/* -*- mode: C++; indent-tabs-mode: nil; -*- * * This file is a part of LEMON, a generic C++ optimization library. * * Copyright (C) 2003-2010 * Egervary Jeno Kombinatorikus Optimalizalasi Kutatocsoport * (Egervary Research Group on Combinatorial Optimization, EGRES). * * Permission to use, modify and distribute this software is granted * provided that this copyright notice appears in all copies. For * precise terms see the accompanying LICENSE file. * * This software is provided "AS IS" with no warranty of any kind, * express or implied, and with no claim as to its suitability for any * purpose. * */ #ifndef LEMON_CAPACITY_SCALING_H #define LEMON_CAPACITY_SCALING_H /// \ingroup min_cost_flow_algs /// /// \file /// \brief Capacity Scaling algorithm for finding a minimum cost flow. #include #include #include #include namespace lemon { /// \brief Default traits class of CapacityScaling algorithm. /// /// Default traits class of CapacityScaling algorithm. /// \tparam GR Digraph type. /// \tparam V The number type used for flow amounts, capacity bounds /// and supply values. By default it is \c int. /// \tparam C The number type used for costs and potentials. /// By default it is the same as \c V. template struct CapacityScalingDefaultTraits { /// The type of the digraph typedef GR Digraph; /// The type of the flow amounts, capacity bounds and supply values typedef V Value; /// The type of the arc costs typedef C Cost; /// \brief The type of the heap used for internal Dijkstra computations. /// /// The type of the heap used for internal Dijkstra computations. /// It must conform to the \ref lemon::concepts::Heap "Heap" concept, /// its priority type must be \c Cost and its cross reference type /// must be \ref RangeMap "RangeMap". typedef BinHeap > Heap; }; /// \addtogroup min_cost_flow_algs /// @{ /// \brief Implementation of the Capacity Scaling algorithm for /// finding a \ref min_cost_flow "minimum cost flow". /// /// \ref CapacityScaling implements the capacity scaling version /// of the successive shortest path algorithm for finding a /// \ref min_cost_flow "minimum cost flow" \ref amo93networkflows, /// \ref edmondskarp72theoretical. It is an efficient dual /// solution method. /// /// Most of the parameters of the problem (except for the digraph) /// can be given using separate functions, and the algorithm can be /// executed using the \ref run() function. If some parameters are not /// specified, then default values will be used. /// /// \tparam GR The digraph type the algorithm runs on. /// \tparam V The number type used for flow amounts, capacity bounds /// and supply values in the algorithm. By default, it is \c int. /// \tparam C The number type used for costs and potentials in the /// algorithm. By default, it is the same as \c V. /// \tparam TR The traits class that defines various types used by the /// algorithm. By default, it is \ref CapacityScalingDefaultTraits /// "CapacityScalingDefaultTraits". /// In most cases, this parameter should not be set directly, /// consider to use the named template parameters instead. /// /// \warning Both number types must be signed and all input data must /// be integer. /// \warning This algorithm does not support negative costs for /// arcs having infinite upper bound. #ifdef DOXYGEN template #else template < typename GR, typename V = int, typename C = V, typename TR = CapacityScalingDefaultTraits > #endif class CapacityScaling { public: /// The type of the digraph typedef typename TR::Digraph Digraph; /// The type of the flow amounts, capacity bounds and supply values typedef typename TR::Value Value; /// The type of the arc costs typedef typename TR::Cost Cost; /// The type of the heap used for internal Dijkstra computations typedef typename TR::Heap Heap; /// The \ref CapacityScalingDefaultTraits "traits class" of the algorithm typedef TR Traits; public: /// \brief Problem type