1.1 --- a/lemon/min_mean_cycle.h Mon Aug 03 14:35:38 2009 +0200
1.2 +++ b/lemon/min_mean_cycle.h Thu Aug 06 20:12:43 2009 +0200
1.3 @@ -74,26 +74,32 @@
1.4 // The length of the arcs
1.5 const LengthMap &_length;
1.6
1.7 - // The total length of the found cycle
1.8 - Value _cycle_length;
1.9 - // The number of arcs on the found cycle
1.10 - int _cycle_size;
1.11 - // The found cycle
1.12 + // Data for the found cycles
1.13 + bool _curr_found, _best_found;
1.14 + Value _curr_length, _best_length;
1.15 + int _curr_size, _best_size;
1.16 + Node _curr_node, _best_node;
1.17 +
1.18 Path *_cycle_path;
1.19 + bool _local_path;
1.20
1.21 - bool _local_path;
1.22 - bool _cycle_found;
1.23 - Node _cycle_node;
1.24 + // Internal data used by the algorithm
1.25 + typename Digraph::template NodeMap<Arc> _policy;
1.26 + typename Digraph::template NodeMap<bool> _reached;
1.27 + typename Digraph::template NodeMap<int> _level;
1.28 + typename Digraph::template NodeMap<double> _dist;
1.29
1.30 - typename Digraph::template NodeMap<bool> _reached;
1.31 - typename Digraph::template NodeMap<double> _dist;
1.32 - typename Digraph::template NodeMap<Arc> _policy;
1.33 -
1.34 + // Data for storing the strongly connected components
1.35 + int _comp_num;
1.36 typename Digraph::template NodeMap<int> _comp;
1.37 - int _comp_num;
1.38 -
1.39 - std::vector<Node> _nodes;
1.40 - std::vector<Arc> _arcs;
1.41 + std::vector<std::vector<Node> > _comp_nodes;
1.42 + std::vector<Node>* _nodes;
1.43 + typename Digraph::template NodeMap<std::vector<Arc> > _in_arcs;
1.44 +
1.45 + // Queue used for BFS search
1.46 + std::vector<Node> _queue;
1.47 + int _qfront, _qback;
1.48 +
1.49 Tolerance<double> _tol;
1.50
1.51 public:
1.52 @@ -106,9 +112,9 @@
1.53 /// \param length The lengths (costs) of the arcs.
1.54 MinMeanCycle( const Digraph &digraph,
1.55 const LengthMap &length ) :
1.56 - _gr(digraph), _length(length), _cycle_length(0), _cycle_size(-1),
1.57 - _cycle_path(NULL), _local_path(false), _reached(digraph),
1.58 - _dist(digraph), _policy(digraph), _comp(digraph)
1.59 + _gr(digraph), _length(length), _cycle_path(NULL), _local_path(false),
1.60 + _policy(digraph), _reached(digraph), _level(digraph), _dist(digraph),
1.61 + _comp(digraph), _in_arcs(digraph)
1.62 {}
1.63
1.64 /// Destructor.
1.65 @@ -172,26 +178,28 @@
1.66 ///
1.67 /// \return \c true if a directed cycle exists in the digraph.
1.68 bool findMinMean() {
1.69 - // Initialize
1.70 - _tol.epsilon(1e-6);
1.71 - if (!_cycle_path) {
1.72 - _local_path = true;
1.73 - _cycle_path = new Path;
1.74 - }
1.75 - _cycle_path->clear();
1.76 - _cycle_found = false;
1.77 -
1.78 + // Initialize and find strongly connected components
1.79 + init();
1.80 + findComponents();
1.81 +
1.82 // Find the minimum cycle mean in the components
1.83 - _comp_num = stronglyConnectedComponents(_gr, _comp);
1.84 for (int comp = 0; comp < _comp_num; ++comp) {
1.85 - if (!initCurrentComponent(comp)) continue;
1.86 + // Find the minimum mean cycle in the current component
1.87 + if (!buildPolicyGraph(comp)) continue;
1.88 while (true) {
1.89 - if (!findPolicyCycles()) break;
1.90 - contractPolicyGraph(comp);
1.91 + findPolicyCycle();
1.92 if (!computeNodeDistances()) break;
1.93 }
1.94 + // Update the best cycle (global minimum mean cycle)
1.95 + if ( !_best_found || (_curr_found &&
1.96 + _curr_length * _best_size < _best_length * _curr_size) ) {
1.97 + _best_found = true;
1.98 + _best_length = _curr_length;
1.99 + _best_size = _curr_size;
1.100 + _best_node = _curr_node;
1.101 + }
1.102 }
1.103 - return _cycle_found;
1.104 + return _best_found;
1.105 }
1.106
1.107 /// \brief Find a minimum mean directed cycle.
