1.1 --- /dev/null Thu Jan 01 00:00:00 1970 +0000
1.2 +++ b/lemon/karp.h Thu Nov 05 15:50:01 2009 +0100
1.3 @@ -0,0 +1,582 @@
1.4 +/* -*- C++ -*-
1.5 + *
1.6 + * This file is a part of LEMON, a generic C++ optimization library
1.7 + *
1.8 + * Copyright (C) 2003-2008
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_KARP_H
1.23 +#define LEMON_KARP_H
1.24 +
1.25 +/// \ingroup min_mean_cycle
1.26 +///
1.27 +/// \file
1.28 +/// \brief Karp's algorithm for finding a minimum mean cycle.
1.29 +
1.30 +#include <vector>
1.31 +#include <limits>
1.32 +#include <lemon/core.h>
1.33 +#include <lemon/path.h>
1.34 +#include <lemon/tolerance.h>
1.35 +#include <lemon/connectivity.h>
1.36 +
1.37 +namespace lemon {
1.38 +
1.39 + /// \brief Default traits class of Karp algorithm.
1.40 + ///
1.41 + /// Default traits class of Karp algorithm.
1.42 + /// \tparam GR The type of the digraph.
1.43 + /// \tparam LEN The type of the length map.
1.44 + /// It must conform to the \ref concepts::ReadMap "ReadMap" concept.
1.45 +#ifdef DOXYGEN
1.46 + template <typename GR, typename LEN>
1.47 +#else
1.48 + template <typename GR, typename LEN,
1.49 + bool integer = std::numeric_limits<typename LEN::Value>::is_integer>
1.50 +#endif
1.51 + struct KarpDefaultTraits
1.52 + {
1.53 + /// The type of the digraph
1.54 + typedef GR Digraph;
1.55 + /// The type of the length map
1.56 + typedef LEN LengthMap;
1.57 + /// The type of the arc lengths
1.58 + typedef typename LengthMap::Value Value;
1.59 +
1.60 + /// \brief The large value type used for internal computations
1.61 + ///
1.62 + /// The large value type used for internal computations.
1.63 + /// It is \c long \c long if the \c Value type is integer,
1.64 + /// otherwise it is \c double.
1.65 + /// \c Value must be convertible to \c LargeValue.
1.66 + typedef double LargeValue;
1.67 +
1.68 + /// The tolerance type used for internal computations
1.69 + typedef lemon::Tolerance<LargeValue> Tolerance;
1.70 +
1.71 + /// \brief The path type of the found cycles
1.72 + ///
1.73 + /// The path type of the found cycles.
1.74 + /// It must conform to the \ref lemon::concepts::Path "Path" concept
1.75 + /// and it must have an \c addFront() function.
1.76 + typedef lemon::Path<Digraph> Path;
1.77 + };
1.78 +
1.79 + // Default traits class for integer value types
1.80 + template <typename GR, typename LEN>
1.81 + struct KarpDefaultTraits<GR, LEN, true>
1.82 + {
1.83 + typedef GR Digraph;
1.84 + typedef LEN LengthMap;
1.85 + typedef typename LengthMap::Value Value;
1.86 +#ifdef LEMON_HAVE_LONG_LONG
1.87 + typedef long long LargeValue;
1.88 +#else
1.89 + typedef long LargeValue;
1.90 +#endif
1.91 + typedef lemon::Tolerance<LargeValue> Tolerance;
1.92 + typedef lemon::Path<Digraph> Path;
1.93 + };
1.94 +
1.95 +
1.96 + /// \addtogroup min_mean_cycle
1.97 + /// @{
1.98 +
1.99 + /// \brief Implementation of Karp's algorithm for finding a minimum
1.100 + /// mean cycle.
1.101 + ///
1.102 + /// This class implements Karp's algorithm for finding a directed
1.103 + /// cycle of minimum mean length (cost) in a digraph
1.104 + /// \ref amo93networkflows, \ref dasdan98minmeancycle.
