lemon/capacity_scaling.h
changeset 2583 7216b6a52ab9
parent 2574 7058c9690e7d
child 2588 4d3bc1d04c1d
equal deleted inserted replaced
9:a49b1b3dcd37 10:56918ba44652
    48   /// \tparam SupplyMap The type of the supply map.
    48   /// \tparam SupplyMap The type of the supply map.
    49   ///
    49   ///
    50   /// \warning
    50   /// \warning
    51   /// - Edge capacities and costs should be \e non-negative \e integers.
    51   /// - Edge capacities and costs should be \e non-negative \e integers.
    52   /// - Supply values should be \e signed \e integers.
    52   /// - Supply values should be \e signed \e integers.
    53   /// - \c LowerMap::Value must be convertible to \c CapacityMap::Value.
    53   /// - The value types of the maps should be convertible to each other.
    54   /// - \c CapacityMap::Value and \c SupplyMap::Value must be
    54   /// - \c CostMap::Value must be signed type.
    55   ///   convertible to each other.
       
    56   /// - All value types must be convertible to \c CostMap::Value, which
       
    57   ///   must be signed type.
       
    58   ///
    55   ///
    59   /// \author Peter Kovacs
    56   /// \author Peter Kovacs
    60 
    57 
    61   template < typename Graph,
    58   template < typename Graph,
    62              typename LowerMap = typename Graph::template EdgeMap<int>,
    59              typename LowerMap = typename Graph::template EdgeMap<int>,
   118       // The processed (i.e. permanently labeled) nodes
   115       // The processed (i.e. permanently labeled) nodes
   119       std::vector<Node> _proc_nodes;
   116       std::vector<Node> _proc_nodes;
   120 
   117 
   121     public:
   118     public:
   122 
   119 
   123       /// The constructor of the class.
   120       /// Constructor.
   124       ResidualDijkstra( const Graph &graph,
   121       ResidualDijkstra( const Graph &graph,
   125                         const FlowMap &flow,
   122                         const FlowMap &flow,
   126                         const CapacityEdgeMap &res_cap,
   123                         const CapacityEdgeMap &res_cap,
   127                         const CostMap &cost,
   124                         const CostMap &cost,
   128                         const SupplyMap &excess,
   125                         const SupplyMap &excess,
   219     // The modified supply map
   216     // The modified supply map
   220     SupplyNodeMap _supply;
   217     SupplyNodeMap _supply;
   221     bool _valid_supply;
   218     bool _valid_supply;
   222 
   219 
   223     // Edge map of the current flow
   220     // Edge map of the current flow
   224     FlowMap _flow;
   221     FlowMap *_flow;
       
   222     bool _local_flow;
   225     // Node map of the current potentials
   223     // Node map of the current potentials
   226     PotentialMap _potential;
   224     PotentialMap *_potential;
       