1.108 @@ -203,10 +211,10 @@
1.109 ///
1.110 /// \pre \ref findMinMean() must be called before using this function.
1.111 bool findCycle() {
1.112 - if (!_cycle_found) return false;
1.113 - _cycle_path->addBack(_policy[_cycle_node]);
1.114 - for ( Node v = _cycle_node;
1.115 - (v = _gr.target(_policy[v])) != _cycle_node; ) {
1.116 + if (!_best_found) return false;
1.117 + _cycle_path->addBack(_policy[_best_node]);
1.118 + for ( Node v = _best_node;
1.119 + (v = _gr.target(_policy[v])) != _best_node; ) {
1.120 _cycle_path->addBack(_policy[v]);
1.121 }
1.122 return true;
1.123 @@ -225,36 +233,36 @@
1.124 ///
1.125 /// This function returns the total length of the found cycle.
1.126 ///
1.127 - /// \pre \ref run() or \ref findCycle() must be called before
1.128 + /// \pre \ref run() or \ref findMinMean() must be called before
1.129 /// using this function.
1.130 Value cycleLength() const {
1.131 - return _cycle_length;
1.132 + return _best_length;
1.133 }
1.134
1.135 /// \brief Return the number of arcs on the found cycle.
1.136 ///
1.137 /// This function returns the number of arcs on the found cycle.
1.138 ///
1.139 - /// \pre \ref run() or \ref findCycle() must be called before
1.140 + /// \pre \ref run() or \ref findMinMean() must be called before
1.141 /// using this function.
1.142 int cycleArcNum() const {
1.143 - return _cycle_size;
1.144 + return _best_size;
1.145 }
1.146
1.147 /// \brief Return the mean length of the found cycle.
1.148 ///
1.149 /// This function returns the mean length of the found cycle.
1.150 ///
1.151 - /// \note <tt>mmc.cycleMean()</tt> is just a shortcut of the
1.152 + /// \note <tt>alg.cycleMean()</tt> is just a shortcut of the
1.153 /// following code.
1.154 /// \code
1.155 - /// return double(mmc.cycleLength()) / mmc.cycleArcNum();
1.156 + /// return static_cast<double>(alg.cycleLength()) / alg.cycleArcNum();
1.157 /// \endcode
1.158 ///
1.159 /// \pre \ref run() or \ref findMinMean() must be called before
1.160 /// using this function.
1.161 double cycleMean() const {
1.162 - return double(_cycle_length) / _cycle_size;
1.163 + return static_cast<double>(_best_length) / _best_size;
1.164 }
1.165
1.166 /// \brief Return the found cycle.
1.167 @@ -274,153 +282,166 @@
1.168
1.169 private:
1.170
1.171 - // Initialize the internal data structures for the current strongly
1.172 - // connected component and create the policy graph.
1.173 - // The policy graph can be represented by the _policy map because
1.174 - // the out-degree of every node is 1.