1.105 + /// It runs in time O(ne) and uses space O(n<sup>2</sup>+e).
1.106 + ///
1.107 + /// \tparam GR The type of the digraph the algorithm runs on.
1.108 + /// \tparam LEN The type of the length map. The default
1.109 + /// map type is \ref concepts::Digraph::ArcMap "GR::ArcMap<int>".
1.110 +#ifdef DOXYGEN
1.111 + template <typename GR, typename LEN, typename TR>
1.112 +#else
1.113 + template < typename GR,
1.114 + typename LEN = typename GR::template ArcMap<int>,
1.115 + typename TR = KarpDefaultTraits<GR, LEN> >
1.116 +#endif
1.117 + class Karp
1.118 + {
1.119 + public:
1.120 +
1.121 + /// The type of the digraph
1.122 + typedef typename TR::Digraph Digraph;
1.123 + /// The type of the length map
1.124 + typedef typename TR::LengthMap LengthMap;
1.125 + /// The type of the arc lengths
1.126 + typedef typename TR::Value Value;
1.127 +
1.128 + /// \brief The large value type
1.129 + ///
1.130 + /// The large value type used for internal computations.
1.131 + /// Using the \ref KarpDefaultTraits "default traits class",
1.132 + /// it is \c long \c long if the \c Value type is integer,
1.133 + /// otherwise it is \c double.
1.134 + typedef typename TR::LargeValue LargeValue;
1.135 +
1.136 + /// The tolerance type
1.137 + typedef typename TR::Tolerance Tolerance;
1.138 +
1.139 + /// \brief The path type of the found cycles
1.140 + ///
1.141 + /// The path type of the found cycles.
1.142 + /// Using the \ref KarpDefaultTraits "default traits class",
1.143 + /// it is \ref lemon::Path "Path<Digraph>".
1.144 + typedef typename TR::Path Path;
1.145 +
1.146 + /// The \ref KarpDefaultTraits "traits class" of the algorithm
1.147 + typedef TR Traits;
1.148 +
1.149 + private:
1.150 +
1.151 + TEMPLATE_DIGRAPH_TYPEDEFS(Digraph);
1.152 +
1.153 + // Data sturcture for path data
1.154 + struct PathData
1.155 + {
1.156 + LargeValue dist;
1.157 + Arc pred;
1.158 + PathData(LargeValue d, Arc p = INVALID) :
1.159 + dist(d), pred(p) {}
1.160 + };
1.161 +
1.162 + typedef typename Digraph::template NodeMap<std::vector<PathData> >
1.163 + PathDataNodeMap;
1.164 +
1.165 + private:
1.166 +
1.167 + // The digraph the algorithm runs on
1.168 + const Digraph &_gr;
1.169 + // The length of the arcs
1.170 + const LengthMap &_length;
1.171 +
1.172 + // Data for storing the strongly connected components
1.173 + int _comp_num;
1.174 + typename Digraph::template NodeMap<int> _comp;
1.175 + std::vector<std::vector<Node> > _comp_nodes;
1.176 + std::vector<Node>* _nodes;
1.177 + typename Digraph::template NodeMap<std::vector<Arc> > _out_arcs;
1.178 +
1.179 + // Data for the found cycle
1.180 + LargeValue _cycle_length;
1.181 + int _cycle_size;
1.182 + Node _cycle_node;
1.183 +
1.184 + Path *_cycle_path;
1.185 + bool _local_path;
1.186 +
1.187 + // Node map for storing path data
1.188 + PathDataNodeMap _data;
1.189 + // The processed nodes in the last round
1.190 + std::vector<Node> _process;
1.191 +
1.192 + Tolerance _tolerance;
1.193 +
1.194 + // Infinite constant
1.195 + const LargeValue INF;
1.196 +
1.197 + public:
1.198 +
1.199 + /// \name Named Template Parameters
1.200 + /// @{
1.201 +
1.202 + template <typename T>
1.203 + struct SetLargeValueTraits : public Traits {
1.204 + typedef T LargeValue;
1.205 + typedef lemon::Tolerance<T> Tolerance;
1.206 + };
1.207 +
1.208 + /// \brief \ref named-templ-param "Named parameter" for setting
1.209 + /// \c LargeValue type.