   225     bool _local_potential;
   227 
   226 
   228     // The residual capacity map
   227     // The residual capacity map
   229     CapacityEdgeMap _res_cap;
   228     CapacityEdgeMap _res_cap;
   230     // The excess map
   229     // The excess map
   231     SupplyNodeMap _excess;
   230     SupplyNodeMap _excess;
   241 
   240 
   242     // The pred edge map
   241     // The pred edge map
   243     PredMap _pred;
   242     PredMap _pred;
   244     // Implementation of the Dijkstra algorithm for finding augmenting
   243     // Implementation of the Dijkstra algorithm for finding augmenting
   245     // shortest paths in the residual network
   244     // shortest paths in the residual network
   246     ResidualDijkstra _dijkstra;
   245     ResidualDijkstra *_dijkstra;
   247 
   246 
   248   public :
   247   public:
   249 
   248 
   250     /// \brief General constructor of the class (with lower bounds).
   249     /// \brief General constructor (with lower bounds).
   251     ///
   250     ///
   252     /// General constructor of the class (with lower bounds).
   251     /// General constructor (with lower bounds).
   253     ///
   252     ///
   254     /// \param graph The directed graph the algorithm runs on.
   253     /// \param graph The directed graph the algorithm runs on.
   255     /// \param lower The lower bounds of the edges.
   254     /// \param lower The lower bounds of the edges.
   256     /// \param capacity The capacities (upper bounds) of the edges.
   255     /// \param capacity The capacities (upper bounds) of the edges.
   257     /// \param cost The cost (length) values of the edges.
   256     /// \param cost The cost (length) values of the edges.
   260                      const LowerMap &lower,
   259                      const LowerMap &lower,
   261                      const CapacityMap &capacity,
   260                      const CapacityMap &capacity,
   262                      const CostMap &cost,
   261                      const CostMap &cost,
   263                      const SupplyMap &supply ) :
   262                      const SupplyMap &supply ) :
   264       _graph(graph), _lower(&lower), _capacity(graph), _cost(cost),
   263       _graph(graph), _lower(&lower), _capacity(graph), _cost(cost),
   265       _supply(graph), _flow(graph, 0), _potential(graph, 0),
   264       _supply(graph), _flow(0), _local_flow(false),
   266       _res_cap(graph), _excess(graph), _pred(graph),
   265       _potential(0), _local_potential(false),
   267       _dijkstra(_graph, _flow, _res_cap, _cost, _excess, _potential, _pred)
   266       _res_cap(graph), _excess(graph), _pred(graph)
   268     {
   267     {
   269       // Removing non-zero lower bounds
   268       // Removing non-zero lower bounds
   270       _capacity = subMap(capacity, lower);
   269       _capacity = subMap(capacity, lower);
   271       _res_cap = _capacity;
   270       _res_cap = _capacity;
   272       Supply sum = 0;
   271       Supply sum = 0;
   280         sum += s;
   279         sum += s;
   281       }
   280       }
   282       _valid_supply = sum == 0;
   281       _valid_supply = sum == 0;
   283     }
   282     }
   284 
   283 
   285     /// \brief General constructor of the class (without lower bounds).
   284     /// \brief General constructor (without lower bounds).
   286     ///
   285     ///
   287     /// General constructor of the class (without lower bounds).
   286     /// General constructor (without lower bounds).
   288     ///
   287     ///
   289     /// \param graph The directed graph the algorithm runs on.
   288     /// \param graph The directed graph the algorithm runs on.
   290     /// \param capacity The capacities (upper bounds) of the edges.
   289     /// \param capacity The capacities (upper bounds) of the edges.
   291     /// \param cost The cost (length) values of the edges.
   290     /// \param cost The cost (length) values of the edges.
   292     /// \param supply The supply values of the nodes (signed).
   291     /// \param supply The supply values of the nodes (signed).
   293     CapacityScaling( const Graph &graph,
   292     CapacityScaling( const Graph &graph,
   294                      const CapacityMap &capacity,
   293                      const CapacityMap &capacity,
   295                      const CostMap &cost,
   294                      const CostMap &cost,
   296                      const SupplyMap &supply ) :
   295                      const SupplyMap &supply ) :
   297       _graph(graph), _lower(NULL), _capacity(capacity), _cost(cost),
   296       _graph(graph), _lower(NULL), _capacity(capacity), _cost(cost),
   298       _supply(supply), _flow(graph, 0), _potential(graph, 0),
   297       _supply(supply), _flow(0), _local_flow(false),
   299       _res_cap(capacity), _excess(graph), _pred(graph),
   298       _potential(0), _local_potential(false),
   300       _dijkstra(_graph, _flow, _res_cap, _cost, _excess, _potential, _pred)
