1.1 --- /dev/null Thu Jan 01 00:00:00 1970 +0000
1.2 +++ b/lemon/suurballe.h Thu Nov 05 15:50:01 2009 +0100
1.3 @@ -0,0 +1,535 @@
1.4 +/* -*- mode: C++; indent-tabs-mode: nil; -*-
1.5 + *
1.6 + * This file is a part of LEMON, a generic C++ optimization library.
1.7 + *
1.8 + * Copyright (C) 2003-2009
1.9 + * Egervary Jeno Kombinatorikus Optimalizalasi Kutatocsoport
1.10 + * (Egervary Research Group on Combinatorial Optimization, EGRES).
1.11 + *
1.12 + * Permission to use, modify and distribute this software is granted
1.13 + * provided that this copyright notice appears in all copies. For
1.14 + * precise terms see the accompanying LICENSE file.
1.15 + *
1.16 + * This software is provided "AS IS" with no warranty of any kind,
1.17 + * express or implied, and with no claim as to its suitability for any
1.18 + * purpose.
1.19 + *
1.20 + */
1.21 +
1.22 +#ifndef LEMON_SUURBALLE_H
1.23 +#define LEMON_SUURBALLE_H
1.24 +
1.25 +///\ingroup shortest_path
1.26 +///\file
1.27 +///\brief An algorithm for finding arc-disjoint paths between two
1.28 +/// nodes having minimum total length.
1.29 +
1.30 +#include <vector>
1.31 +#include <limits>
1.32 +#include <lemon/bin_heap.h>
1.33 +#include <lemon/path.h>
1.34 +#include <lemon/list_graph.h>
1.35 +#include <lemon/maps.h>
1.36 +
1.37 +namespace lemon {
1.38 +
1.39 + /// \addtogroup shortest_path
1.40 + /// @{
1.41 +
1.42 + /// \brief Algorithm for finding arc-disjoint paths between two nodes
1.43 + /// having minimum total length.
1.44 + ///
1.45 + /// \ref lemon::Suurballe "Suurballe" implements an algorithm for
1.46 + /// finding arc-disjoint paths having minimum total length (cost)
1.47 + /// from a given source node to a given target node in a digraph.
1.48 + ///
1.49 + /// Note that this problem is a special case of the \ref min_cost_flow
1.50 + /// "minimum cost flow problem". This implementation is actually an
1.51 + /// efficient specialized version of the \ref CapacityScaling
1.52 + /// "Successive Shortest Path" algorithm directly for this problem.
1.53 + /// Therefore this class provides query functions for flow values and
1.54 + /// node potentials (the dual solution) just like the minimum cost flow
1.55 + /// algorithms.
1.56 + ///
1.57 + /// \tparam GR The digraph type the algorithm runs on.
1.58 + /// \tparam LEN The type of the length map.
1.59 + /// The default value is <tt>GR::ArcMap<int></tt>.
1.60 + ///
1.61 + /// \warning Length values should be \e non-negative \e integers.
1.62 + ///
1.63 + /// \note For finding node-disjoint paths this algorithm can be used
1.64 + /// along with the \ref SplitNodes adaptor.
1.65 +#ifdef DOXYGEN
1.66 + template <typename GR, typename LEN>
1.67 +#else
1.68 + template < typename GR,
1.69 + typename LEN = typename GR::template ArcMap<int> >
1.70 +#endif
1.71 + class Suurballe
1.72 + {
1.73 + TEMPLATE_DIGRAPH_TYPEDEFS(GR);
1.74 +
1.75 + typedef ConstMap<Arc, int> ConstArcMap;
1.76 + typedef typename GR::template NodeMap<Arc> PredMap;
1.77 +
1.78 + public:
1.79 +
1.80 + /// The type of the digraph the algorithm runs on.
1.81 + typedef GR Digraph;
1.82 + /// The type of the length map.
1.83 + typedef LEN LengthMap;
1.84 + /// The type of the lengths.
1.85 + typedef typename LengthMap::Value Length;
1.86 +#ifdef DOXYGEN
1.87 + /// The type of the flow map.
1.88 + typedef GR::ArcMap<int> FlowMap;
1.89 + /// The type of the potential map.
1.90 + typedef GR::NodeMap<Length> PotentialMap;
1.91 +#else
1.92 + /// The type of the flow map.
1.93 + typedef typename Digraph::template ArcMap<int> FlowMap;
1.94 + /// The type of the potential map.
