COIN-OR::LEMON - Graph Library

Changeset 760:83ce7ce39f21 in lemon-1.2 for lemon


Ignore:
Timestamp:
08/06/09 20:12:43 (10 years ago)
Author:
Peter Kovacs <kpeter@…>
Branch:
default
Phase:
public
Message:

Rework and fix the implementation of MinMeanCycle? (#179)

  • Fix the handling of the cycle means.
  • Many implementation improvements:
    • More efficient data storage for the strongly connected components.
    • Better handling of BFS queues.
    • Merge consecutive BFS searches (perform two BFS searches instead of three).

This version is about two times faster on average and an order of
magnitude faster if there are a lot of strongly connected components.

File:
1 edited

Legend:

Unmodified
Added
Removed
  • lemon/min_mean_cycle.h

    r759 r760  
    7575    const LengthMap &_length;
    7676
    77     // The total length of the found cycle
    78     Value _cycle_length;
    79     // The number of arcs on the found cycle
    80     int _cycle_size;
    81     // The found cycle
     77    // Data for the found cycles
     78    bool _curr_found, _best_found;
     79    Value _curr_length, _best_length;
     80    int _curr_size, _best_size;
     81    Node _curr_node, _best_node;
     82
    8283    Path *_cycle_path;
    83 
    8484    bool _local_path;
    85     bool _cycle_found;
    86     Node _cycle_node;
    87 
     85
     86    // Internal data used by the algorithm
     87    typename Digraph::template NodeMap<Arc> _policy;
    8888    typename Digraph::template NodeMap<bool> _reached;
     89    typename Digraph::template NodeMap<int> _level;
    8990    typename Digraph::template NodeMap<double> _dist;
    90     typename Digraph::template NodeMap<Arc> _policy;
    91 
     91
     92    // Data for storing the strongly connected components
     93    int _comp_num;
    9294    typename Digraph::template NodeMap<int> _comp;
    93     int _comp_num;
    94 
    95     std::vector<Node> _nodes;
    96     std::vector<Arc> _arcs;
     95    std::vector<std::vector<Node> > _comp_nodes;
     96    std::vector<Node>* _nodes;
     97    typename Digraph::template NodeMap<std::vector<Arc> > _in_arcs;
     98   
     99    // Queue used for BFS search
     100    std::vector<Node> _queue;
     101    int _qfront, _qback;
     102   
    97103    Tolerance<double> _tol;
    98104
     
    107113    MinMeanCycle( const Digraph &digraph,
    108114                  const LengthMap &length ) :
    109       _gr(digraph), _length(length), _cycle_length(0), _cycle_size(-1),
    110       _cycle_path(NULL), _local_path(false), _reached(digraph),
    111       _dist(digraph), _policy(digraph), _comp(digraph)
     115      _gr(digraph), _length(length), _cycle_path(NULL), _local_path(false),
     116      _policy(digraph), _reached(digraph), _level(digraph), _dist(digraph),
     117      _comp(digraph), _in_arcs(digraph)
    112118    {}
    113119
     