   299       _res_cap(capacity), _excess(graph), _pred(graph)
   301     {
   300     {
   302       // Checking the sum of supply values
   301       // Checking the sum of supply values
   303       Supply sum = 0;
   302       Supply sum = 0;
   304       for (NodeIt n(_graph); n != INVALID; ++n) sum += _supply[n];
   303       for (NodeIt n(_graph); n != INVALID; ++n) sum += _supply[n];
   305       _valid_supply = sum == 0;
   304       _valid_supply = sum == 0;
   306     }
   305     }
   307 
   306 
   308     /// \brief Simple constructor of the class (with lower bounds).
   307     /// \brief Simple constructor (with lower bounds).
   309     ///
   308     ///
   310     /// Simple constructor of the class (with lower bounds).
   309     /// Simple constructor (with lower bounds).
   311     ///
   310     ///
   312     /// \param graph The directed graph the algorithm runs on.
   311     /// \param graph The directed graph the algorithm runs on.
   313     /// \param lower The lower bounds of the edges.
   312     /// \param lower The lower bounds of the edges.
   314     /// \param capacity The capacities (upper bounds) of the edges.
   313     /// \param capacity The capacities (upper bounds) of the edges.
   315     /// \param cost The cost (length) values of the edges.
   314     /// \param cost The cost (length) values of the edges.
   322                      const CapacityMap &capacity,
   321                      const CapacityMap &capacity,
   323                      const CostMap &cost,
   322                      const CostMap &cost,
   324                      Node s, Node t,
   323                      Node s, Node t,
   325                      Supply flow_value ) :
   324                      Supply flow_value ) :
   326       _graph(graph), _lower(&lower), _capacity(graph), _cost(cost),
   325       _graph(graph), _lower(&lower), _capacity(graph), _cost(cost),
   327       _supply(graph), _flow(graph, 0), _potential(graph, 0),
   326       _supply(graph), _flow(0), _local_flow(false),
   328       _res_cap(graph), _excess(graph), _pred(graph),
   327       _potential(0), _local_potential(false),
   329       _dijkstra(_graph, _flow, _res_cap, _cost, _excess, _potential, _pred)
   328       _res_cap(graph), _excess(graph), _pred(graph)
   330     {
   329     {
   331       // Removing non-zero lower bounds
   330       // Removing non-zero lower bounds
   332       _capacity = subMap(capacity, lower);
   331       _capacity = subMap(capacity, lower);
   333       _res_cap = _capacity;
   332       _res_cap = _capacity;
   334       for (NodeIt n(_graph); n != INVALID; ++n) {
   333       for (NodeIt n(_graph); n != INVALID; ++n) {
   342         _supply[n] = sum;
   341         _supply[n] = sum;
   343       }
   342       }
   344       _valid_supply = true;
   343       _valid_supply = true;
   345     }
   344     }
   346 
   345 
   347     /// \brief Simple constructor of the class (without lower bounds).
   346     /// \brief Simple constructor (without lower bounds).
   348     ///
   347     ///
   349     /// Simple constructor of the class (without lower bounds).
   348     /// Simple constructor (without lower bounds).
   350     ///
   349     ///
   351     /// \param graph The directed graph the algorithm runs on.
   350     /// \param graph The directed graph the algorithm runs on.
   352     /// \param capacity The capacities (upper bounds) of the edges.
   351     /// \param capacity The capacities (upper bounds) of the edges.
   353     /// \param cost The cost (length) values of the edges.
   352     /// \param cost The cost (length) values of the edges.
   354     /// \param s The source node.
   353     /// \param s The source node.
   359                      const CapacityMap &capacity,
   358                      const CapacityMap &capacity,
   360                      const CostMap &cost,
   359                      const CostMap &cost,
   361                      Node s, Node t,
   360                      Node s, Node t,
   362                      Supply flow_value ) :
   361                      Supply flow_value ) :
   363       _graph(graph), _lower(NULL), _capacity(capacity), _cost(cost),
   362       _graph(graph), _lower(NULL), _capacity(capacity), _cost(cost),
   364       _supply(graph, 0), _flow(graph, 0), _potential(graph, 0),
   363       _supply(graph, 0), _flow(0), _local_flow(false),
   365       _res_cap(capacity), _excess(graph), _pred(graph),
   364       _potential(0), _local_potential(false),
   366       _dijkstra(_graph, _flow, _res_cap, _cost, _excess, _potential, _pred)
   365       _res_cap(capacity), _excess(graph), _pred(graph)
   367     {
   366     {
   368       _supply[s] =  flow_value;
   367       _supply[s] =  flow_value;
   369       _supply[t] = -flow_value;
   368       _supply[t] = -flow_value;
   370       _valid_supply = true;
   369       _valid_supply = true;
   371     }
   370     }
   372 
   371 
       