1.210 + ///
1.211 + /// \ref named-templ-param "Named parameter" for setting \c LargeValue
1.212 + /// type. It is used for internal computations in the algorithm.
1.213 + template <typename T>
1.214 + struct SetLargeValue
1.215 + : public Karp<GR, LEN, SetLargeValueTraits<T> > {
1.216 + typedef Karp<GR, LEN, SetLargeValueTraits<T> > Create;
1.217 + };
1.218 +
1.219 + template <typename T>
1.220 + struct SetPathTraits : public Traits {
1.221 + typedef T Path;
1.222 + };
1.223 +
1.224 + /// \brief \ref named-templ-param "Named parameter" for setting
1.225 + /// \c %Path type.
1.226 + ///
1.227 + /// \ref named-templ-param "Named parameter" for setting the \c %Path
1.228 + /// type of the found cycles.
1.229 + /// It must conform to the \ref lemon::concepts::Path "Path" concept
1.230 + /// and it must have an \c addFront() function.
1.231 + template <typename T>
1.232 + struct SetPath
1.233 + : public Karp<GR, LEN, SetPathTraits<T> > {
1.234 + typedef Karp<GR, LEN, SetPathTraits<T> > Create;
1.235 + };
1.236 +
1.237 + /// @}
1.238 +
1.239 + public:
1.240 +
1.241 + /// \brief Constructor.
1.242 + ///
1.243 + /// The constructor of the class.
1.244 + ///
1.245 + /// \param digraph The digraph the algorithm runs on.
1.246 + /// \param length The lengths (costs) of the arcs.
1.247 + Karp( const Digraph &digraph,
1.248 + const LengthMap &length ) :
1.249 + _gr(digraph), _length(length), _comp(digraph), _out_arcs(digraph),
1.250 + _cycle_length(0), _cycle_size(1), _cycle_node(INVALID),
1.251 + _cycle_path(NULL), _local_path(false), _data(digraph),
1.252 + INF(std::numeric_limits<LargeValue>::has_infinity ?
1.253 + std::numeric_limits<LargeValue>::infinity() :
1.254 + std::numeric_limits<LargeValue>::max())
1.255 + {}
1.256 +
1.257 + /// Destructor.
1.258 + ~Karp() {
1.259 + if (_local_path) delete _cycle_path;
1.260 + }
1.261 +
1.262 + /// \brief Set the path structure for storing the found cycle.
1.263 + ///
1.264 + /// This function sets an external path structure for storing the
1.265 + /// found cycle.
1.266 + ///
1.267 + /// If you don't call this function before calling \ref run() or
1.268 + /// \ref findMinMean(), it will allocate a local \ref Path "path"
1.269 + /// structure. The destuctor deallocates this automatically
1.270 + /// allocated object, of course.
1.271 + ///
1.272 + /// \note The algorithm calls only the \ref lemon::Path::addFront()
1.273 + /// "addFront()" function of the given path structure.
1.274 + ///
1.275 + /// \return <tt>(*this)</tt>
1.276 + Karp& cycle(Path &path) {
1.277 + if (_local_path) {
1.278 + delete _cycle_path;
1.279 + _local_path = false;
1.280 + }
1.281 + _cycle_path = &path;
1.282 + return *this;
1.283 + }
1.284 +
1.285 + /// \brief Set the tolerance used by the algorithm.
1.286 + ///
1.287 + /// This function sets the tolerance object used by the algorithm.
1.288 + ///
1.289 + /// \return <tt>(*this)</tt>
1.290 + Karp& tolerance(const Tolerance& tolerance) {
1.291 + _tolerance = tolerance;
1.292 + return *this;
1.293 + }
1.294 +
1.295 + /// \brief Return a const reference to the tolerance.