    173179    /// \return \c true if a directed cycle exists in the digraph.
    174180    bool findMinMean() {
    175       // Initialize
     181      // Initialize and find strongly connected components
     182      init();
     183      findComponents();
     184     
     185      // Find the minimum cycle mean in the components
     186      for (int comp = 0; comp < _comp_num; ++comp) {
     187        // Find the minimum mean cycle in the current component
     188        if (!buildPolicyGraph(comp)) continue;
     189        while (true) {
     190          findPolicyCycle();
     191          if (!computeNodeDistances()) break;
     192        }
     193        // Update the best cycle (global minimum mean cycle)
     194        if ( !_best_found || (_curr_found &&
     195             _curr_length * _best_size < _best_length * _curr_size) ) {
     196          _best_found = true;
     197          _best_length = _curr_length;
     198          _best_size = _curr_size;
     199          _best_node = _curr_node;
     200        }
     201      }
     202      return _best_found;
     203    }
     204
     205    /// \brief Find a minimum mean directed cycle.
     206    ///
     207    /// This function finds a directed cycle of minimum mean length
     208    /// in the digraph using the data computed by findMinMean().
     209    ///
     210    /// \return \c true if a directed cycle exists in the digraph.
     211    ///
     212    /// \pre \ref findMinMean() must be called before using this function.
     213    bool findCycle() {
     214      if (!_best_found) return false;
     215      _cycle_path->addBack(_policy[_best_node]);
     216      for ( Node v = _best_node;
     217            (v = _gr.target(_policy[v])) != _best_node; ) {
     218        _cycle_path->addBack(_policy[v]);
     219      }
     220      return true;
     221    }
     222
     223    /// @}
     224
     225    /// \name Query Functions
     226    /// The results of the algorithm can be obtained using these
     227    /// functions.\n
     228    /// The algorithm should be executed before using them.
     229
     230    /// @{
     231
     232    /// \brief Return the total length of the found cycle.
     233    ///
     234    /// This function returns the total length of the found cycle.
     235    ///
     236    /// \pre \ref run() or \ref findMinMean() must be called before
     237    /// using this function.
     238    Value cycleLength() const {
     239      return _best_length;
     240    }
     241
     242    /// \brief Return the number of arcs on the found cycle.
     243    ///
     244    /// This function returns the number of arcs on the found cycle.
     245    ///
     246    /// \pre \ref run() or \ref findMinMean() must be called before
     247    /// using this function.
     248    int cycleArcNum() const {
     249      return _best_size;
     250    }
     251
     252    /// \brief Return the mean length of the found cycle.
     253    ///
     254    /// This function returns the mean length of the found cycle.
     255    ///
     256    /// \note <tt>alg.cycleMean()</tt> is just a shortcut of the
     257    /// following code.
     258    /// \code
     259    ///   return static_cast<double>(alg.cycleLength()) / alg.cycleArcNum();
     260    /// \endcode
     261    ///
     262    /// \pre \ref run() or \ref findMinMean() must be called before
     263    /// using this function.
     264    double cycleMean() const {
     265      return static_cast<double>(_best_length) / _best_size;
     266    }
     267
     268    /// \brief Return the found cycle.
     269    ///
     270    /// This function returns a const reference to the path structure
     271    /// storing the found cycle.
     272    ///
     273    /// \pre \ref run() or \ref findCycle() must be called before using
     274    /// this function.
     275    ///
     276    /// \sa cyclePath()
     277    const Path& cycle() const {
     278      return *_cycle_path;
     279    }
     280
     281    ///@}
     282
     283  private:
     284
     285    // Initialize
     286    void init() {
    176287      _tol.epsilon(1e-6);
    177288      if (!_cycle_path) {
     