1.95 + typedef typename Digraph::template NodeMap<Length> PotentialMap;
1.96 +#endif
1.97 +
1.98 + /// The type of the path structures.
1.99 + typedef SimplePath<GR> Path;
1.100 +
1.101 + private:
1.102 +
1.103 + // ResidualDijkstra is a special implementation of the
1.104 + // Dijkstra algorithm for finding shortest paths in the
1.105 + // residual network with respect to the reduced arc lengths
1.106 + // and modifying the node potentials according to the
1.107 + // distance of the nodes.
1.108 + class ResidualDijkstra
1.109 + {
1.110 + typedef typename Digraph::template NodeMap<int> HeapCrossRef;
1.111 + typedef BinHeap<Length, HeapCrossRef> Heap;
1.112 +
1.113 + private:
1.114 +
1.115 + // The digraph the algorithm runs on
1.116 + const Digraph &_graph;
1.117 +
1.118 + // The main maps
1.119 + const FlowMap &_flow;
1.120 + const LengthMap &_length;
1.121 + PotentialMap &_potential;
1.122 +
1.123 + // The distance map
1.124 + PotentialMap _dist;
1.125 + // The pred arc map
1.126 + PredMap &_pred;
1.127 + // The processed (i.e. permanently labeled) nodes
1.128 + std::vector<Node> _proc_nodes;
1.129 +
1.130 + Node _s;
1.131 + Node _t;
1.132 +
1.133 + public:
1.134 +
1.135 + /// Constructor.
1.136 + ResidualDijkstra( const Digraph &graph,
1.137 + const FlowMap &flow,
1.138 + const LengthMap &length,
1.139 + PotentialMap &potential,
1.140 + PredMap &pred,
1.141 + Node s, Node t ) :
1.142 + _graph(graph), _flow(flow), _length(length), _potential(potential),
1.143 + _dist(graph), _pred(pred), _s(s), _t(t) {}
1.144 +
1.145 + /// \brief Run the algorithm. It returns \c true if a path is found
1.146 + /// from the source node to the target node.
1.147 + bool run() {
1.148 + HeapCrossRef heap_cross_ref(_graph, Heap::PRE_HEAP);
1.149 + Heap heap(heap_cross_ref);
1.150 + heap.push(_s, 0);
1.151 + _pred[_s] = INVALID;
1.152 + _proc_nodes.clear();
1.153 +
1.154 + // Process nodes
1.155 + while (!heap.empty() && heap.top() != _t) {
1.156 + Node u = heap.top(), v;
1.157 + Length d = heap.prio() + _potential[u], nd;
1.158 + _dist[u] = heap.prio();
1.159 + heap.pop();
1.160 + _proc_nodes.push_back(u);
1.161 +
1.162 + // Traverse outgoing arcs
1.163 + for (OutArcIt e(_graph, u); e != INVALID; ++e) {
1.164 + if (_flow[e] == 0) {
1.165 + v = _graph.target(e);
1.166 + switch(heap.state(v)) {
1.167 + case Heap::PRE_HEAP:
1.168 + heap.push(v, d + _length[e] - _potential[v]);
1.169 + _pred[v] = e;
1.170 + break;
1.171 + case Heap::IN_HEAP:
1.172 + nd = d + _length[e] - _potential[v];
1.173 + if (nd < heap[v]) {
1.174 + heap.decrease(v, nd);
1.175 + _pred[v] = e;
1.176 + }
1.177 + break;
1.178 + case Heap::POST_HEAP:
1.179 + break;
1.180 + }
1.181 + }
1.182 + }
1.183 +
1.184 + // Traverse incoming arcs
1.185 + for (InArcIt e(_graph, u); e != INVALID; ++e) {
1.186 + if (_flow[e] == 1) {
1.187 + v = _graph.source(e);
1.188 + switch(heap.state(v)) {
1.189 + case Heap::PRE_HEAP:
1.190 + heap.push(v, d - _length[e] - _potential[v]);
1.191 + _pred[v] = e;
1.192 + break;
1.193 + case Heap::IN_HEAP:
1.194 + nd = d - _length[e] - _potential[v];
1.195 + if (nd < heap[v]) {
1.196 + heap.decrease(v, nd);
1.197 + _pred[v] = e;
1.198 + }
1.199 + break;
1.200 + case Heap::POST_HEAP:
1.201 + break;
1.202 + }
1.203 + }
1.204 + }
1.205 + }
1.206 + if (heap.empty()) return false;
1.207 +
1.208 + // Update potentials of processed nodes
1.209 + Length t_dist = heap.prio();
1.210 + for (int i = 0; i < int(_proc_nodes.size()); ++i)