1.296 + ///
1.297 + /// This function returns a const reference to the tolerance object
1.298 + /// used by the algorithm.
1.299 + const Tolerance& tolerance() const {
1.300 + return _tolerance;
1.301 + }
1.302 +
1.303 + /// \name Execution control
1.304 + /// The simplest way to execute the algorithm is to call the \ref run()
1.305 + /// function.\n
1.306 + /// If you only need the minimum mean length, you may call
1.307 + /// \ref findMinMean().
1.308 +
1.309 + /// @{
1.310 +
1.311 + /// \brief Run the algorithm.
1.312 + ///
1.313 + /// This function runs the algorithm.
1.314 + /// It can be called more than once (e.g. if the underlying digraph
1.315 + /// and/or the arc lengths have been modified).
1.316 + ///
1.317 + /// \return \c true if a directed cycle exists in the digraph.
1.318 + ///
1.319 + /// \note <tt>mmc.run()</tt> is just a shortcut of the following code.
1.320 + /// \code
1.321 + /// return mmc.findMinMean() && mmc.findCycle();
1.322 + /// \endcode
1.323 + bool run() {
1.324 + return findMinMean() && findCycle();
1.325 + }
1.326 +
1.327 + /// \brief Find the minimum cycle mean.
1.328 + ///
1.329 + /// This function finds the minimum mean length of the directed
1.330 + /// cycles in the digraph.
1.331 + ///
1.332 + /// \return \c true if a directed cycle exists in the digraph.
1.333 + bool findMinMean() {
1.334 + // Initialization and find strongly connected components
1.335 + init();
1.336 + findComponents();
1.337 +
1.338 + // Find the minimum cycle mean in the components
1.339 + for (int comp = 0; comp < _comp_num; ++comp) {
1.340 + if (!initComponent(comp)) continue;
1.341 + processRounds();
1.342 + updateMinMean();
1.343 + }
1.344 + return (_cycle_node != INVALID);
1.345 + }
1.346 +
1.347 + /// \brief Find a minimum mean directed cycle.
1.348 + ///
1.349 + /// This function finds a directed cycle of minimum mean length
1.350 + /// in the digraph using the data computed by findMinMean().
1.351 + ///
1.352 + /// \return \c true if a directed cycle exists in the digraph.
1.353 + ///
1.354 + /// \pre \ref findMinMean() must be called before using this function.
1.355 + bool findCycle() {
1.356 + if (_cycle_node == INVALID) return false;
1.357 + IntNodeMap reached(_gr, -1);
1.358 + int r = _data[_cycle_node].size();
1.359 + Node u = _cycle_node;
1.360 + while (reached[u] < 0) {
1.361 + reached[u] = --r;
1.362 + u = _gr.source(_data[u][r].pred);
1.363 + }
1.364 + r = reached[u];
1.365 + Arc e = _data[u][r].pred;
1.366 + _cycle_path->addFront(e);
1.367 + _cycle_length = _length[e];
1.368 + _cycle_size = 1;
1.369 + Node v;
1.370 + while ((v = _gr.source(e)) != u) {
1.371 + e = _data[v][--r].pred;
1.372 + _cycle_path->addFront(e);
1.373 + _cycle_length += _length[e];
1.374 + ++_cycle_size;
1.375 + }
1.376 + return true;
1.377 + }
1.378 +
1.379 + /// @}
1.380 +
1.381 + /// \name Query Functions
1.382 + /// The results of the algorithm can be obtained using these
1.383 + /// functions.\n
1.384 + /// The algorithm should be executed before using them.
1.385 +
1.386 + /// @{
1.387 +
1.388 + /// \brief Return the total length of the found cycle.
1.389 + ///
1.390 + /// This function returns the total length of the found cycle.
1.391 + ///
1.392 + /// \pre \ref run() or \ref findMinMean() must be called before
1.393 + /// using this function.