1.175 - bool initCurrentComponent(int comp) {
1.176 - // Find the nodes of the current component
1.177 - _nodes.clear();
1.178 - for (NodeIt n(_gr); n != INVALID; ++n) {
1.179 - if (_comp[n] == comp) _nodes.push_back(n);
1.180 + // Initialize
1.181 + void init() {
1.182 + _tol.epsilon(1e-6);
1.183 + if (!_cycle_path) {
1.184 + _local_path = true;
1.185 + _cycle_path = new Path;
1.186 }
1.187 - if (_nodes.size() <= 1) return false;
1.188 - // Find the arcs of the current component
1.189 - _arcs.clear();
1.190 - for (ArcIt e(_gr); e != INVALID; ++e) {
1.191 - if ( _comp[_gr.source(e)] == comp &&
1.192 - _comp[_gr.target(e)] == comp )
1.193 - _arcs.push_back(e);
1.194 + _queue.resize(countNodes(_gr));
1.195 + _best_found = false;
1.196 + _best_length = 0;
1.197 + _best_size = 1;
1.198 + _cycle_path->clear();
1.199 + }
1.200 +
1.201 + // Find strongly connected components and initialize _comp_nodes
1.202 + // and _in_arcs
1.203 + void findComponents() {
1.204 + _comp_num = stronglyConnectedComponents(_gr, _comp);
1.205 + _comp_nodes.resize(_comp_num);
1.206 + if (_comp_num == 1) {
1.207 + _comp_nodes[0].clear();
1.208 + for (NodeIt n(_gr); n != INVALID; ++n) {
1.209 + _comp_nodes[0].push_back(n);
1.210 + _in_arcs[n].clear();
1.211 + for (InArcIt a(_gr, n); a != INVALID; ++a) {
1.212 + _in_arcs[n].push_back(a);
1.213 + }
1.214 + }
1.215 + } else {
1.216 + for (int i = 0; i < _comp_num; ++i)
1.217 + _comp_nodes[i].clear();
1.218 + for (NodeIt n(_gr); n != INVALID; ++n) {
1.219 + int k = _comp[n];
1.220 + _comp_nodes[k].push_back(n);
1.221 + _in_arcs[n].clear();
1.222 + for (InArcIt a(_gr, n); a != INVALID; ++a) {
1.223 + if (_comp[_gr.source(a)] == k) _in_arcs[n].push_back(a);
1.224 + }
1.225 + }
1.226 }
1.227 - // Initialize _reached, _dist, _policy maps
1.228 - for (int i = 0; i < int(_nodes.size()); ++i) {
1.229 - _reached[_nodes[i]] = false;
1.230 - _policy[_nodes[i]] = INVALID;
1.231 + }
1.232 +
1.233 + // Build the policy graph in the given strongly connected component
1.234 + // (the out-degree of every node is 1)
1.235 + bool buildPolicyGraph(int comp) {
1.236 + _nodes = &(_comp_nodes[comp]);
1.237 + if (_nodes->size() < 1 ||
1.238 + (_nodes->size() == 1 && _in_arcs[(*_nodes)[0]].size() == 0)) {
1.239 + return false;
1.240 }
1.241 - Node u; Arc e;
1.242 - for (int j = 0; j < int(_arcs.size()); ++j) {
1.243 - e = _arcs[j];
1.244 - u = _gr.source(e);
1.245 - if (!_reached[u] || _length[e] < _dist[u]) {
1.246 - _dist[u] = _length[e];
1.247 - _policy[u] = e;
1.248 - _reached[u] = true;
1.249 + for (int i = 0; i < int(_nodes->size()); ++i) {
1.250 + _dist[(*_nodes)[i]] = std::numeric_limits<double>::max();
1.251 + }
1.252 + Node u, v;
1.253 + Arc e;
1.254 + for (int i = 0; i < int(_nodes->size()); ++i) {
1.255 + v = (*_nodes)[i];
1.256 + for (int j = 0; j < int(_in_arcs[v].size()); ++j) {
1.257 + e = _in_arcs[v][j];
1.258 + u = _gr.source(e);
1.259 + if (_length[e] < _dist[u]) {
1.260 + _dist[u] = _length[e];
1.261 + _policy[u] = e;
1.262 + }
1.263 }
1.264 }
1.265 return true;
1.266 }
1.267
1.268 - // Find all cycles in the policy graph.
1.269 - // Set _cycle_found to true if a cycle is found and set
1.270 - // _cycle_length, _cycle_size, _cycle_node to represent the minimum
1.271 - // mean cycle in the policy graph.