   372     /// Destructor.
       
   373     ~CapacityScaling() {
       
   374       if (_local_flow) delete _flow;
       
   375       if (_local_potential) delete _potential;
       
   376       delete _dijkstra;
       
   377     }
       
   378 
       
   379     /// \brief Sets the flow map.
       
   380     ///
       
   381     /// Sets the flow map.
       
   382     ///
       
   383     /// \return \c (*this)
       
   384     CapacityScaling& flowMap(FlowMap &map) {
       
   385       if (_local_flow) {
       
   386         delete _flow;
       
   387         _local_flow = false;
       
   388       }
       
   389       _flow = &map;
       
   390       return *this;
       
   391     }
       
   392 
       
   393     /// \brief Sets the potential map.
       
   394     ///
       
   395     /// Sets the potential map.
       
   396     ///
       
   397     /// \return \c (*this)
       
   398     CapacityScaling& potentialMap(PotentialMap &map) {
       
   399       if (_local_potential) {
       
   400         delete _potential;
       
   401         _local_potential = false;
       
   402       }
       
   403       _potential = &map;
       
   404       return *this;
       
   405     }
       
   406 
       
   407     /// \name Execution control
       
   408     /// The only way to execute the algorithm is to call the run()
       
   409     /// function.
       
   410 
       
   411     /// @{
       
   412 
   373     /// \brief Runs the algorithm.
   413     /// \brief Runs the algorithm.
   374     ///
   414     ///
   375     /// Runs the algorithm.
   415     /// Runs the algorithm.
   376     ///
   416     ///
   377     /// \param scaling Enable or disable capacity scaling.
   417     /// \param scaling Enable or disable capacity scaling.
   382     /// \return \c true if a feasible flow can be found.
   422     /// \return \c true if a feasible flow can be found.
   383     bool run(bool scaling = true) {
   423     bool run(bool scaling = true) {
   384       return init(scaling) && start();
   424       return init(scaling) && start();
   385     }
   425     }
   386 
   426 
       
   427     /// @}
       
   428 
       
   429     /// \name Query Functions
       
   430     /// The result of the algorithm can be obtained using these
       
   431     /// functions.
       
   432     /// \n run() must be called before using them.
       
   433 
       
   434     /// @{
       
   435 
   387     /// \brief Returns a const reference to the edge map storing the
   436     /// \brief Returns a const reference to the edge map storing the
   388     /// found flow.
   437     /// found flow.
   389     ///
   438     ///
   390     /// Returns a const reference to the edge map storing the found flow.
   439     /// Returns a const reference to the edge map storing the found flow.
   391     ///
   440     ///
   392     /// \pre \ref run() must be called before using this function.
   441     /// \pre \ref run() must be called before using this function.
   393     const FlowMap& flowMap() const {
   442     const FlowMap& flowMap() const {
   394       return _flow;
   443       return *_flow;
   395     }
   444     }
   396 
   445 
   397     /// \brief Returns a const reference to the node map storing the
   446     /// \brief Returns a const reference to the node map storing the
   398     /// found potentials (the dual solution).
   447     /// found potentials (the dual solution).
   399     ///
   448     ///
   400     /// Returns a const reference to the node map storing the found
   449     /// Returns a const reference to the node map storing the found
   401     /// potentials (the dual solution).
   450     /// potentials (the dual solution).
   402     ///
   451     ///
   403     /// \pre \ref run() must be called before using this function.
   452     /// \pre \ref run() must be called before using this function.
   404     const PotentialMap& potentialMap() const {
   453     const PotentialMap& potentialMap() const {
   405       return _potential;
   454       return *_potential;
       
   455     }
       
   456 
       
   457     /// \brief Returns the flow on the edge.
       