1.394 + LargeValue cycleLength() const {
1.395 + return _cycle_length;
1.396 + }
1.397 +
1.398 + /// \brief Return the number of arcs on the found cycle.
1.399 + ///
1.400 + /// This function returns the number of arcs on the found cycle.
1.401 + ///
1.402 + /// \pre \ref run() or \ref findMinMean() must be called before
1.403 + /// using this function.
1.404 + int cycleArcNum() const {
1.405 + return _cycle_size;
1.406 + }
1.407 +
1.408 + /// \brief Return the mean length of the found cycle.
1.409 + ///
1.410 + /// This function returns the mean length of the found cycle.
1.411 + ///
1.412 + /// \note <tt>alg.cycleMean()</tt> is just a shortcut of the
1.413 + /// following code.
1.414 + /// \code
1.415 + /// return static_cast<double>(alg.cycleLength()) / alg.cycleArcNum();
1.416 + /// \endcode
1.417 + ///
1.418 + /// \pre \ref run() or \ref findMinMean() must be called before
1.419 + /// using this function.
1.420 + double cycleMean() const {
1.421 + return static_cast<double>(_cycle_length) / _cycle_size;
1.422 + }
1.423 +
1.424 + /// \brief Return the found cycle.
1.425 + ///
1.426 + /// This function returns a const reference to the path structure
1.427 + /// storing the found cycle.
1.428 + ///
1.429 + /// \pre \ref run() or \ref findCycle() must be called before using
1.430 + /// this function.
1.431 + const Path& cycle() const {
1.432 + return *_cycle_path;
1.433 + }
1.434 +
1.435 + ///@}
1.436 +
1.437 + private:
1.438 +
1.439 + // Initialization
1.440 + void init() {
1.441 + if (!_cycle_path) {
1.442 + _local_path = true;
1.443 + _cycle_path = new Path;
1.444 + }
1.445 + _cycle_path->clear();
1.446 + _cycle_length = 0;
1.447 + _cycle_size = 1;
1.448 + _cycle_node = INVALID;
1.449 + for (NodeIt u(_gr); u != INVALID; ++u)
1.450 + _data[u].clear();
1.451 + }
1.452 +
1.453 + // Find strongly connected components and initialize _comp_nodes
1.454 + // and _out_arcs
1.455 + void findComponents() {
1.456 + _comp_num = stronglyConnectedComponents(_gr, _comp);
1.457 + _comp_nodes.resize(_comp_num);
1.458 + if (_comp_num == 1) {
1.459 + _comp_nodes[0].clear();
1.460 + for (NodeIt n(_gr); n != INVALID; ++n) {
1.461 + _comp_nodes[0].push_back(n);
1.462 + _out_arcs[n].clear();
1.463 + for (OutArcIt a(_gr, n); a != INVALID; ++a) {
1.464 + _out_arcs[n].push_back(a);
1.465 + }
1.466 + }
1.467 + } else {
1.468 + for (int i = 0; i < _comp_num; ++i)
1.469 + _comp_nodes[i].clear();
1.470 + for (NodeIt n(_gr); n != INVALID; ++n) {
1.471 + int k = _comp[n];
1.472 + _comp_nodes[k].push_back(n);
1.473 + _out_arcs[n].clear();
1.474 + for (OutArcIt a(_gr, n); a != INVALID; ++a) {
1.475 + if (_comp[_gr.target(a)] == k) _out_arcs[n].push_back(a);
1.476 + }
1.477 + }
1.478 + }
1.479 + }
1.480 +
1.481 + // Initialize path data for the current component
1.482 + bool initComponent(int comp) {
1.483 + _nodes = &(_comp_nodes[comp]);
1.484 + int n = _nodes->size();
1.485 + if (n < 1 || (n == 1 && _out_arcs[(*_nodes)[0]].size() == 0)) {
1.486 + return false;
1.487 + }
1.488 + for (int i = 0; i < n; ++i) {
1.489 + _data[(*_nodes)[i]].resize(n + 1, PathData(INF));
1.490 + }
1.491 + return true;
1.492 + }
1.493 +
1.494 + // Process all rounds of computing path data for the current component.