1.211 + _potential[_proc_nodes[i]] += _dist[_proc_nodes[i]] - t_dist;
1.212 + return true;
1.213 + }
1.214 +
1.215 + }; //class ResidualDijkstra
1.216 +
1.217 + private:
1.218 +
1.219 + // The digraph the algorithm runs on
1.220 + const Digraph &_graph;
1.221 + // The length map
1.222 + const LengthMap &_length;
1.223 +
1.224 + // Arc map of the current flow
1.225 + FlowMap *_flow;
1.226 + bool _local_flow;
1.227 + // Node map of the current potentials
1.228 + PotentialMap *_potential;
1.229 + bool _local_potential;
1.230 +
1.231 + // The source node
1.232 + Node _source;
1.233 + // The target node
1.234 + Node _target;
1.235 +
1.236 + // Container to store the found paths
1.237 + std::vector< SimplePath<Digraph> > paths;
1.238 + int _path_num;
1.239 +
1.240 + // The pred arc map
1.241 + PredMap _pred;
1.242 + // Implementation of the Dijkstra algorithm for finding augmenting
1.243 + // shortest paths in the residual network
1.244 + ResidualDijkstra *_dijkstra;
1.245 +
1.246 + public:
1.247 +
1.248 + /// \brief Constructor.
1.249 + ///
1.250 + /// Constructor.
1.251 + ///
1.252 + /// \param graph The digraph the algorithm runs on.
1.253 + /// \param length The length (cost) values of the arcs.
1.254 + Suurballe( const Digraph &graph,
1.255 + const LengthMap &length ) :
1.256 + _graph(graph), _length(length), _flow(0), _local_flow(false),
1.257 + _potential(0), _local_potential(false), _pred(graph)
1.258 + {
1.259 + LEMON_ASSERT(std::numeric_limits<Length>::is_integer,
1.260 + "The length type of Suurballe must be integer");
1.261 + }
1.262 +
1.263 + /// Destructor.
1.264 + ~Suurballe() {
1.265 + if (_local_flow) delete _flow;
1.266 + if (_local_potential) delete _potential;
1.267 + delete _dijkstra;
1.268 + }
1.269 +
1.270 + /// \brief Set the flow map.
1.271 + ///
1.272 + /// This function sets the flow map.
1.273 + /// If it is not used before calling \ref run() or \ref init(),
1.274 + /// an instance will be allocated automatically. The destructor
1.275 + /// deallocates this automatically allocated map, of course.
1.276 + ///
1.277 + /// The found flow contains only 0 and 1 values, since it is the
1.278 + /// union of the found arc-disjoint paths.
1.279 + ///
1.280 + /// \return <tt>(*this)</tt>
1.281 + Suurballe& flowMap(FlowMap &map) {
1.282 + if (_local_flow) {
1.283 + delete _flow;
1.284 + _local_flow = false;
1.285 + }
1.286 + _flow = ↦
1.287 + return *this;
1.288 + }
1.289 +
1.290 + /// \brief Set the potential map.
1.291 + ///
1.292 + /// This function sets the potential map.
1.293 + /// If it is not used before calling \ref run() or \ref init(),
1.294 + /// an instance will be allocated automatically. The destructor
1.295 + /// deallocates this automatically allocated map, of course.
1.296 + ///
1.297 + /// The node potentials provide the dual solution of the underlying
1.298 + /// \ref min_cost_flow "minimum cost flow problem".
1.299 + ///
1.300 + /// \return <tt>(*this)</tt>
1.301 + Suurballe& potentialMap(PotentialMap &map) {
1.302 + if (_local_potential) {
1.303 + delete _potential;
1.304 + _local_potential = false;
1.305 + }
1.306 + _potential = ↦
1.307 + return *this;
1.308 + }
1.309 +
1.310 + /// \name Execution Control
1.311 + /// The simplest way to execute the algorithm is to call the run()
1.312 + /// function.
1.313 + /// \n
1.314 + /// If you only need the flow that is the union of the found
1.315 + /// arc-disjoint paths, you may call init() and findFlow().
