief Return a const reference to a node map storing the
1.340 + /// found potentials (the dual solution).
1.341 ///
1.342 - /// This function returns the total length (cost) of the found paths
1.343 - /// (flow). The complexity of the function is O(e).
1.344 + /// This function returns a const reference to a node map storing
1.345 + /// the found potentials that provide the dual solution of the
1.346 + /// underlying \ref min_cost_flow "minimum cost flow problem".
1.347 ///
1.348 /// \pre \ref run() or \ref findFlow() must be called before using
1.349 /// this function.
1.350 - Length totalLength() const {
1.351 - Length c = 0;
1.352 - for (ArcIt e(_graph); e != INVALID; ++e)
1.353 - c += (*_flow)[e] * _length[e];
1.354 - return c;
1.355 + const PotentialMap& potentialMap() const {
1.356 + return *_potential;
1.357 }
1.358
1.359 /// \brief Return the number of the found paths.
1.360 @@ -488,7 +515,7 @@
1.361 ///
1.362 /// This function returns a const reference to the specified path.
1.363 ///
1.364 - /// \param i The function returns the \c i-th path.
1.365 + /// \param i The function returns the <tt>i</tt>-th path.
1.366 /// \c i must be between \c 0 and <tt>%pathNum()-1</tt>.
1.367 ///
1.368 /// \pre \ref run() or \ref findPaths() must be called before using