constants for the \c run() function. /// /// Enum type containing the problem type constants that can be /// returned by the \ref run() function of the algorithm. enum ProblemType { /// The problem has no feasible solution (flow). INFEASIBLE, /// The problem has optimal solution (i.e. it is feasible and /// bounded), and the algorithm has found optimal flow and node /// potentials (primal and dual solutions). OPTIMAL, /// The digraph contains an arc of negative cost and infinite /// upper bound. It means that the objective function is unbounded /// on that arc, however, note that it could actually be bounded /// over the feasible flows, but this algroithm cannot handle /// these cases. UNBOUNDED }; private: TEMPLATE_DIGRAPH_TYPEDEFS(GR); typedef std::vector IntVector; typedef std::vector ValueVector; typedef std::vector CostVector; typedef std::vector BoolVector; // Note: vector is used instead of vector for efficiency reasons private: // Data related to the underlying digraph const GR &_graph; int _node_num; int _arc_num; int _res_arc_num; int _root; // Parameters of the problem bool _have_lower; Value _sum_supply; // Data structures for storing the digraph IntNodeMap _node_id; IntArcMap _arc_idf; IntArcMap _arc_idb; IntVector _first_out; BoolVector _forward; IntVector _source; IntVector _target; IntVector _reverse; // Node and arc data ValueVector _lower; ValueVector _upper; CostVector _cost; ValueVector _supply; ValueVector _res_cap; CostVector _pi; ValueVector _excess; IntVector _excess_nodes; IntVector _deficit_nodes; Value _delta; int _factor; IntVector _pred; public: /// \brief Constant for infinite upper bounds (capacities). /// /// Constant for infinite upper bounds (capacities). /// It is \c std::numeric_limits::infinity() if available, /// \c std::numeric_limits::max() otherwise. const Value INF; private: // Special implementation of the Dijkstra algorithm for finding // shortest paths in the residual network of the digraph with // respect to the reduced arc costs and modifying the node // potentials according to the found distance labels. class ResidualDijkstra { private: int _node_num; bool _geq; const IntVector &_first_out; const IntVector &_target; const CostVector &_cost; const ValueVector &_res_cap; const ValueVector &_excess; CostVector &_pi; IntVector &_pred; IntVector _proc_nodes; CostVector _dist; public: ResidualDijkstra(CapacityScaling& cs) : _node_num(cs._node_num), _geq(cs._sum_supply < 0), _first_out(cs._first_out), _target(cs._target), _cost(cs._cost), _res_cap(cs._res_cap), _excess(cs._excess), _pi(cs._pi), _pred(cs._pred), _dist(cs._node_num) {} int run(int s, Value delta = 1) { RangeMap heap_cross_ref(_node_num, Heap::PRE_HEAP); Heap heap(heap_cross_ref); heap.push(s, 0); _pred[s] = -1; _proc_nodes.clear(); // Process nodes while (!heap.empty() && _excess[heap.top()] > -delta) { int u = heap.top(), v; Cost d = heap.prio() + _pi[u], dn; _dist[u] = heap.prio(); _proc_nodes.push_back(u); heap.pop(); // Traverse outgoing residual arcs int last_out = _geq ? _first_out[u+1] : _first_out[u+1] - 1; for (int a = _first_out[u]; a != last_out; ++a) { if (_res_cap[a] < delta) continue; v = _target[a]; switch (heap.state(v)) { case Heap::PRE_HEAP: heap.push(v, d + _cost[a] - _pi[v]); _pred[v] = a; break; case Heap::IN_HEAP: dn = d + _cost[a] - _pi[v]; if (dn < heap[v]) { heap.decrease(v, dn); _pred[v] = a; } break; case Heap::POST_HEAP: break; } } } if (heap.empty()) return -1; // Update potentials of processed nodes int t = heap.top(); Cost dt = heap.prio(); for (int i = 0; i < int(_proc_nodes.size()); ++i) { _pi[_proc_nodes[i]] += _dist[_proc_nodes[i]] - dt; } return t; } }; //class ResidualDijkstra public: /// \name Named Template Parameters /// @{ template struct SetHeapTraits : public Traits { typedef T Heap; }; /// \brief \ref named-templ-param "Named parameter" for setting /// \c Heap type. /// /// \ref