   458     ///
       
   459     /// Returns the flow on the edge.
       
   460     ///
       
   461     /// \pre \ref run() must be called before using this function.
       
   462     Capacity flow(const Edge& edge) const {
       
   463       return (*_flow)[edge];
       
   464     }
       
   465 
       
   466     /// \brief Returns the potential of the node.
       
   467     ///
       
   468     /// Returns the potential of the node.
       
   469     ///
       
   470     /// \pre \ref run() must be called before using this function.
       
   471     Cost potential(const Node& node) const {
       
   472       return (*_potential)[node];
   406     }
   473     }
   407 
   474 
   408     /// \brief Returns the total cost of the found flow.
   475     /// \brief Returns the total cost of the found flow.
   409     ///
   476     ///
   410     /// Returns the total cost of the found flow. The complexity of the
   477     /// Returns the total cost of the found flow. The complexity of the
   412     ///
   479     ///
   413     /// \pre \ref run() must be called before using this function.
   480     /// \pre \ref run() must be called before using this function.
   414     Cost totalCost() const {
   481     Cost totalCost() const {
   415       Cost c = 0;
   482       Cost c = 0;
   416       for (EdgeIt e(_graph); e != INVALID; ++e)
   483       for (EdgeIt e(_graph); e != INVALID; ++e)
   417         c += _flow[e] * _cost[e];
   484         c += (*_flow)[e] * _cost[e];
   418       return c;
   485       return c;
   419     }
   486     }
       
   487 
       
   488     /// @}
   420 
   489 
   421   private:
   490   private:
   422 
   491 
   423     /// Initializes the algorithm.
   492     /// Initializes the algorithm.
   424     bool init(bool scaling) {
   493     bool init(bool scaling) {
   425       if (!_valid_supply) return false;
   494       if (!_valid_supply) return false;
       
   495 
       
   496       // Initializing maps
       
   497       if (!_flow) {
       
   498         _flow = new FlowMap(_graph);
       
   499         _local_flow = true;
       
   500       }
       
   501       if (!_potential) {
       
   502         _potential = new PotentialMap(_graph);
       
   503         _local_potential = true;
       
   504       }
       
   505       for (EdgeIt e(_graph); e != INVALID; ++e) (*_flow)[e] = 0;
       
   506       for (NodeIt n(_graph); n != INVALID; ++n) (*_potential)[n] = 0;
   426       _excess = _supply;
   507       _excess = _supply;
   427 
   508 
   428       // Initilaizing delta value
   509       _dijkstra = new ResidualDijkstra( _graph, *_flow, _res_cap, _cost,
       
   510                                         _excess, *_potential, _pred );
       
   511 
       
   512       // Initializing delta value
   429       if (scaling) {
   513       if (scaling) {
   430         // With scaling
   514         // With scaling
   431         Supply max_sup = 0, max_dem = 0;
   515         Supply max_sup = 0, max_dem = 0;
   432         for (NodeIt n(_graph); n != INVALID; ++n) {
   516         for (NodeIt n(_graph); n != INVALID; ++n) {
   433           if ( _supply[n] > max_sup) max_sup =  _supply[n];
   517           if ( _supply[n] > max_sup) max_sup =  _supply[n];
   439           ++_phase_num;
   523           ++_phase_num;
   440       } else {
   524       } else {
   441         // Without scaling
   525         // Without scaling
   442         _delta = 1;
   526         _delta = 1;
   443       }
   527       }
       
