1.1 --- /dev/null Thu Jan 01 00:00:00 1970 +0000
1.2 +++ b/lemon/howard_mmc.h Sun Aug 11 15:28:12 2013 +0200
1.3 @@ -0,0 +1,605 @@
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) 2003-2010
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_HOWARD_MMC_H
1.23 +#define LEMON_HOWARD_MMC_H
1.24 +
1.25 +/// \ingroup min_mean_cycle
1.26 +///
1.27 +/// \file
1.28 +/// \brief Howard'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 HowardMmc class.
1.40 + ///
1.41 + /// Default traits class of HowardMmc class.
1.42 + /// \tparam GR The type of the digraph.
1.43 + /// \tparam CM The type of the cost map.
1.44 + /// It must conform to the \ref concepts::ReadMap "ReadMap" concept.
1.45 +#ifdef DOXYGEN
1.46 + template <typename GR, typename CM>
1.47 +#else
1.48 + template <typename GR, typename CM,
1.49 + bool integer = std::numeric_limits<typename CM::Value>::is_integer>
1.50 +#endif
1.51 + struct HowardMmcDefaultTraits
1.52 + {
1.53 + /// The type of the digraph
1.54 + typedef GR Digraph;
1.55 + /// The type of the cost map
1.56 + typedef CM CostMap;
1.57 + /// The type of the arc costs
1.58 + typedef typename CostMap::Value Cost;
1.59 +
1.60 + /// \brief The large cost type used for internal computations
1.61 + ///
1.62 + /// The large cost type used for internal computations.
1.63 + /// It is \c long \c long if the \c Cost type is integer,
1.64 + /// otherwise it is \c double.
1.65 + /// \c Cost must be convertible to \c LargeCost.
1.66 + typedef double LargeCost;
1.67 +
1.68 + /// The tolerance type used for internal computations
1.69 + typedef lemon::Tolerance<LargeCost> 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 addBack() function.
1.76 + typedef lemon::Path<Digraph> Path;
1.77 + };
1.78 +
1.79 + // Default traits class for integer cost types
1.80 + template <typename GR, typename CM>
1.81 + struct HowardMmcDefaultTraits<GR, CM, true>
1.82 + {
1.83 + typedef GR Digraph;
1.84 + typedef CM CostMap;
1.85 + typedef typename CostMap::Value Cost;
1.86 +#ifdef LEMON_HAVE_LONG_LONG
1.87 + typedef long long LargeCost;
1.88 +#else
1.89 + typedef long LargeCost;
1.90 +#endif
1.91 + typedef lemon::Tolerance<LargeCost> 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 Howard's algorithm for finding a minimum
1.100 + /// mean cycle.
1.101 + ///
1.102 + /// This class implements Howard's policy iteration algorithm for finding
1.103 + /// a directed cycle of minimum mean cost in a digraph
1.104 + /// \ref amo93networkflows, \ref dasdan98minmeancycle.
1.105 + /// This class provides the most efficient algorithm for the
1.106 + /// minimum mean cycle problem, though the best known theoretical
1.107 + /// bound on its running time is exponential.
1.108 + ///
1.109 + /// \tparam GR The type of the digraph the algorithm runs on.
1.110 + /// \tparam CM The type of the cost map. The default
1.111 + /// map type is \ref concepts::Digraph::ArcMap "GR::ArcMap<int>".
1.112 + /// \tparam TR The traits class that defines various types used by the
1.113 + /// algorithm. By default, it is \ref HowardMmcDefaultTraits
1.114 + /// "HowardMmcDefaultTraits<GR, CM>".
1.115 + /// In most cases, this parameter should not be set directly,
1.116 + /// consider to use the named template parameters instead.
1.117 +#ifdef DOXYGEN
1.118 + template <typename GR, typename CM, typename TR>
1.119 +#else
1.120 + template < typename GR,
1.121 + typename CM = typename GR::template ArcMap<int>,
1.122 + typename TR = HowardMmcDefaultTraits<GR, CM> >
1.123 +#endif
1.124 + class HowardMmc
1.125 + {
1.126 + public:
1.127 +
1.128 + /// The type of the digraph
1.129 + typedef typename TR::Digraph Digraph;
1.130 + /// The type of the cost map
1.131 + typedef typename TR::CostMap CostMap;
1.132 + /// The type of the arc costs
1.133 + typedef typename TR::Cost Cost;
1.134 +
1.135 + /// \brief The large cost type
1.136 + ///
1.137 + /// The large cost type used for internal computations.