1.495 + // _data[v][k] is the length of a shortest directed walk from the root
1.496 + // node to node v containing exactly k arcs.
1.497 + void processRounds() {
1.498 + Node start = (*_nodes)[0];
1.499 + _data[start][0] = PathData(0);
1.500 + _process.clear();
1.501 + _process.push_back(start);
1.502 +
1.503 + int k, n = _nodes->size();
1.504 + for (k = 1; k <= n && int(_process.size()) < n; ++k) {
1.505 + processNextBuildRound(k);
1.506 + }
1.507 + for ( ; k <= n; ++k) {
1.508 + processNextFullRound(k);
1.509 + }
1.510 + }
1.511 +
1.512 + // Process one round and rebuild _process
1.513 + void processNextBuildRound(int k) {
1.514 + std::vector<Node> next;
1.515 + Node u, v;
1.516 + Arc e;
1.517 + LargeValue d;
1.518 + for (int i = 0; i < int(_process.size()); ++i) {
1.519 + u = _process[i];
1.520 + for (int j = 0; j < int(_out_arcs[u].size()); ++j) {
1.521 + e = _out_arcs[u][j];
1.522 + v = _gr.target(e);
1.523 + d = _data[u][k-1].dist + _length[e];
1.524 + if (_tolerance.less(d, _data[v][k].dist)) {
1.525 + if (_data[v][k].dist == INF) next.push_back(v);
1.526 + _data[v][k] = PathData(d, e);
1.527 + }
1.528 + }
1.529 + }
1.530 + _process.swap(next);
1.531 + }
1.532 +
1.533 + // Process one round using _nodes instead of _process
1.534 + void processNextFullRound(int k) {
1.535 + Node u, v;
1.536 + Arc e;
1.537 + LargeValue d;
1.538 + for (int i = 0; i < int(_nodes->size()); ++i) {
1.539 + u = (*_nodes)[i];
1.540 + for (int j = 0; j < int(_out_arcs[u].size()); ++j) {
1.541 + e = _out_arcs[u][j];
1.542 + v = _gr.target(e);
1.543 + d = _data[u][k-1].dist + _length[e];
1.544 + if (_tolerance.less(d, _data[v][k].dist)) {
1.545 + _data[v][k] = PathData(d, e);
1.546 + }
1.547 + }
1.548 + }
1.549 + }
1.550 +
1.551 + // Update the minimum cycle mean
1.552 + void updateMinMean() {
1.553 + int n = _nodes->size();
1.554 + for (int i = 0; i < n; ++i) {
1.555 + Node u = (*_nodes)[i];
1.556 + if (_data[u][n].dist == INF) continue;
1.557 + LargeValue length, max_length = 0;
1.558 + int size, max_size = 1;
1.559 + bool found_curr = false;
1.560 + for (int k = 0; k < n; ++k) {
1.561 + if (_data[u][k].dist == INF) continue;
1.562 + length = _data[u][n].dist - _data[u][k].dist;
1.563 + size = n - k;
1.564 + if (!found_curr || length * max_size > max_length * size) {
1.565 + found_curr = true;
1.566 + max_length = length;
1.567 + max_size = size;
1.568 + }
1.569 + }
1.570 + if ( found_curr && (_cycle_node == INVALID ||
1.571 + max_length * _cycle_size < _cycle_length * max_size) ) {
1.572 + _cycle_length = max_length;
1.573 + _cycle_size = max_size;
1.574 + _cycle_node = u;
1.575 + }
1.576 + }
1.577 + }
1.578 +
1.579 + }; //class Karp
1.580 +
1.581 + ///@}
1.582 +
1.583 +} //namespace lemon
1.584 +
1.585 +#endif //LEMON_KARP_H