    179290        _cycle_path = new Path;
    180291      }
     292      _queue.resize(countNodes(_gr));
     293      _best_found = false;
     294      _best_length = 0;
     295      _best_size = 1;
    181296      _cycle_path->clear();
    182       _cycle_found = false;
    183 
    184       // Find the minimum cycle mean in the components
     297    }
     298   
     299    // Find strongly connected components and initialize _comp_nodes
     300    // and _in_arcs
     301    void findComponents() {
    185302      _comp_num = stronglyConnectedComponents(_gr, _comp);
    186       for (int comp = 0; comp < _comp_num; ++comp) {
    187         if (!initCurrentComponent(comp)) continue;
    188         while (true) {
    189           if (!findPolicyCycles()) break;
    190           contractPolicyGraph(comp);
    191           if (!computeNodeDistances()) break;
    192         }
    193       }
    194       return _cycle_found;
    195     }
    196 
    197     /// \brief Find a minimum mean directed cycle.
    198     ///
    199     /// This function finds a directed cycle of minimum mean length
    200     /// in the digraph using the data computed by findMinMean().
    201     ///
    202     /// \return \c true if a directed cycle exists in the digraph.
    203     ///
    204     /// \pre \ref findMinMean() must be called before using this function.
    205     bool findCycle() {
    206       if (!_cycle_found) return false;
    207       _cycle_path->addBack(_policy[_cycle_node]);
    208       for ( Node v = _cycle_node;
    209             (v = _gr.target(_policy[v])) != _cycle_node; ) {
    210         _cycle_path->addBack(_policy[v]);
     303      _comp_nodes.resize(_comp_num);
     304      if (_comp_num == 1) {
     305        _comp_nodes[0].clear();
     306        for (NodeIt n(_gr); n != INVALID; ++n) {
     307          _comp_nodes[0].push_back(n);
     308          _in_arcs[n].clear();
     309          for (InArcIt a(_gr, n); a != INVALID; ++a) {
     310            _in_arcs[n].push_back(a);
     311          }
     312        }
     313      } else {
     314        for (int i = 0; i < _comp_num; ++i)
     315          _comp_nodes[i].clear();
     316        for (NodeIt n(_gr); n != INVALID; ++n) {
     317          int k = _comp[n];
     318          _comp_nodes[k].push_back(n);
     319          _in_arcs[n].clear();
     320          for (InArcIt a(_gr, n); a != INVALID; ++a) {
     321            if (_comp[_gr.source(a)] == k) _in_arcs[n].push_back(a);
     322          }
     323        }
     324      }
     325    }
     326
     327    // Build the policy graph in the given strongly connected component
     328    // (the out-degree of every node is 1)
     329    bool buildPolicyGraph(int comp) {
     330      _nodes = &(_comp_nodes[comp]);
     331      if (_nodes->size() < 1 ||
     332          (_nodes->size() == 1 && _in_arcs[(*_nodes)[0]].size() == 0)) {
     333        return false;
     334      }
     335      for (int i = 0; i < int(_nodes->size()); ++i) {
     336        _dist[(*_nodes)[i]] = std::numeric_limits<double>::max();
     337      }
     338      Node u, v;
     339      Arc e;
     340      for (int i = 0; i < int(_nodes->size()); ++i) {
     341        v = (*_nodes)[i];
     342        for (int j = 0; j < int(_in_arcs[v].size()); ++j) {
     343          e = _in_arcs[v][j];
     344          u = _gr.source(e);
     345          if (_length[e] < _dist[u]) {
     346            _dist[u] = _length[e];
     347            _policy[u] = e;
     348          }
     349        }
    211350      }
    212351      return true;
    213352    }
    214353
    215     /// @}
    216 
    217     /// \name Query Functions
    218     /// The results of the algorithm can be obtained using these
    219     /// functions.\n
    220     /// The algorithm should be executed before using them.
    221 
    222     /// @{
    223 
    224     /// \brief Return the total length of the found cycle.
    225     ///
    226     /// This function returns the total length of the found cycle.
    227     ///
    228     /// \pre \ref run() or \ref findCycle() must be called before
    229     /// using this function.
    230     Value cycleLength() const {
    231       return _cycle_length;
    232     }
    233 
    234     /// \brief Return the number of arcs on the found cycle.
    235     ///
    236     /// This function returns the number of arcs on the found cycle.
    237     ///
    238     /// \pre \ref run() or \ref findCycle() must be called before
    239     /// using this function.
    240     int cycleArcNum() const {
    241       return _cycle_size;
    242     }
    243 
    244     /// \brief Return the mean length of the found cycle.
    245     ///
    246     /// This function returns the mean length of the found cycle.
    247     ///
    248     /// \note <tt>mmc.cycleMean()</tt> is just a shortcut of the
    249     /// following code.
    250     /// \code
    251     ///   return double(mmc.cycleLength()) / mmc.cycleArcNum();
    252     /// \endcode
    253     ///
    254     /// \pre \ref run() or \ref findMinMean() must be called before