1.138 + /// By default, it is \c long \c long if the \c Cost type is integer,
1.139 + /// otherwise it is \c double.
1.140 + typedef typename TR::LargeCost LargeCost;
1.141 +
1.142 + /// The tolerance type
1.143 + typedef typename TR::Tolerance Tolerance;
1.144 +
1.145 + /// \brief The path type of the found cycles
1.146 + ///
1.147 + /// The path type of the found cycles.
1.148 + /// Using the \ref HowardMmcDefaultTraits "default traits class",
1.149 + /// it is \ref lemon::Path "Path<Digraph>".
1.150 + typedef typename TR::Path Path;
1.151 +
1.152 + /// The \ref HowardMmcDefaultTraits "traits class" of the algorithm
1.153 + typedef TR Traits;
1.154 +
1.155 + private:
1.156 +
1.157 + TEMPLATE_DIGRAPH_TYPEDEFS(Digraph);
1.158 +
1.159 + // The digraph the algorithm runs on
1.160 + const Digraph &_gr;
1.161 + // The cost of the arcs
1.162 + const CostMap &_cost;
1.163 +
1.164 + // Data for the found cycles
1.165 + bool _curr_found, _best_found;
1.166 + LargeCost _curr_cost, _best_cost;
1.167 + int _curr_size, _best_size;
1.168 + Node _curr_node, _best_node;
1.169 +
1.170 + Path *_cycle_path;
1.171 + bool _local_path;
1.172 +
1.173 + // Internal data used by the algorithm
1.174 + typename Digraph::template NodeMap<Arc> _policy;
1.175 + typename Digraph::template NodeMap<bool> _reached;
1.176 + typename Digraph::template NodeMap<int> _level;
1.177 + typename Digraph::template NodeMap<LargeCost> _dist;
1.178 +
1.179 + // Data for storing the strongly connected components
1.180 + int _comp_num;
1.181 + typename Digraph::template NodeMap<int> _comp;
1.182 + std::vector<std::vector<Node> > _comp_nodes;
1.183 + std::vector<Node>* _nodes;
1.184 + typename Digraph::template NodeMap<std::vector<Arc> > _in_arcs;
1.185 +
1.186 + // Queue used for BFS search
1.187 + std::vector<Node> _queue;
1.188 + int _qfront, _qback;
1.189 +
1.190 + Tolerance _tolerance;
1.191 +
1.192 + // Infinite constant
1.193 + const LargeCost INF;
1.194 +
1.195 + public:
1.196 +
1.197 + /// \name Named Template Parameters
1.198 + /// @{
1.199 +
1.200 + template <typename T>
1.201 + struct SetLargeCostTraits : public Traits {
1.202 + typedef T LargeCost;
1.203 + typedef lemon::Tolerance<T> Tolerance;
1.204 + };
1.205 +
1.206 + /// \brief \ref named-templ-param "Named parameter" for setting
1.207 + /// \c LargeCost type.
1.208 + ///
1.209 + /// \ref named-templ-param "Named parameter" for setting \c LargeCost
1.210 + /// type. It is used for internal computations in the algorithm.
1.211 + template <typename T>
1.212 + struct SetLargeCost
1.213 + : public HowardMmc<GR, CM, SetLargeCostTraits<T> > {
1.214 + typedef HowardMmc<GR, CM, SetLargeCostTraits<T> > Create;
1.215 + };
1.216 +
1.217 + template <typename T>
1.218 + struct SetPathTraits : public Traits {
1.219 + typedef T Path;
1.220 + };
1.221 +
1.222 + /// \brief \ref named-templ-param "Named parameter" for setting
1.223 + /// \c %Path type.
1.224 + ///
1.225 + /// \ref named-templ-param "Named parameter" for setting the \c %Path
1.226 + /// type of the found cycles.
1.227 + /// It must conform to the \ref lemon::concepts::Path "Path" concept
1.228 + /// and it must have an \c addBack() function.
1.229 + template <typename T>
1.230 + struct SetPath
1.231 + : public HowardMmc<GR, CM, SetPathTraits<T> > {
1.232 + typedef HowardMmc<GR, CM, SetPathTraits<T> > Create;
1.233 + };
1.234 +
1.235 + /// @}
1.236 +
1.237 + protected:
1.238 +
1.239 + HowardMmc() {}
1.240 +
1.241 + public:
1.242 +
1.243 + /// \brief Constructor.
1.244 + ///
1.245 + /// The constructor of the class.
1.246 + ///
1.247 + /// \param digraph The digraph the algorithm runs on.
1.248 + /// \param cost The costs of the arcs.
