1.1 --- a/lemon/karp.h Mon Mar 08 08:33:41 2010 +0100
1.2 +++ /dev/null Thu Jan 01 00:00:00 1970 +0000
1.3 @@ -1,590 +0,0 @@
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 - /// \tparam TR The traits class that defines various types used by the
1.111 - /// algorithm. By default, it is \ref KarpDefaultTraits
1.112 - /// "KarpDefaultTraits<GR, LEN>".
1.113 - /// In most cases, this parameter should not be set directly,
1.114 - /// consider to use the named template parameters instead.
1.115 -#ifdef DOXYGEN
1.116 - template <typename GR, typename LEN, typename TR>
1.117 -#else
1.118 - template < typename GR,
1.119 - typename LEN = typename GR::template ArcMap<int>,
1.120 - typename TR = KarpDefaultTraits<GR, LEN> >
1.121 -#endif
1.122 - class Karp
1.123 - {
1.124 - public:
1.125 -
1.126 - /// The type of the digraph
1.127 - typedef typename TR::Digraph Digraph;
1.128 - /// The type of the length map
1.129 - typedef typename TR::LengthMap LengthMap;
1.130 - /// The type of the arc lengths
1.131 - typedef typename TR::Value Value;
1.132 -
1.133 - /// \brief The large value type
1.134 - ///
1.135 - /// The large value type used for internal computations.
1.136 - /// By default, it is \c long \c long if the \c Value type is integer,
1.137 - /// otherwise it is \c double.
1.138 - typedef typename TR::LargeValue LargeValue;
1.139 -
1.140 - /// The tolerance type
1.141 - typedef typename TR::Tolerance Tolerance;
1.142 -
1.143 - /// \brief The path type of the found cycles
1.144 - ///
1.145 - /// The path type of the found cycles.
1.146 - /// Using the \ref KarpDefaultTraits "default traits class",
1.147 - /// it is \ref lemon::Path "Path<Digraph>".
1.148 - typedef typename TR::Path Path;
1.149 -
1.150 - /// The \ref KarpDefaultTraits "traits class" of the algorithm
1.151 - typedef TR Traits;
1.152 -
1.153 - private:
1.154 -
1.155 - TEMPLATE_DIGRAPH_TYPEDEFS(Digraph);
1.156 -
1.157 - // Data sturcture for path data
1.158 - struct PathData
1.159 - {
1.160 - LargeValue dist;
1.161 - Arc pred;
1.162 - PathData(LargeValue d, Arc p = INVALID) :
1.163 - dist(d), pred(p) {}
1.164 - };
1.165 -
1.166 - typedef typename Digraph::template NodeMap<std::vector<PathData> >
1.167 - PathDataNodeMap;
1.168 -
1.169 - private:
1.170 -
1.171 - // The digraph the algorithm runs on
1.172 - const Digraph &_gr;
1.173 - // The length of the arcs
1.174 - const LengthMap &_length;
1.175 -
1.176 - // Data for storing the strongly connected components
1.177 - int _comp_num;
1.178 - typename Digraph::template NodeMap<int> _comp;
1.179 - std::vector<std::vector<Node> > _comp_nodes;
1.180 - std::vector<Node>* _nodes;
1.181 - typename Digraph::template NodeMap<std::vector<Arc> > _out_arcs;
1.182 -
1.183 - // Data for the found cycle
1.184 - LargeValue _cycle_length;
1.185 - int _cycle_size;
1.186 - Node _cycle_node;
1.187 -
1.188 - Path *_cycle_path;
1.189 - bool _local_path;
1.190 -
1.191 - // Node map for storing path data
1.192 - PathDataNodeMap _data;
1.193 - // The processed nodes in the last round
1.194 - std::vector<Node> _process;
1.195 -
1.196 - Tolerance _tolerance;
1.197 -
1.198 - // Infinite constant
1.199 - const LargeValue INF;
1.200 -
1.201 - public:
1.202 -
1.203 - /// \name Named Template Parameters
1.204 - /// @{
1.205 -
1.206 - template <typename T>
1.207 - struct SetLargeValueTraits : public Traits {
1.208 - typedef T LargeValue;
1.209 - typedef lemon::Tolerance<T> Tolerance;
1.210 - };
1.211 -
1.212 - /// \brief \ref named-templ-param "Named parameter" for setting
1.213 - /// \c LargeValue type.