named-templ-param "Named parameter" for setting \c Heap /// type, which is used for internal Dijkstra computations. /// It must conform to the \ref lemon::concepts::Heap "Heap" concept, /// its priority type must be \c Cost and its cross reference type /// must be \ref RangeMap "RangeMap". template struct SetHeap : public CapacityScaling > { typedef CapacityScaling > Create; }; /// @} protected: CapacityScaling() {} public: /// \brief Constructor. /// /// The constructor of the class. /// /// \param graph The digraph the algorithm runs on. CapacityScaling(const GR& graph) : _graph(graph), _node_id(graph), _arc_idf(graph), _arc_idb(graph), INF(std::numeric_limits::has_infinity ? std::numeric_limits::infinity() : std::numeric_limits::max()) { // Check the number types LEMON_ASSERT(std::numeric_limits::is_signed, "The flow type of CapacityScaling must be signed"); LEMON_ASSERT(std::numeric_limits::is_signed, "The cost type of CapacityScaling must be signed"); // Reset data structures reset(); } /// \name Parameters /// The parameters of the algorithm can be specified using these /// functions. /// @{ /// \brief Set the lower bounds on the arcs. /// /// This function sets the lower bounds on the arcs. /// If it is not used before calling \ref run(), the lower bounds /// will be set to zero on all arcs. /// /// \param map An arc map storing the lower bounds. /// Its \c Value type must be convertible to the \c Value type /// of the algorithm. /// /// \return (*this) template CapacityScaling& lowerMap(const LowerMap& map) { _have_lower = true; for (ArcIt a(_graph); a != INVALID; ++a) { _lower[_arc_idf[a]] = map[a]; _lower[_arc_idb[a]] = map[a]; } return *this; } /// \brief Set the upper bounds (capacities) on the arcs. /// /// This function sets the upper bounds (capacities) on the arcs. /// If it is not used before calling \ref run(), the upper bounds /// will be set to \ref INF on all arcs (i.e. the flow value will be /// unbounded from above). /// /// \param map An arc map storing the upper bounds. /// Its \c Value type must be convertible to the \c Value type /// of the algorithm. /// /// \return (*this) template CapacityScaling& upperMap(const UpperMap& map) { for (ArcIt a(_graph); a != INVALID; ++a) { _upper[_arc_idf[a]] = map[a]; } return *this; } /// \brief Set the costs of the arcs. /// /// This function sets the costs of the arcs. /// If it is not used before calling \ref run(), the costs /// will be set to \c 1 on all arcs. /// /// \param map An arc map storing the costs. /// Its \c Value type must be convertible to the \c Cost type /// of the algorithm. /// /// \return (*this) template CapacityScaling& costMap(const CostMap& map) { for (ArcIt a(_graph); a != INVALID; ++a) { _cost[_arc_idf[a]] = map[a]; _cost[_arc_idb[a]] = -map[a]; } return *this; } /// \brief Set the supply values of the nodes. /// /// This function sets the supply values of the nodes. /// If neither this function nor \ref stSupply() is used before /// calling \ref run(), the supply of each node will be set to zero. /// /// \param map A node map storing the supply values. /// Its \c Value type must be convertible to the \c Value type /// of the algorithm. /// /// \return (*this) template CapacityScaling& supplyMap(const SupplyMap& map) { for (NodeIt n(_graph); n != INVALID; ++n) { _supply[_node_id[n]] = map[n]; } return *this; } /// \brief Set single source and target nodes and a supply value. /// /// This function sets a single source node and a single target node /// and the required flow value. /// If neither this function nor \ref supplyMap() is used before /// calling \ref run(), the supply of each node will be set to zero. /// /// Using this function has the same effect as using \ref supplyMap() /// with a map in which \c k is assigned to \c s, \c -k is /// assigned to \c t and all other nodes have zero supply value. /// /// \param s The source node. /// \param