1.272 - bool findPolicyCycles() {
1.273 - typename Digraph::template NodeMap<int> level(_gr, -1);
1.274 - bool curr_cycle_found = false;
1.275 + // Find the minimum mean cycle in the policy graph
1.276 + void findPolicyCycle() {
1.277 + for (int i = 0; i < int(_nodes->size()); ++i) {
1.278 + _level[(*_nodes)[i]] = -1;
1.279 + }
1.280 Value clength;
1.281 int csize;
1.282 - int path_cnt = 0;
1.283 Node u, v;
1.284 - // Searching for cycles
1.285 - for (int i = 0; i < int(_nodes.size()); ++i) {
1.286 - if (level[_nodes[i]] < 0) {
1.287 - u = _nodes[i];
1.288 - level[u] = path_cnt;
1.289 - while (level[u = _gr.target(_policy[u])] < 0)
1.290 - level[u] = path_cnt;
1.291 - if (level[u] == path_cnt) {
1.292 - // A cycle is found
1.293 - curr_cycle_found = true;
1.294 - clength = _length[_policy[u]];
1.295 - csize = 1;
1.296 - for (v = u; (v = _gr.target(_policy[v])) != u; ) {
1.297 - clength += _length[_policy[v]];
1.298 - ++csize;
1.299 - }
1.300 - if ( !_cycle_found ||
1.301 - clength * _cycle_size < _cycle_length * csize ) {
1.302 - _cycle_found = true;
1.303 - _cycle_length = clength;
1.304 - _cycle_size = csize;
1.305 - _cycle_node = u;
1.306 - }
1.307 + _curr_found = false;
1.308 + for (int i = 0; i < int(_nodes->size()); ++i) {
1.309 + u = (*_nodes)[i];
1.310 + if (_level[u] >= 0) continue;
1.311 + for (; _level[u] < 0; u = _gr.target(_policy[u])) {
1.312 + _level[u] = i;
1.313 + }
1.314 + if (_level[u] == i) {
1.315 + // A cycle is found
1.316 + clength = _length[_policy[u]];
1.317 + csize = 1;
1.318 + for (v = u; (v = _gr.target(_policy[v])) != u; ) {
1.319 + clength += _length[_policy[v]];
1.320 + ++csize;
1.321 }
1.322 - ++path_cnt;
1.323 - }
1.324 - }
1.325 - return curr_cycle_found;
1.326 - }
1.327 -
1.328 - // Contract the policy graph to be connected by cutting all cycles
1.329 - // except for the main cycle (i.e. the minimum mean cycle).
1.330 - void contractPolicyGraph(int comp) {
1.331 - // Find the component of the main cycle using reverse BFS search
1.332 - typename Digraph::template NodeMap<int> found(_gr, false);
1.333 - std::deque<Node> queue;
1.334 - queue.push_back(_cycle_node);
1.335 - found[_cycle_node] = true;
1.336 - Node u, v;
1.337 - while (!queue.empty()) {
1.338 - v = queue.front(); queue.pop_front();
1.339 - for (InArcIt e(_gr, v); e != INVALID; ++e) {
1.340 - u = _gr.source(e);
1.341 - if (_policy[u] == e && !found[u]) {
1.342 - found[u] = true;
1.343 - queue.push_back(u);
1.344 - }
1.345 - }
1.346 - }
1.347 - // Connect all other nodes to this component using reverse BFS search
1.348 - queue.clear();
1.349 - for (int i = 0; i < int(_nodes.size()); ++i)
1.350 - if (found[_nodes[i]]) queue.push_back(_nodes[i]);
1.351 - int found_cnt = queue.size();
1.352 - while (found_cnt < int(_nodes.size())) {
1.353 - v = queue.front(); queue.pop_front();
1.354 - for (InArcIt e(_gr, v); e != INVALID; ++e) {
1.355 - u = _gr.source(e);
1.356 - if (_comp[u] == comp && !found[u]) {
1.357 - found[u] = true;
1.358 - ++found_cnt;
1.359 - _policy[u] = e;
1.360 - queue.push_back(u);
1.361 + if ( !_curr_found ||
1.362 + (clength * _curr_size < _curr_length * csize) ) {
1.363 + _curr_found = true;
1.364 + _curr_length = clength;
1.365 + _curr_size = csize;
1.366 + _curr_node = u;
1.367 }
1.368 }
1.369 }
1.370 }
1.371
1.372 - // Compute node distances in the policy graph and update the
1.373 - // policy graph if the node distances can be improved.