1.214 - ///
1.215 - /// \ref named-templ-param "Named parameter" for setting \c LargeValue
1.216 - /// type. It is used for internal computations in the algorithm.
1.217 - template <typename T>
1.218 - struct SetLargeValue
1.219 - : public Karp<GR, LEN, SetLargeValueTraits<T> > {
1.220 - typedef Karp<GR, LEN, SetLargeValueTraits<T> > Create;
1.221 - };
1.222 -
1.223 - template <typename T>
1.224 - struct SetPathTraits : public Traits {
1.225 - typedef T Path;
1.226 - };
1.227 -
1.228 - /// \brief \ref named-templ-param "Named parameter" for setting
1.229 - /// \c %Path type.
1.230 - ///
1.231 - /// \ref named-templ-param "Named parameter" for setting the \c %Path
1.232 - /// type of the found cycles.
1.233 - /// It must conform to the \ref lemon::concepts::Path "Path" concept
1.234 - /// and it must have an \c addFront() function.
1.235 - template <typename T>
1.236 - struct SetPath
1.237 - : public Karp<GR, LEN, SetPathTraits<T> > {
1.238 - typedef Karp<GR, LEN, SetPathTraits<T> > Create;
1.239 - };
1.240 -
1.241 - /// @}
1.242 -
1.243 - protected:
1.244 -
1.245 - Karp() {}
1.246 -
1.247 - public:
1.248 -
1.249 - /// \brief Constructor.
1.250 - ///
1.251 - /// The constructor of the class.
1.252 - ///
1.253 - /// \param digraph The digraph the algorithm runs on.
1.254 - /// \param length The lengths (costs) of the arcs.
1.255 - Karp( const Digraph &digraph,
1.256 - const LengthMap &length ) :
1.257 - _gr(digraph), _length(length), _comp(digraph), _out_arcs(digraph),
1.258 - _cycle_length(0), _cycle_size(1), _cycle_node(INVALID),
1.259 - _cycle_path(NULL), _local_path(false), _data(digraph),
1.260 - INF(std::numeric_limits<LargeValue>::has_infinity ?
1.261 - std::numeric_limits<LargeValue>::infinity() :
1.262 - std::numeric_limits<LargeValue>::max())
1.263 - {}
1.264 -
1.265 - /// Destructor.
1.266 - ~Karp() {
1.267 - if (_local_path) delete _cycle_path;
1.268 - }
1.269 -
1.270 - /// \brief Set the path structure for storing the found cycle.
1.271 - ///
1.272 - /// This function sets an external path structure for storing the
1.273 - /// found cycle.
1.274 - ///
1.275 - /// If you don't call this function before calling \ref run() or
1.276 - /// \ref findMinMean(), it will allocate a local \ref Path "path"
1.277 - /// structure. The destuctor deallocates this automatically
1.278 - /// allocated object, of course.
1.279 - ///
1.280 - /// \note The algorithm calls only the \ref lemon::Path::addFront()
1.281 - /// "addFront()" function of the given path structure.
1.282 - ///
1.283 - /// \return <tt>(*this)</tt>
1.284 - Karp& cycle(Path &path) {
1.285 - if (_local_path) {
1.286 - delete _cycle_path;
1.287 - _local_path = false;
1.288 - }
1.289 - _cycle_path = &path;
1.290 - return *this;
1.291 - }
1.292 -
1.293 - /// \brief Set the tolerance used by the algorithm.
1.294 - ///
1.295 - /// This function sets the tolerance object used by the algorithm.