t The target node. /// \param k The required amount of flow from node \c s to node \c t /// (i.e. the supply of \c s and the demand of \c t). /// /// \return (*this) CapacityScaling& stSupply(const Node& s, const Node& t, Value k) { for (int i = 0; i != _node_num; ++i) { _supply[i] = 0; } _supply[_node_id[s]] = k; _supply[_node_id[t]] = -k; return *this; } /// @} /// \name Execution control /// The algorithm can be executed using \ref run(). /// @{ /// \brief Run the algorithm. /// /// This function runs the algorithm. /// The paramters can be specified using functions \ref lowerMap(), /// \ref upperMap(), \ref costMap(), \ref supplyMap(), \ref stSupply(). /// For example, /// \code /// CapacityScaling cs(graph); /// cs.lowerMap(lower).upperMap(upper).costMap(cost) /// .supplyMap(sup).run(); /// \endcode /// /// This function can be called more than once. All the given parameters /// are kept for the next call, unless \ref resetParams() or \ref reset() /// is used, thus only the modified parameters have to be set again. /// If the underlying digraph was also modified after the construction /// of the class (or the last \ref reset() call), then the \ref reset() /// function must be called. /// /// \param factor The capacity scaling factor. It must be larger than /// one to use scaling. If it is less or equal to one, then scaling /// will be disabled. /// /// \return \c INFEASIBLE if no feasible flow exists, /// \n \c OPTIMAL if the problem has optimal solution /// (i.e. it is feasible and bounded), and the algorithm has found /// optimal flow and node potentials (primal and dual solutions), /// \n \c UNBOUNDED if the digraph contains an arc of negative cost /// and infinite upper bound. It means that the objective function /// is unbounded on that arc, however, note that it could actually be /// bounded over the feasible flows, but this algroithm cannot handle /// these cases. /// /// \see ProblemType /// \see resetParams(), reset() ProblemType run(int factor = 4) { _factor = factor; ProblemType pt = init(); if (pt != OPTIMAL) return pt; return start(); } /// \brief Reset all the parameters that have been given before. /// /// This function resets all the paramaters that have been given /// before using functions \ref lowerMap(), \ref upperMap(), /// \ref costMap(), \ref supplyMap(), \ref stSupply(). /// /// It is useful for multiple \ref run() calls. Basically, all the given /// parameters are kept for the next \ref run() call, unless /// \ref resetParams() or \ref reset() is used. /// If the underlying digraph was also modified after the construction /// of the class or the last \ref reset() call, then the \ref reset() /// function must be used, otherwise \ref resetParams() is sufficient. /// /// For example, /// \code /// CapacityScaling cs(graph); /// /// // First run /// cs.lowerMap(lower).upperMap(upper).costMap(cost) /// .supplyMap(sup).run(); /// /// // Run again with modified cost map (resetParams() is not called, /// // so only the cost map have to be set again) /// cost[e] += 100; /// cs.costMap(cost).run(); /// /// // Run again from scratch using resetParams() /// // (the lower bounds will be set to zero on all arcs) /// cs.resetParams(); /// cs.upperMap(capacity).costMap(cost) /// .supplyMap(sup).run(); /// \endcode /// /// \return (*this) /// /// \see reset(), run() CapacityScaling& resetParams() { for (int i = 0; i != _node_num; ++i) { _supply[i] = 0; } for (int j = 0; j != _res_arc_num; ++j) { _lower[j] = 0; _upper[j] = INF; _cost[j] = _forward[j] ? 