1.316 +
1.317 + /// @{
1.318 +
1.319 + /// \brief Run the algorithm.
1.320 + ///
1.321 + /// This function runs the algorithm.
1.322 + ///
1.323 + /// \param s The source node.
1.324 + /// \param t The target node.
1.325 + /// \param k The number of paths to be found.
1.326 + ///
1.327 + /// \return \c k if there are at least \c k arc-disjoint paths from
1.328 + /// \c s to \c t in the digraph. Otherwise it returns the number of
1.329 + /// arc-disjoint paths found.
1.330 + ///
1.331 + /// \note Apart from the return value, <tt>s.run(s, t, k)</tt> is
1.332 + /// just a shortcut of the following code.
1.333 + /// \code
1.334 + /// s.init(s);
1.335 + /// s.findFlow(t, k);
1.336 + /// s.findPaths();
1.337 + /// \endcode
1.338 + int run(const Node& s, const Node& t, int k = 2) {
1.339 + init(s);
1.340 + findFlow(t, k);
1.341 + findPaths();
1.342 + return _path_num;
1.343 + }
1.344 +
1.345 + /// \brief Initialize the algorithm.
1.346 + ///
1.347 + /// This function initializes the algorithm.
1.348 + ///
1.349 + /// \param s The source node.
1.350 + void init(const Node& s) {
1.351 + _source = s;
1.352 +
1.353 + // Initialize maps
1.354 + if (!_flow) {
1.355 + _flow = new FlowMap(_graph);
1.356 + _local_flow = true;
1.357 + }
1.358 + if (!_potential) {
1.359 + _potential = new PotentialMap(_graph);
1.360 + _local_potential = true;
1.361 + }
1.362 + for (ArcIt e(_graph); e != INVALID; ++e) (*_flow)[e] = 0;
1.363 + for (NodeIt n(_graph); n != INVALID; ++n) (*_potential)[n] = 0;
1.364 + }
1.365 +
1.366 + /// \brief Execute the algorithm to find an optimal flow.
1.367 + ///
1.368 + /// This function executes the successive shortest path algorithm to
1.369 + /// find a minimum cost flow, which is the union of \c k (or less)
1.370 + /// arc-disjoint paths.
1.371 + ///
1.372 + /// \param t The target node.
1.373 + /// \param k The number of paths to be found.
1.374 + ///
1.375 + /// \return \c k if there are at least \c k arc-disjoint paths from
1.376 + /// the source node to the given node \c t in the digraph.
1.377 + /// Otherwise it returns the number of arc-disjoint paths found.
1.378 + ///
1.379 + /// \pre \ref init() must be called before using this function.
1.380 + int findFlow(const Node& t, int k = 2) {
1.381 + _target = t;
1.382 + _dijkstra =
1.383 + new ResidualDijkstra( _graph, *_flow, _length, *_potential, _pred,
1.384 + _source, _target );
1.385 +
1.386 + // Find shortest paths
1.387 + _path_num = 0;
1.388 + while (_path_num < k) {
1.389 + // Run Dijkstra
1.390 + if (!_dijkstra->run()) break;
1.391 + ++_path_num;
1.392 +
1.393 + // Set the flow along the found shortest path
1.394 + Node u = _target;
1.395 + Arc e;
1.396 + while ((e = _pred[u]) != INVALID) {
1.397 + if (u == _graph.target(e)) {
1.398 + (*_flow)[e] = 1;
1.399 + u = _graph.source(e);
1.400 + } else {
1.401 + (*_flow)[e] = 0;
1.402 + u = _graph.target(e);
1.403 + }
1.404 + }
1.405 + }
1.406 + return _path_num;
1.407 + }
1.408 +
1.409 + /// \brief Compute the paths from the flow.
1.410 + ///
1.411 + /// This function computes the paths from the found minimum cost flow,
1.412 + /// which is the union of some arc-disjoint paths.
1.413 + ///
1.414 + /// \pre \ref init() and \ref findFlow() must be called before using
1.415 + /// this function.