1.296 - ///
1.297 - /// \return <tt>(*this)</tt>
1.298 - Karp& tolerance(const Tolerance& tolerance) {
1.299 - _tolerance = tolerance;
1.300 - return *this;
1.301 - }
1.302 -
1.303 - /// \brief Return a const reference to the tolerance.
1.304 - ///
1.305 - /// This function returns a const reference to the tolerance object
1.306 - /// used by the algorithm.
1.307 - const Tolerance& tolerance() const {
1.308 - return _tolerance;
1.309 - }
1.310 -
1.311 - /// \name Execution control
1.312 - /// The simplest way to execute the algorithm is to call the \ref run()
1.313 - /// function.\n
1.314 - /// If you only need the minimum mean length, you may call
1.315 - /// \ref findMinMean().
1.316 -
1.317 - /// @{
1.318 -
1.319 - /// \brief Run the algorithm.
1.320 - ///
1.321 - /// This function runs the algorithm.
1.322 - /// It can be called more than once (e.g. if the underlying digraph
1.323 - /// and/or the arc lengths have been modified).
1.324 - ///
1.325 - /// \return \c true if a directed cycle exists in the digraph.
1.326 - ///
1.327 - /// \note <tt>mmc.run()</tt> is just a shortcut of the following code.
1.328 - /// \code
1.329 - /// return mmc.findMinMean() && mmc.findCycle();
1.330 - /// \endcode
1.331 - bool run() {
1.332 - return findMinMean() && findCycle();
1.333 - }
1.334 -
1.335 - /// \brief Find the minimum cycle mean.
1.336 - ///
1.337 - /// This function finds the minimum mean length of the directed
1.338 - /// cycles in the digraph.
1.339 - ///
1.340 - /// \return \c true if a directed cycle exists in the digraph.
1.341 - bool findMinMean() {
1.342 - // Initialization and find strongly connected components
1.343 - init();
1.344 - findComponents();
1.345 -
1.346 - // Find the minimum cycle mean in the components
1.347 - for (int comp = 0; comp < _comp_num; ++comp) {
1.348 - if (!initComponent(comp)) continue;
1.349 - processRounds();
1.350 - updateMinMean();
1.351 - }
1.352 - return (_cycle_node != INVALID);
1.353 - }
1.354 -
1.355 - /// \brief Find a minimum mean directed cycle.
1.356 - ///
1.357 - /// This function finds a directed cycle of minimum mean length
1.358 - /// in the digraph using the data computed by findMinMean().
1.359 - ///
1.360 - /// \return \c true if a directed cycle exists in the digraph.
1.361 - ///
1.362 - /// \pre \ref findMinMean() must be called before using this function.
1.363 - bool findCycle() {
1.364 - if (_cycle_node == INVALID) return false;
1.365 - IntNodeMap reached(_gr, -1);
1.366 - int r = _data[_cycle_node].size();
1.367 - Node u = _cycle_node;
1.368 - while (reached[u] < 0) {
1.369 - reached[u] = --r;
1.370 - u = _gr.source(_data[u][r].pred);
1.371 - }
1.372 - r = reached[u];
1.373 - Arc e = _data[u][r].pred;
1.374 - _cycle_path->addFront(e);
1.375 - _cycle_length = _length[e];
1.376 - _cycle_size = 1;
1.377 - Node v;
1.378 - while ((v = _gr.source(e)) != u) {
1.379 - e = _data[v][--r].pred;
1.380 - _cycle_path->addFront(e);
1.381 - _cycle_length += _length[e];
1.382 - ++_cycle_size;
1.383 - }
1.384 - return true;
1.385 - }
1.386 -
1.387 - /// @}
1.388 -
1.389 - /// \name Query Functions
1.390 - /// The results of the algorithm can be obtained using these
1.391 - /// functions.\n
1.392 - /// The algorithm should be executed before using them.
1.393 -
1.394 - /// @{
1.395 -
1.396 - /// \brief Return the total length of the found cycle.
1.397 - ///
1.398 - /// This function returns the total length of the found cycle.