1.374 + // Contract the policy graph and compute node distances
1.375 bool computeNodeDistances() {
1.376 - // Compute node distances using reverse BFS search
1.377 - double cycle_mean = double(_cycle_length) / _cycle_size;
1.378 - typename Digraph::template NodeMap<int> found(_gr, false);
1.379 - std::deque<Node> queue;
1.380 - queue.push_back(_cycle_node);
1.381 - found[_cycle_node] = true;
1.382 - _dist[_cycle_node] = 0;
1.383 + // Find the component of the main cycle and compute node distances
1.384 + // using reverse BFS
1.385 + for (int i = 0; i < int(_nodes->size()); ++i) {
1.386 + _reached[(*_nodes)[i]] = false;
1.387 + }
1.388 + double curr_mean = double(_curr_length) / _curr_size;
1.389 + _qfront = _qback = 0;
1.390 + _queue[0] = _curr_node;
1.391 + _reached[_curr_node] = true;
1.392 + _dist[_curr_node] = 0;
1.393 Node u, v;
1.394 - while (!queue.empty()) {
1.395 - v = queue.front(); queue.pop_front();
1.396 - for (InArcIt e(_gr, v); e != INVALID; ++e) {
1.397 + Arc e;
1.398 + while (_qfront <= _qback) {
1.399 + v = _queue[_qfront++];
1.400 + for (int j = 0; j < int(_in_arcs[v].size()); ++j) {
1.401 + e = _in_arcs[v][j];
1.402 u = _gr.source(e);
1.403 - if (_policy[u] == e && !found[u]) {
1.404 - found[u] = true;
1.405 - _dist[u] = _dist[v] + _length[e] - cycle_mean;
1.406 - queue.push_back(u);
1.407 + if (_policy[u] == e && !_reached[u]) {
1.408 + _reached[u] = true;
1.409 + _dist[u] = _dist[v] + _length[e] - curr_mean;
1.410 + _queue[++_qback] = u;
1.411 }
1.412 }
1.413 }
1.414 - // Improving node distances
1.415 +
1.416 + // Connect all other nodes to this component and compute node
1.417 + // distances using reverse BFS
1.418 + _qfront = 0;
1.419 + while (_qback < int(_nodes->size())-1) {
1.420 + v = _queue[_qfront++];
1.421 + for (int j = 0; j < int(_in_arcs[v].size()); ++j) {
1.422 + e = _in_arcs[v][j];
1.423 + u = _gr.source(e);
1.424 + if (!_reached[u]) {
1.425 + _reached[u] = true;
1.426 + _policy[u] = e;
1.427 + _dist[u] = _dist[v] + _length[e] - curr_mean;
1.428 + _queue[++_qback] = u;
1.429 + }
1.430 + }
1.431 + }
1.432 +
1.433 + // Improve node distances
1.434 bool improved = false;
1.435 - for (int j = 0; j < int(_arcs.size()); ++j) {
1.436 - Arc e = _arcs[j];
1.437 - u = _gr.source(e); v = _gr.target(e);
1.438 - double delta = _dist[v] + _length[e] - cycle_mean;
1.439 - if (_tol.less(delta, _dist[u])) {
1.440 - improved = true;
1.441 - _dist[u] = delta;
1.442 - _policy[u] = e;
1.443 + for (int i = 0; i < int(_nodes->size()); ++i) {
1.444 + v = (*_nodes)[i];
1.445 + for (int j = 0; j < int(_in_arcs[v].size()); ++j) {
1.446 + e = _in_arcs[v][j];
1.447 + u = _gr.source(e);
1.448 + double delta = _dist[v] + _length[e] - curr_mean;
1.449 + if (_tol.less(delta, _dist[u])) {
1.450 + _dist[u] = delta;
1.451 + _policy[u] = e;
1.452 + improved = true;
1.453 + }
1.454 }
1.455 }
1.456 return improved;