1 : -1; } _have_lower = false; return *this; } /// \brief Reset the internal data structures and all the parameters /// that have been given before. /// /// This function resets the internal data structures and all the /// paramaters that have been given before using functions \ref lowerMap(), /// \ref upperMap(), \ref costMap(), \ref supplyMap(), \ref stSupply(). /// /// It is useful for multiple \ref run() calls. Basically, all the given /// parameters are kept for the next \ref run() call, unless /// \ref resetParams() or \ref reset() is used. /// If the underlying digraph was also modified after the construction /// of the class or the last \ref reset() call, then the \ref reset() /// function must be used, otherwise \ref resetParams() is sufficient. /// /// See \ref resetParams() for examples. /// /// \return (*this) /// /// \see resetParams(), run() CapacityScaling& reset() { // Resize vectors _node_num = countNodes(_graph); _arc_num = countArcs(_graph); _res_arc_num = 2 * (_arc_num + _node_num); _root = _node_num; ++_node_num; _first_out.resize(_node_num + 1); _forward.resize(_res_arc_num); _source.resize(_res_arc_num); _target.resize(_res_arc_num); _reverse.resize(_res_arc_num); _lower.resize(_res_arc_num); _upper.resize(_res_arc_num); _cost.resize(_res_arc_num); _supply.resize(_node_num); _res_cap.resize(_res_arc_num); _pi.resize(_node_num); _excess.resize(_node_num); _pred.resize(_node_num); // Copy the graph int i = 0, j = 0, k = 2 * _arc_num + _node_num - 1; for (NodeIt n(_graph); n != INVALID; ++n, ++i) { _node_id[n] = i; } i = 0; for (NodeIt n(_graph); n != INVALID; ++n, ++i) { _first_out[i] = j; for (OutArcIt a(_graph, n); a != INVALID; ++a, ++j) { _arc_idf[a] = j; _forward[j] = true; _source[j] = i; _target[j] = _node_id[_graph.runningNode(a)]; } for (InArcIt a(_graph, n); a != INVALID; ++a, ++j) { _arc_idb[a] = j; _forward[j] = false; _source[j] = i; _target[j] = _node_id[_graph.runningNode(a)]; } _forward[j] = false; _source[j] = i; _target[j] = _root; _reverse[j] = k; _forward[k] = true; _source[k] = _root; _target[k] = i; _reverse[k] = j; ++j; ++k; } _first_out[i] = j; _first_out[_node_num] = k; for (ArcIt a(_graph); a != INVALID; ++a) { int fi = _arc_idf[a]; int bi = _arc_idb[a]; _reverse[fi] = bi; _reverse[bi] = fi; } // Reset parameters resetParams(); return *this; } /// @} /// \name Query Functions /// The results of the algorithm can be obtained using these /// functions.\n /// The \ref run() function must be called before using them. /// @{ /// \brief Return the total cost of the found flow. /// /// This function returns the total cost of the found flow. /// Its complexity is O(e). /// /// \note The return type of the function can be specified as a /// template parameter. For example, /// \code /// cs.totalCost(); /// \endcode /// It is useful if the total cost cannot be stored in the \c Cost /// type of the algorithm, which is the default return type of the /// function. /// /// \pre \ref run() must be called before using this function. template Number totalCost() const { Number c = 0; for (ArcIt a(_graph); a != INVALID; ++a) { int i = _arc_idb[a]; c += static_cast(_res_cap[i]) * (-static_cast(_cost[i])); } return c; } #ifndef DOXYGEN Cost totalCost() const { return totalCost(); } #endif /// \brief Return the flow on the given arc. /// /// This function returns the flow on the given arc. /// /// \pre \ref run() must be called before using this function. Value flow(const Arc& a) const { return _res_cap[_arc_idb[a]]; } /// \brief Return the flow map (the primal solution). /// /// This function copies the flow value on each arc into the given /// map. The \c Value type of the algorithm must be convertible to /// the \c Value type of the map. /// /// \pre \ref run() must be called before using this function. template void flowMap(FlowMap &map) const { for (ArcIt a(_graph); a != INVALID; ++a) { map.set(a, _res_cap[_arc_idb[a]]); } } /// \brief Return the potential (dual value) of the given node. /// /// This function returns the potential (dual value) of the /// given node. /// /// \pre \ref run() must be called before using this function. Cost potential(const Node& n) const { return _pi[_node_id[n]]; } /// \brief Return the potential map (the dual solution). /// /// This