    255     /// using this function.
    256     double cycleMean() const {
    257       return double(_cycle_length) / _cycle_size;
    258     }
    259 
    260     /// \brief Return the found cycle.
    261     ///
    262     /// This function returns a const reference to the path structure
    263     /// storing the found cycle.
    264     ///
    265     /// \pre \ref run() or \ref findCycle() must be called before using
    266     /// this function.
    267     ///
    268     /// \sa cyclePath()
    269     const Path& cycle() const {
    270       return *_cycle_path;
    271     }
    272 
    273     ///@}
    274 
    275   private:
    276 
    277     // Initialize the internal data structures for the current strongly
    278     // connected component and create the policy graph.
    279     // The policy graph can be represented by the _policy map because
    280     // the out-degree of every node is 1.
    281     bool initCurrentComponent(int comp) {
    282       // Find the nodes of the current component
    283       _nodes.clear();
    284       for (NodeIt n(_gr); n != INVALID; ++n) {
    285         if (_comp[n] == comp) _nodes.push_back(n);
    286       }
    287       if (_nodes.size() <= 1) return false;
    288       // Find the arcs of the current component
    289       _arcs.clear();
    290       for (ArcIt e(_gr); e != INVALID; ++e) {
    291         if ( _comp[_gr.source(e)] == comp &&
    292              _comp[_gr.target(e)] == comp )
    293           _arcs.push_back(e);
    294       }
    295       // Initialize _reached, _dist, _policy maps
    296       for (int i = 0; i < int(_nodes.size()); ++i) {
    297         _reached[_nodes[i]] = false;
    298         _policy[_nodes[i]] = INVALID;
    299       }
    300       Node u; Arc e;
    301       for (int j = 0; j < int(_arcs.size()); ++j) {
    302         e = _arcs[j];
    303         u = _gr.source(e);
    304         if (!_reached[u] || _length[e] < _dist[u]) {
    305           _dist[u] = _length[e];
    306           _policy[u] = e;
    307           _reached[u] = true;
    308         }
    309       }
    310       return true;
    311     }
    312 
    313     // Find all cycles in the policy graph.
    314     // Set _cycle_found to true if a cycle is found and set
    315     // _cycle_length, _cycle_size, _cycle_node to represent the minimum
    316     // mean cycle in the policy graph.
    317     bool findPolicyCycles() {
    318       typename Digraph::template NodeMap<int> level(_gr, -1);
    319       bool curr_cycle_found = false;
     354    // Find the minimum mean cycle in the policy graph
     355    void findPolicyCycle() {
     356      for (int i = 0; i < int(_nodes->size()); ++i) {
     357        _level[(*_nodes)[i]] = -1;
     358      }
    320359      Value clength;
    321360      int csize;
    322       int path_cnt = 0;
    323361      Node u, v;
    324       // Searching for cycles
    325       for (int i = 0; i < int(_nodes.size()); ++i) {
    326         if (level[_nodes[i]] < 0) {
    327           u = _nodes[i];
    328           level[u] = path_cnt;
    329           while (level[u = _gr.target(_policy[u])] < 0)
    330             level[u] = path_cnt;
    331           if (level[u] == path_cnt) {
    332             // A cycle is found
    333             curr_cycle_found = true;
    334             clength = _length[_policy[u]];
    335             csize = 1;
    336             for (v = u; (v = _gr.target(_policy[v])) != u; ) {
    337               clength += _length[_policy[v]];
    338               ++csize;
    339             }
    340             if ( !_cycle_found ||
    341                  clength * _cycle_size < _cycle_length * csize ) {
    342               _cycle_found = true;
    343               _cycle_length = clength;
    344               _cycle_size = csize;
    345               _cycle_node = u;
    346             }
    347           }
    348           ++path_cnt;
    349         }
    350       }
    351       return curr_cycle_found;
    352     }
    353 
    354     // Contract the policy graph to be connected by cutting all cycles
    355     // except for the main cycle (i.e. the minimum mean cycle).
    356     void contractPolicyGraph(int comp) {
    357       // Find the component of the main cycle using reverse BFS search
    358       typename Digraph::template NodeMap<int> found(_gr, false);
    359       std::deque<Node> queue;
    360       queue.push_back(_cycle_node);
    361       found[_cycle_node] = true;
     362      _curr_found = false;
     363      for (int i = 0; i < int(_nodes->size()); ++i) {
     364        u = (*_nodes)[i];
     365        if (_level[u] >= 0) continue;
     366        for (; _level[u] < 0; u = _gr.target(_policy[u])) {
     367          _level[u] = i;
     368        }
     369        if (_level[u] == i) {
     370          // A cycle is found
     371          clength = _length[_policy[u]];
     372          csize = 1;
     373          for (v = u; (v = _gr.target(_policy[v])) != u; ) {
     374            clength += _length[_policy[v]];
     375            ++csize;
     376          }
     377          if ( !_curr_found ||