1.249 + HowardMmc( const Digraph &digraph,
1.250 + const CostMap &cost ) :
1.251 + _gr(digraph), _cost(cost), _best_found(false),
1.252 + _best_cost(0), _best_size(1), _cycle_path(NULL), _local_path(false),
1.253 + _policy(digraph), _reached(digraph), _level(digraph), _dist(digraph),
1.254 + _comp(digraph), _in_arcs(digraph),
1.255 + INF(std::numeric_limits<LargeCost>::has_infinity ?
1.256 + std::numeric_limits<LargeCost>::infinity() :
1.257 + std::numeric_limits<LargeCost>::max())
1.258 + {}
1.259 +
1.260 + /// Destructor.
1.261 + ~HowardMmc() {
1.262 + if (_local_path) delete _cycle_path;
1.263 + }
1.264 +
1.265 + /// \brief Set the path structure for storing the found cycle.
1.266 + ///
1.267 + /// This function sets an external path structure for storing the
1.268 + /// found cycle.
1.269 + ///
1.270 + /// If you don't call this function before calling \ref run() or
1.271 + /// \ref findCycleMean(), it will allocate a local \ref Path "path"
1.272 + /// structure. The destuctor deallocates this automatically
1.273 + /// allocated object, of course.
1.274 + ///
1.275 + /// \note The algorithm calls only the \ref lemon::Path::addBack()
1.276 + /// "addBack()" function of the given path structure.
1.277 + ///
1.278 + /// \return <tt>(*this)</tt>
1.279 + HowardMmc& cycle(Path &path) {
1.280 + if (_local_path) {
1.281 + delete _cycle_path;
1.282 + _local_path = false;
1.283 + }
1.284 + _cycle_path = &path;
1.285 + return *this;
1.286 + }
1.287 +
1.288 + /// \brief Set the tolerance used by the algorithm.
1.289 + ///
1.290 + /// This function sets the tolerance object used by the algorithm.
1.291 + ///
1.292 + /// \return <tt>(*this)</tt>
1.293 + HowardMmc& tolerance(const Tolerance& tolerance) {
1.294 + _tolerance = tolerance;
1.295 + return *this;
1.296 + }
1.297 +
1.298 + /// \brief Return a const reference to the tolerance.
1.299 + ///
1.300 + /// This function returns a const reference to the tolerance object
1.301 + /// used by the algorithm.
1.302 + const Tolerance& tolerance() const {
1.303 + return _tolerance;
1.304 + }
1.305 +
1.306 + /// \name Execution control
1.307 + /// The simplest way to execute the algorithm is to call the \ref run()
1.308 + /// function.\n
1.309 + /// If you only need the minimum mean cost, you may call
1.310 + /// \ref findCycleMean().
1.311 +
1.312 + /// @{
1.313 +
1.314 + /// \brief Run the algorithm.
1.315 + ///
1.316 + /// This function runs the algorithm.
1.317 + /// It can be called more than once (e.g. if the underlying digraph
1.318 + /// and/or the arc costs have been modified).
1.319 + ///
1.320 + /// \return \c true if a directed cycle exists in the digraph.
1.321 + ///
1.322 + /// \note <tt>mmc.run()</tt> is just a shortcut of the following code.
1.323 + /// \code
1.324 + /// return mmc.findCycleMean() && mmc.findCycle();
1.325 + /// \endcode
1.326 + bool run() {
1.327 + return findCycleMean() && findCycle();
1.328 + }
1.329 +
1.330 + /// \brief Find the minimum cycle mean.
1.331 + ///
1.332 + /// This function finds the minimum mean cost of the directed
1.333 + /// cycles in the digraph.
1.334 + ///
1.335 + /// \return \c true if a directed cycle exists in the digraph.
1.336 + bool findCycleMean() {
1.337 + // Initialize and find strongly connected components
1.338 + init();
1.339 + findComponents();
1.340 +
1.341 + // Find the minimum cycle mean in the components
1.342 + for (int comp = 0; comp < _comp_num; ++comp) {
1.343 + // Find the minimum mean cycle in the current component
1.344 + if (!buildPolicyGraph(comp)) continue;
1.345 + while (true) {
1.346 + findPolicyCycle();
1.347 + if (!computeNodeDistances()) break;
1.348 + }
1.349 + // Update the best cycle (global minimum mean cycle)
1.350 + if ( _curr_found && (!_best_found ||
1.351 + _curr_cost * _best_size < _best_cost * _curr_size) ) {
1.352 + _best_found = true;
1.353 + _best_cost = _curr_cost;
1.354 + _best_size = _curr_size;
1.355 + _best_node = _curr_node;
1.356 + }
1.357 + }
1.358 + return _best_found;
1.359 + }
1.360 +
1.361 + /// \brief Find a minimum mean directed cycle.