   528 
   444       return true;
   529       return true;
   445     }
   530     }
   446 
   531 
   447     bool start() {
   532     bool start() {
   448       if (_delta > 1)
   533       if (_delta > 1)
   459       int factor = 4;
   544       int factor = 4;
   460       while (true) {
   545       while (true) {
   461         // Saturating all edges not satisfying the optimality condition
   546         // Saturating all edges not satisfying the optimality condition
   462         for (EdgeIt e(_graph); e != INVALID; ++e) {
   547         for (EdgeIt e(_graph); e != INVALID; ++e) {
   463           Node u = _graph.source(e), v = _graph.target(e);
   548           Node u = _graph.source(e), v = _graph.target(e);
   464           Cost c = _cost[e] + _potential[u] - _potential[v];
   549           Cost c = _cost[e] + (*_potential)[u] - (*_potential)[v];
   465           if (c < 0 && _res_cap[e] >= _delta) {
   550           if (c < 0 && _res_cap[e] >= _delta) {
   466             _excess[u] -= _res_cap[e];
   551             _excess[u] -= _res_cap[e];
   467             _excess[v] += _res_cap[e];
   552             _excess[v] += _res_cap[e];
   468             _flow[e] = _capacity[e];
   553             (*_flow)[e] = _capacity[e];
   469             _res_cap[e] = 0;
   554             _res_cap[e] = 0;
   470           }
   555           }
   471           else if (c > 0 && _flow[e] >= _delta) {
   556           else if (c > 0 && (*_flow)[e] >= _delta) {
   472             _excess[u] += _flow[e];
   557             _excess[u] += (*_flow)[e];
   473             _excess[v] -= _flow[e];
   558             _excess[v] -= (*_flow)[e];
   474             _flow[e] = 0;
   559             (*_flow)[e] = 0;
   475             _res_cap[e] = _capacity[e];
   560             _res_cap[e] = _capacity[e];
   476           }
   561           }
   477         }
   562         }
   478 
   563 
   479         // Finding excess nodes and deficit nodes
   564         // Finding excess nodes and deficit nodes
   499             if (!delta_deficit) break;
   584             if (!delta_deficit) break;
   500           }
   585           }
   501 
   586 
   502           // Running Dijkstra
   587           // Running Dijkstra
   503           s = _excess_nodes[next_node];
   588           s = _excess_nodes[next_node];
   504           if ((t = _dijkstra.run(s, _delta)) == INVALID) {
   589           if ((t = _dijkstra->run(s, _delta)) == INVALID) {
   505             if (_delta > 1) {
   590             if (_delta > 1) {
   506               ++next_node;
   591               ++next_node;
   507               continue;
   592               continue;
   508             }
   593             }
   509             return false;
   594             return false;
   518               Capacity rc;
   603               Capacity rc;
   519               if (u == _graph.target(e)) {
   604               if (u == _graph.target(e)) {
   520                 rc = _res_cap[e];
   605                 rc = _res_cap[e];
   521                 u = _graph.source(e);
   606                 u = _graph.source(e);
   522               } else {
   607               } else {
   523                 rc = _flow[e];
   608                 rc = (*_flow)[e];
   524                 u = _graph.target(e);
   609                 u = _graph.target(e);
   525               }
   610               }
   526               if (rc < d) d = rc;
   611               if (rc < d) d = rc;
   527             }
   612             }
   528           }
   613           }
   529           u = t;
   614           u = t;
   530           while ((e = _pred[u]) != INVALID) {
   615           while ((e = _pred[u]) != INVALID) {
   531             if (u == _graph.target(e)) {
   616             if (u == _graph.target(e)) {
   532               _flow[e] += d;
   617               (*_flow)[e] += d;
   533               _res_cap[e] -= d;
   618               _res_cap[e] -= d;
   534               u = _graph.source(e);
   619               u = _graph.source(e);
   535             } else {
   620             } else {