     378               (clength * _curr_size < _curr_length * csize) ) {
     379            _curr_found = true;
     380            _curr_length = clength;
     381            _curr_size = csize;
     382            _curr_node = u;
     383          }
     384        }
     385      }
     386    }
     387
     388    // Contract the policy graph and compute node distances
     389    bool computeNodeDistances() {
     390      // Find the component of the main cycle and compute node distances
     391      // using reverse BFS
     392      for (int i = 0; i < int(_nodes->size()); ++i) {
     393        _reached[(*_nodes)[i]] = false;
     394      }
     395      double curr_mean = double(_curr_length) / _curr_size;
     396      _qfront = _qback = 0;
     397      _queue[0] = _curr_node;
     398      _reached[_curr_node] = true;
     399      _dist[_curr_node] = 0;
    362400      Node u, v;
    363       while (!queue.empty()) {
    364         v = queue.front(); queue.pop_front();
    365         for (InArcIt e(_gr, v); e != INVALID; ++e) {
     401      Arc e;
     402      while (_qfront <= _qback) {
     403        v = _queue[_qfront++];
     404        for (int j = 0; j < int(_in_arcs[v].size()); ++j) {
     405          e = _in_arcs[v][j];
    366406          u = _gr.source(e);
    367           if (_policy[u] == e && !found[u]) {
    368             found[u] = true;
    369             queue.push_back(u);
    370           }
    371         }
    372       }
    373       // Connect all other nodes to this component using reverse BFS search
    374       queue.clear();
    375       for (int i = 0; i < int(_nodes.size()); ++i)
    376         if (found[_nodes[i]]) queue.push_back(_nodes[i]);
    377       int found_cnt = queue.size();
    378       while (found_cnt < int(_nodes.size())) {
    379         v = queue.front(); queue.pop_front();
    380         for (InArcIt e(_gr, v); e != INVALID; ++e) {
     407          if (_policy[u] == e && !_reached[u]) {
     408            _reached[u] = true;
     409            _dist[u] = _dist[v] + _length[e] - curr_mean;
     410            _queue[++_qback] = u;
     411          }
     412        }
     413      }
     414
     415      // Connect all other nodes to this component and compute node
     416      // distances using reverse BFS
     417      _qfront = 0;
     418      while (_qback < int(_nodes->size())-1) {
     419        v = _queue[_qfront++];
     420        for (int j = 0; j < int(_in_arcs[v].size()); ++j) {
     421          e = _in_arcs[v][j];
    381422          u = _gr.source(e);
    382           if (_comp[u] == comp && !found[u]) {
    383             found[u] = true;
    384             ++found_cnt;
     423          if (!_reached[u]) {
     424            _reached[u] = true;
    385425            _policy[u] = e;
    386             queue.push_back(u);
    387           }
    388         }
    389       }
    390     }
    391 
    392     // Compute node distances in the policy graph and update the
    393     // policy graph if the node distances can be improved.
    394     bool computeNodeDistances() {
    395       // Compute node distances using reverse BFS search
    396       double cycle_mean = double(_cycle_length) / _cycle_size;
    397       typename Digraph::template NodeMap<int> found(_gr, false);
    398       std::deque<Node> queue;
    399       queue.push_back(_cycle_node);
    400       found[_cycle_node] = true;
    401       _dist[_cycle_node] = 0;
    402       Node u, v;
    403       while (!queue.empty()) {
    404         v = queue.front(); queue.pop_front();
    405         for (InArcIt e(_gr, v); e != INVALID; ++e) {
     426            _dist[u] = _dist[v] + _length[e] - curr_mean;
     427            _queue[++_qback] = u;
     428          }
     429        }
     430      }
     431
     432      // Improve node distances
     433      bool improved = false;
     434      for (int i = 0; i < int(_nodes->size()); ++i) {
     435        v = (*_nodes)[i];
     436        for (int j = 0; j < int(_in_arcs[v].size()); ++j) {
     437          e = _in_arcs[v][j];
    406438          u = _gr.source(e);
    407           if (_policy[u] == e && !found[u]) {
    408             found[u] = true;
    409             _dist[u] = _dist[v] + _length[e] - cycle_mean;
    410             queue.push_back(u);
    411           }
    412         }
    413       }
    414       // Improving node distances
    415       bool improved = false;
    416       for (int j = 0; j < int(_arcs.size()); ++j) {
    417         Arc e = _arcs[j];
    418         u = _gr.source(e); v = _gr.target(e);
    419         double delta = _dist[v] + _length[e] - cycle_mean;
    420         if (_tol.less(delta, _dist[u])) {
    421           improved = true;
    422           _dist[u] = delta;
    423           _policy[u] = e;
     439          double delta = _dist[v] + _length[e] - curr_mean;
     440          if (_tol.less(delta, _dist[u])) {
     441            _dist[u] = delta;
     442            _policy[u] = e;
     443            improved = true;
     444          }
    424445        }
    425446      }
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