1.362 + ///
1.363 + /// This function finds a directed cycle of minimum mean cost
1.364 + /// in the digraph using the data computed by findCycleMean().
1.365 + ///
1.366 + /// \return \c true if a directed cycle exists in the digraph.
1.367 + ///
1.368 + /// \pre \ref findCycleMean() must be called before using this function.
1.369 + bool findCycle() {
1.370 + if (!_best_found) return false;
1.371 + _cycle_path->addBack(_policy[_best_node]);
1.372 + for ( Node v = _best_node;
1.373 + (v = _gr.target(_policy[v])) != _best_node; ) {
1.374 + _cycle_path->addBack(_policy[v]);
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 cost of the found cycle.
1.389 + ///
1.390 + /// This function returns the total cost of the found cycle.
1.391 + ///
1.392 + /// \pre \ref run() or \ref findCycleMean() must be called before
1.393 + /// using this function.
1.394 + Cost cycleCost() const {
1.395 + return static_cast<Cost>(_best_cost);
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 findCycleMean() must be called before
1.403 + /// using this function.
1.404 + int cycleSize() const {
1.405 + return _best_size;
1.406 + }
1.407 +
1.408 + /// \brief Return the mean cost of the found cycle.
1.409 + ///
1.410 + /// This function returns the mean cost 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.cycleCost()) / alg.cycleSize();
1.416 + /// \endcode
1.417 + ///
1.418 + /// \pre \ref run() or \ref findCycleMean() must be called before
1.419 + /// using this function.
1.420 + double cycleMean() const {
1.421 + return static_cast<double>(_best_cost) / _best_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 + // Initialize
1.440 + void init() {
1.441 + if (!_cycle_path) {
1.442 + _local_path = true;
1.443 + _cycle_path = new Path;
1.444 + }
1.445 + _queue.resize(countNodes(_gr));
1.446 + _best_found = false;
1.447 + _best_cost = 0;
1.448 + _best_size = 1;
1.449 + _cycle_path->clear();
1.450 + }
1.451 +
1.452 + // Find strongly connected components and initialize _comp_nodes
1.453 + // and _in_arcs
1.454 + void findComponents() {
1.455 + _comp_num = stronglyConnectedComponents(_gr, _comp);
1.456 + _comp_nodes.resize(_comp_num);
1.457 + if (_comp_num == 1) {
1.458 + _comp_nodes[0].clear();
1.459 + for (NodeIt n(_gr); n != INVALID; ++n) {
1.460 + _comp_nodes[0].push_back(n);
1.461 + _in_arcs[n].clear();
1.462 + for (InArcIt a(_gr, n); a != INVALID; ++a) {
1.463 + _in_arcs[n].push_back(a);
1.464 + }
1.465 + }
1.466 + } else {
1.467 + for (int i = 0; i < _comp_num; ++i)
1.468 + _comp_nodes[i].clear();
1.469 + for (NodeIt n(_gr); n != INVALID; ++n) {
1.470 + int k = _comp[n];
1.471 + _comp_nodes[k].push_back(n);
1.472 + _in_arcs[n].clear();
1.473 + for (InArcIt a(_gr, n); a != INVALID; ++a) {
1.474 + if (_comp[_gr.source(a)] == k) _in_arcs[n].push_back(a);
1.475 + }
1.476 + }
1.477 + }
1.478 + }
1.479 +
1.480 + // Build the policy graph in the given strongly connected component
1.481 + // (the out-degree of every node is 1)
1.482 + bool buildPolicyGraph(int comp) {
1.483 + _nodes = &(_comp_nodes[comp]);
1.484 + if (_nodes->size() < 1 ||
1.485 + (_nodes->size() == 1 && _in_arcs[(*_nodes)[0]].size() == 0)) {
1.486 + return false;
1.487 + }
1.488 + for (int i = 0; i < int(_nodes->size()); ++i) {
1.489 + _dist[(*_nodes)[i]] = INF;
1.490 + }
1.491 + Node u, v;
1.492 + Arc e;
1.493 + for (int i = 0; i < int(_nodes->size()); ++i) {