1.399 - ///
1.400 - /// \pre \ref run() or \ref findMinMean() must be called before
1.401 - /// using this function.
1.402 - Value cycleLength() const {
1.403 - return static_cast<Value>(_cycle_length);
1.404 - }
1.405 -
1.406 - /// \brief Return the number of arcs on the found cycle.
1.407 - ///
1.408 - /// This function returns the number of arcs on the found cycle.
1.409 - ///
1.410 - /// \pre \ref run() or \ref findMinMean() must be called before
1.411 - /// using this function.
1.412 - int cycleArcNum() const {
1.413 - return _cycle_size;
1.414 - }
1.415 -
1.416 - /// \brief Return the mean length of the found cycle.
1.417 - ///
1.418 - /// This function returns the mean length of the found cycle.
1.419 - ///
1.420 - /// \note <tt>alg.cycleMean()</tt> is just a shortcut of the
1.421 - /// following code.
1.422 - /// \code
1.423 - /// return static_cast<double>(alg.cycleLength()) / alg.cycleArcNum();
1.424 - /// \endcode
1.425 - ///
1.426 - /// \pre \ref run() or \ref findMinMean() must be called before
1.427 - /// using this function.
1.428 - double cycleMean() const {
1.429 - return static_cast<double>(_cycle_length) / _cycle_size;
1.430 - }
1.431 -
1.432 - /// \brief Return the found cycle.
1.433 - ///
1.434 - /// This function returns a const reference to the path structure
1.435 - /// storing the found cycle.
1.436 - ///
1.437 - /// \pre \ref run() or \ref findCycle() must be called before using
1.438 - /// this function.
1.439 - const Path& cycle() const {
1.440 - return *_cycle_path;
1.441 - }
1.442 -
1.443 - ///@}
1.444 -
1.445 - private:
1.446 -
1.447 - // Initialization
1.448 - void init() {
1.449 - if (!_cycle_path) {
1.450 - _local_path = true;
1.451 - _cycle_path = new Path;
1.452 - }
1.453 - _cycle_path->clear();
1.454 - _cycle_length = 0;
1.455 - _cycle_size = 1;
1.456 - _cycle_node = INVALID;
1.457 - for (NodeIt u(_gr); u != INVALID; ++u)
1.458 - _data[u].clear();
1.459 - }
1.460 -
1.461 - // Find strongly connected components and initialize _comp_nodes
1.462 - // and _out_arcs
1.463 - void findComponents() {
1.464 - _comp_num = stronglyConnectedComponents(_gr, _comp);
1.465 - _comp_nodes.resize(_comp_num);
1.466 - if (_comp_num == 1) {
1.467 - _comp_nodes[0].clear();
1.468 - for (NodeIt n(_gr); n != INVALID; ++n) {
1.469 - _comp_nodes[0].push_back(n);
1.470 - _out_arcs[n].clear();
1.471 - for (OutArcIt a(_gr, n); a != INVALID; ++a) {
1.472 - _out_arcs[n].push_back(a);
1.473 - }
1.474 - }
1.475 - } else {
1.476 - for (int i = 0; i < _comp_num; ++i)
1.477 - _comp_nodes[i].clear();
1.478 - for (NodeIt n(_gr); n != INVALID; ++n) {
1.479 - int k = _comp[n];
1.480 - _comp_nodes[k].push_back(n);
1.481 - _out_arcs[n].clear();
1.482 - for (OutArcIt a(_gr, n); a != INVALID; ++a) {
1.483 - if (_comp[_gr.target(a)] == k) _out_arcs[n].push_back(a);
1.484 - }
1.485 - }
1.486 - }
1.487 - }
1.488 -
1.489 - // Initialize path data for the current component
1.490 - bool initComponent(int comp) {
1.491 - _nodes = &(_comp_nodes[comp]);
1.492 - int n = _nodes->size();
1.493 - if (n < 1 || (n == 1 && _out_arcs[(*_nodes)[0]].size() == 0)) {
1.494 - return false;
1.495 - }
1.496 - for (int i = 0; i < n; ++i) {
1.497 - _data[(*_nodes)[i]].resize(n + 1, PathData(INF));
1.498 - }
1.499 - return true;
1.500 - }
1.501 -
1.502 - // Process all rounds of computing path data for the current component.