   536               _flow[e] -= d;
   621               (*_flow)[e] -= d;
   537               _res_cap[e] += d;
   622               _res_cap[e] += d;
   538               u = _graph.target(e);
   623               u = _graph.target(e);
   539             }
   624             }
   540           }
   625           }
   541           _excess[s] -= d;
   626           _excess[s] -= d;
   550       }
   635       }
   551 
   636 
   552       // Handling non-zero lower bounds
   637       // Handling non-zero lower bounds
   553       if (_lower) {
   638       if (_lower) {
   554         for (EdgeIt e(_graph); e != INVALID; ++e)
   639         for (EdgeIt e(_graph); e != INVALID; ++e)
   555           _flow[e] += (*_lower)[e];
   640           (*_flow)[e] += (*_lower)[e];
   556       }
   641       }
   557       return true;
   642       return true;
   558     }
   643     }
   559 
   644 
   560     /// Executes the successive shortest path algorithm.
   645     /// Executes the successive shortest path algorithm.
   570       while ( _excess[_excess_nodes[next_node]] > 0 ||
   655       while ( _excess[_excess_nodes[next_node]] > 0 ||
   571               ++next_node < int(_excess_nodes.size()) )
   656               ++next_node < int(_excess_nodes.size()) )
   572       {
   657       {
   573         // Running Dijkstra
   658         // Running Dijkstra
   574         s = _excess_nodes[next_node];
   659         s = _excess_nodes[next_node];
   575         if ((t = _dijkstra.run(s, 1)) == INVALID)
   660         if ((t = _dijkstra->run(s, 1)) == INVALID)
   576           return false;
   661           return false;
   577 
   662 
   578         // Augmenting along a shortest path from s to t
   663         // Augmenting along a shortest path from s to t
   579         Capacity d = _excess[s] < -_excess[t] ? _excess[s] : -_excess[t];
   664         Capacity d = _excess[s] < -_excess[t] ? _excess[s] : -_excess[t];
   580         Node u = t;
   665         Node u = t;
   583           Capacity rc;
   668           Capacity rc;
   584           if (u == _graph.target(e)) {
   669           if (u == _graph.target(e)) {
   585             rc = _res_cap[e];
   670             rc = _res_cap[e];
   586             u = _graph.source(e);
   671             u = _graph.source(e);
   587           } else {
   672           } else {
   588             rc = _flow[e];
   673             rc = (*_flow)[e];
   589             u = _graph.target(e);
   674             u = _graph.target(e);
   590           }
   675           }
   591           if (rc < d) d = rc;
   676           if (rc < d) d = rc;
   592         }
   677         }
   593         u = t;
   678         u = t;
   594         while ((e = _pred[u]) != INVALID) {
   679         while ((e = _pred[u]) != INVALID) {
   595           if (u == _graph.target(e)) {
   680           if (u == _graph.target(e)) {
   596             _flow[e] += d;
   681             (*_flow)[e] += d;
   597             _res_cap[e] -= d;
   682             _res_cap[e] -= d;
   598             u = _graph.source(e);
   683             u = _graph.source(e);
   599           } else {
   684           } else {
   600             _flow[e] -= d;
   685             (*_flow)[e] -= d;
   601             _res_cap[e] += d;
   686             _res_cap[e] += d;
   602             u = _graph.target(e);
   687             u = _graph.target(e);
   603           }
   688           }
   604         }
   689         }
   605         _excess[s] -= d;
   690         _excess[s] -= d;
   607       }
   692       }
   608 
   693 
   609       // Handling non-zero lower bounds
   694       // Handling non-zero lower bounds
   610       if (_lower) {
   695       if (_lower) {
   611         for (EdgeIt e(_graph); e != INVALID; ++e)
   696         for (EdgeIt e(_graph); e != INVALID; ++e)
   612           _flow[e] += (*_lower)[e];
   697           (*_flow)[e] += (*_lower)[e];
   613       }
   698       }
   614       return true;
   699       return true;
   615     }
   700     }
   616 
   701 
   617   }; //class CapacityScaling
   702   }; //class CapacityScaling