1.416 + void findPaths() {
1.417 + FlowMap res_flow(_graph);
1.418 + for(ArcIt a(_graph); a != INVALID; ++a) res_flow[a] = (*_flow)[a];
1.419 +
1.420 + paths.clear();
1.421 + paths.resize(_path_num);
1.422 + for (int i = 0; i < _path_num; ++i) {
1.423 + Node n = _source;
1.424 + while (n != _target) {
1.425 + OutArcIt e(_graph, n);
1.426 + for ( ; res_flow[e] == 0; ++e) ;
1.427 + n = _graph.target(e);
1.428 + paths[i].addBack(e);
1.429 + res_flow[e] = 0;
1.430 + }
1.431 + }
1.432 + }
1.433 +
1.434 + /// @}
1.435 +
1.436 + /// \name Query Functions
1.437 + /// The results of the algorithm can be obtained using these
1.438 + /// functions.
1.439 + /// \n The algorithm should be executed before using them.
1.440 +
1.441 + /// @{
1.442 +
1.443 + /// \brief Return the total length of the found paths.
1.444 + ///
1.445 + /// This function returns the total length of the found paths, i.e.
1.446 + /// the total cost of the found flow.
1.447 + /// The complexity of the function is O(e).
1.448 + ///
1.449 + /// \pre \ref run() or \ref findFlow() must be called before using
1.450 + /// this function.
1.451 + Length totalLength() const {
1.452 + Length c = 0;
1.453 + for (ArcIt e(_graph); e != INVALID; ++e)
1.454 + c += (*_flow)[e] * _length[e];
1.455 + return c;
1.456 + }
1.457 +
1.458 + /// \brief Return the flow value on the given arc.
1.459 + ///
1.460 + /// This function returns the flow value on the given arc.
1.461 + /// It is \c 1 if the arc is involved in one of the found arc-disjoint
1.462 + /// paths, otherwise it is \c 0.
1.463 + ///
1.464 + /// \pre \ref run() or \ref findFlow() must be called before using
1.465 + /// this function.
1.466 + int flow(const Arc& arc) const {
1.467 + return (*_flow)[arc];
1.468 + }
1.469 +
1.470 + /// \brief Return a const reference to an arc map storing the
1.471 + /// found flow.
1.472 + ///
1.473 + /// This function returns a const reference to an arc map storing
1.474 + /// the flow that is the union of the found arc-disjoint paths.
1.475 + ///
1.476 + /// \pre \ref run() or \ref findFlow() must be called before using
1.477 + /// this function.
1.478 + const FlowMap& flowMap() const {
1.479 + return *_flow;
1.480 + }
1.481 +
1.482 + /// \brief Return the potential of the given node.
1.483 + ///
1.484 + /// This function returns the potential of the given node.
1.485 + /// The node potentials provide the dual solution of the
1.486 + /// underlying \ref min_cost_flow "minimum cost flow problem".
1.487 + ///
1.488 + /// \pre \ref run() or \ref findFlow() must be called before using
1.489 + /// this function.
1.490 + Length potential(const Node& node) const {
1.491 + return (*_potential)[node];
1.492 + }
1.493 +
1.494 + /// \brief Return a const reference to a node map storing the
1.495 + /// found potentials (the dual solution).
1.496 + ///
1.497 + /// This function returns a const reference to a node map storing
1.498 + /// the found potentials that provide the dual solution of the
1.499 + /// underlying \ref min_cost_flow "minimum cost flow problem".
1.500 + ///
1.501 + /// \pre \ref run() or \ref findFlow() must be called before using
1.502 + /// this function.
1.503 + const PotentialMap& potentialMap() const {
1.504 + return *_potential;
1.505 + }
1.506 +
1.507 + /// \brief Return the number of the found paths.
1.508 + ///
1.509 + /// This function returns the number of the found paths.
1.510 + ///
1.511 + /// \pre \ref run() or \ref findFlow() must be called before using
1.512 + /// this function.
1.513 + int pathNum() const {
1.514 + return _path_num;
1.515 + }
1.516 +
1.517 + /// \brief Return a const reference to the specified path.
1.518 + ///
1.519 + /// This function returns a const reference to the specified path.
1.520 + ///
1.521 + /// \param i The function returns the <tt>i</tt>-th path.
1.522 + /// \c i must be between \c 0 and <tt>%pathNum()-1</tt>.
1.523 + ///
1.524 + /// \pre \ref run() or \ref findPaths() must be called before using
1.525 + /// this function.
1.526 + Path path(int i) const {
1.527 + return paths[i];
1.528 + }
1.529 +
1.530 + /// @}
1.531 +
1.532 + }; //class Suurballe
1.533 +
1.534 + ///@}
1.535 +
1.536 +} //namespace lemon
1.537 +
1.538 +#endif //LEMON_SUURBALLE_H