1.503 - // _data[v][k] is the length of a shortest directed walk from the root
1.504 - // node to node v containing exactly k arcs.
1.505 - void processRounds() {
1.506 - Node start = (*_nodes)[0];
1.507 - _data[start][0] = PathData(0);
1.508 - _process.clear();
1.509 - _process.push_back(start);
1.510 -
1.511 - int k, n = _nodes->size();
1.512 - for (k = 1; k <= n && int(_process.size()) < n; ++k) {
1.513 - processNextBuildRound(k);
1.514 - }
1.515 - for ( ; k <= n; ++k) {
1.516 - processNextFullRound(k);
1.517 - }
1.518 - }
1.519 -
1.520 - // Process one round and rebuild _process
1.521 - void processNextBuildRound(int k) {
1.522 - std::vector<Node> next;
1.523 - Node u, v;
1.524 - Arc e;
1.525 - LargeValue d;
1.526 - for (int i = 0; i < int(_process.size()); ++i) {
1.527 - u = _process[i];
1.528 - for (int j = 0; j < int(_out_arcs[u].size()); ++j) {
1.529 - e = _out_arcs[u][j];
1.530 - v = _gr.target(e);
1.531 - d = _data[u][k-1].dist + _length[e];
1.532 - if (_tolerance.less(d, _data[v][k].dist)) {
1.533 - if (_data[v][k].dist == INF) next.push_back(v);
1.534 - _data[v][k] = PathData(d, e);
1.535 - }
1.536 - }
1.537 - }
1.538 - _process.swap(next);
1.539 - }
1.540 -
1.541 - // Process one round using _nodes instead of _process
1.542 - void processNextFullRound(int k) {
1.543 - Node u, v;
1.544 - Arc e;
1.545 - LargeValue d;
1.546 - for (int i = 0; i < int(_nodes->size()); ++i) {
1.547 - u = (*_nodes)[i];
1.548 - for (int j = 0; j < int(_out_arcs[u].size()); ++j) {
1.549 - e = _out_arcs[u][j];
1.550 - v = _gr.target(e);
1.551 - d = _data[u][k-1].dist + _length[e];
1.552 - if (_tolerance.less(d, _data[v][k].dist)) {
1.553 - _data[v][k] = PathData(d, e);
1.554 - }
1.555 - }
1.556 - }
1.557 - }
1.558 -
1.559 - // Update the minimum cycle mean
1.560 - void updateMinMean() {
1.561 - int n = _nodes->size();
1.562 - for (int i = 0; i < n; ++i) {
1.563 - Node u = (*_nodes)[i];
1.564 - if (_data[u][n].dist == INF) continue;
1.565 - LargeValue length, max_length = 0;
1.566 - int size, max_size = 1;
1.567 - bool found_curr = false;
1.568 - for (int k = 0; k < n; ++k) {
1.569 - if (_data[u][k].dist == INF) continue;
1.570 - length = _data[u][n].dist - _data[u][k].dist;
1.571 - size = n - k;
1.572 - if (!found_curr || length * max_size > max_length * size) {
1.573 - found_curr = true;
1.574 - max_length = length;
1.575 - max_size = size;
1.576 - }
1.577 - }
1.578 - if ( found_curr && (_cycle_node == INVALID ||
1.579 - max_length * _cycle_size < _cycle_length * max_size) ) {
1.580 - _cycle_length = max_length;
1.581 - _cycle_size = max_size;
1.582 - _cycle_node = u;
1.583 - }
1.584 - }
1.585 - }
1.586 -
1.587 - }; //class Karp
1.588 -
1.589 - ///@}
1.590 -
1.591 -} //namespace lemon
1.592 -
1.593 -#endif //LEMON_KARP_H