1.494 + v = (*_nodes)[i];
1.495 + for (int j = 0; j < int(_in_arcs[v].size()); ++j) {
1.496 + e = _in_arcs[v][j];
1.497 + u = _gr.source(e);
1.498 + if (_cost[e] < _dist[u]) {
1.499 + _dist[u] = _cost[e];
1.500 + _policy[u] = e;
1.501 + }
1.502 + }
1.503 + }
1.504 + return true;
1.505 + }
1.506 +
1.507 + // Find the minimum mean cycle in the policy graph
1.508 + void findPolicyCycle() {
1.509 + for (int i = 0; i < int(_nodes->size()); ++i) {
1.510 + _level[(*_nodes)[i]] = -1;
1.511 + }
1.512 + LargeCost ccost;
1.513 + int csize;
1.514 + Node u, v;
1.515 + _curr_found = false;
1.516 + for (int i = 0; i < int(_nodes->size()); ++i) {
1.517 + u = (*_nodes)[i];
1.518 + if (_level[u] >= 0) continue;
1.519 + for (; _level[u] < 0; u = _gr.target(_policy[u])) {
1.520 + _level[u] = i;
1.521 + }
1.522 + if (_level[u] == i) {
1.523 + // A cycle is found
1.524 + ccost = _cost[_policy[u]];
1.525 + csize = 1;
1.526 + for (v = u; (v = _gr.target(_policy[v])) != u; ) {
1.527 + ccost += _cost[_policy[v]];
1.528 + ++csize;
1.529 + }
1.530 + if ( !_curr_found ||
1.531 + (ccost * _curr_size < _curr_cost * csize) ) {
1.532 + _curr_found = true;
1.533 + _curr_cost = ccost;
1.534 + _curr_size = csize;
1.535 + _curr_node = u;
1.536 + }
1.537 + }
1.538 + }
1.539 + }
1.540 +
1.541 + // Contract the policy graph and compute node distances
1.542 + bool computeNodeDistances() {
1.543 + // Find the component of the main cycle and compute node distances
1.544 + // using reverse BFS
1.545 + for (int i = 0; i < int(_nodes->size()); ++i) {
1.546 + _reached[(*_nodes)[i]] = false;
1.547 + }
1.548 + _qfront = _qback = 0;
1.549 + _queue[0] = _curr_node;
1.550 + _reached[_curr_node] = true;
1.551 + _dist[_curr_node] = 0;
1.552 + Node u, v;
1.553 + Arc e;
1.554 + while (_qfront <= _qback) {
1.555 + v = _queue[_qfront++];
1.556 + for (int j = 0; j < int(_in_arcs[v].size()); ++j) {
1.557 + e = _in_arcs[v][j];
1.558 + u = _gr.source(e);
1.559 + if (_policy[u] == e && !_reached[u]) {
1.560 + _reached[u] = true;
1.561 + _dist[u] = _dist[v] + _cost[e] * _curr_size - _curr_cost;
1.562 + _queue[++_qback] = u;
1.563 + }
1.564 + }
1.565 + }
1.566 +
1.567 + // Connect all other nodes to this component and compute node
1.568 + // distances using reverse BFS
1.569 + _qfront = 0;
1.570 + while (_qback < int(_nodes->size())-1) {
1.571 + v = _queue[_qfront++];
1.572 + for (int j = 0; j < int(_in_arcs[v].size()); ++j) {
1.573 + e = _in_arcs[v][j];
1.574 + u = _gr.source(e);
1.575 + if (!_reached[u]) {
1.576 + _reached[u] = true;
1.577 + _policy[u] = e;
1.578 + _dist[u] = _dist[v] + _cost[e] * _curr_size - _curr_cost;
1.579 + _queue[++_qback] = u;
1.580 + }
1.581 + }
1.582 + }
1.583 +
1.584 + // Improve node distances
1.585 + bool improved = false;
1.586 + for (int i = 0; i < int(_nodes->size()); ++i) {
1.587 + v = (*_nodes)[i];
1.588 + for (int j = 0; j < int(_in_arcs[v].size()); ++j) {
1.589 + e = _in_arcs[v][j];
1.590 + u = _gr.source(e);
1.591 + LargeCost delta = _dist[v] + _cost[e] * _curr_size - _curr_cost;
1.592 + if (_tolerance.less(delta, _dist[u])) {
1.593 + _dist[u] = delta;
1.594 + _policy[u] = e;
1.595 + improved = true;
1.596 + }
1.597 + }
1.598 + }
1.599 + return improved;
1.600 + }
1.601 +
1.602 + }; //class HowardMmc
1.603 +
1.604 + ///@}
1.605 +
1.606 +} //namespace lemon
1.607 +
1.608 +#endif //LEMON_HOWARD_MMC_H