function copies the potential (dual value) of each node /// into the given map. /// The \c Cost type of the algorithm must be convertible to the /// \c Value type of the map. /// /// \pre \ref run() must be called before using this function. template void potentialMap(PotentialMap &map) const { for (NodeIt n(_graph); n != INVALID; ++n) { map.set(n, _pi[_node_id[n]]); } } /// @} private: // Initialize the algorithm ProblemType init() { if (_node_num <= 1) return INFEASIBLE; // Check the sum of supply values _sum_supply = 0; for (int i = 0; i != _root; ++i) { _sum_supply += _supply[i]; } if (_sum_supply > 0) return INFEASIBLE; // Initialize vectors for (int i = 0; i != _root; ++i) { _pi[i] = 0; _excess[i] = _supply[i]; } // Remove non-zero lower bounds const Value MAX = std::numeric_limits::max(); int last_out; if (_have_lower) { for (int i = 0; i != _root; ++i) { last_out = _first_out[i+1]; for (int j = _first_out[i]; j != last_out; ++j) { if (_forward[j]) { Value c = _lower[j]; if (c >= 0) { _res_cap[j] = _upper[j] < MAX ? _upper[j] - c : INF; } else { _res_cap[j] = _upper[j] < MAX + c ? _upper[j] - c : INF; } _excess[i] -= c; _excess[_target[j]] += c; } else { _res_cap[j] = 0; } } } } else { for (int j = 0; j != _res_arc_num; ++j) { _res_cap[j] = _forward[j] ? _upper[j] : 0; } } // Handle negative costs for (int i = 0; i != _root; ++i) { last_out = _first_out[i+1] - 1; for (int j = _first_out[i]; j != last_out; ++j) { Value rc = _res_cap[j]; if (_cost[j] < 0 && rc > 0) { if (rc >= MAX) return UNBOUNDED; _excess[i] -= rc; _excess[_target[j]] += rc; _res_cap[j] = 0; _res_cap[_reverse[j]] += rc; } } } // Handle GEQ supply type if (_sum_supply < 0) { _pi[_root] = 0; _excess[_root] = -_sum_supply; for (int a = _first_out[_root]; a != _res_arc_num; ++a) { int ra = _reverse[a]; _res_cap[a] = -_sum_supply + 1; _res_cap[ra] = 0; _cost[a] = 0; _cost[ra] = 0; } } else { _pi[_root] = 0; _excess[_root] = 0; for (int a = _first_out[_root]; a != _res_arc_num; ++a) { int ra = _reverse[a]; _res_cap[a] = 1; _res_cap[ra] = 0; _cost[a] = 0; _cost[ra] = 0; } } // Initialize delta value if (_factor > 1) { // With scaling Value max_sup = 0, max_dem = 0, max_cap = 0; for (int i = 0; i != _root; ++i) { Value ex = _excess[i]; if ( ex > max_sup) max_sup = ex; if (-ex > max_dem) max_dem = -ex; int last_out = _first_out[i+1] - 1; for (int j = _first_out[i]; j != last_out; ++j) { if (_res_cap[j] > max_cap) max_cap = _res_cap[j]; } } max_sup = std::min(std::min(max_sup, max_dem), max_cap); for (_delta = 1; 2 * _delta <= max_sup; _delta *= 2) ; } else { // Without scaling _delta = 1; } return OPTIMAL; } ProblemType start() { // Execute the algorithm ProblemType pt; if (_delta > 1) pt = startWithScaling(); else pt = startWithoutScaling(); // Handle non-zero lower bounds if (_have_lower) { int limit = _first_out[_root]; for (int j = 0; j != limit; ++j) { if (!_forward[j]) _res_cap[j] += _lower[j]; } } // Shift potentials if necessary Cost pr = _pi[_root]; if (_sum_supply < 0 || pr > 0) { for (int i = 0; i != _node_num; ++i) { _pi[i] -= pr; } } return pt; } // Execute the capacity scaling algorithm ProblemType startWithScaling() { // Perform capacity scaling phases int s, t; ResidualDijkstra _dijkstra(*this); while (true) { // Saturate all arcs not satisfying the optimality condition int last_out; for (int u = 0; u != _node_num; ++u) { last_out = _sum_supply < 0 ? _first_out[u+1] : _first_out[u+1] - 1; for (int a = _first_out[u]; a != last_out; ++a) { int v = _target[a]; Cost c = _cost[a] + _pi[u] - _pi[v]; Value rc = _res_cap[a]; if (c < 0 && rc >= _delta) { _excess[u] -= rc; _excess[v] += rc; _res_cap[a] = 0; _res_cap[_reverse[a]] += rc; } } } // Find excess nodes and deficit nodes _excess_nodes.clear(); _deficit_nodes.clear(); for (int u = 0; u != _node_num; ++u) { Value ex = _excess[u]; if (ex >= _delta) _excess_nodes.push_back(u); if (ex <= -_delta) _deficit_nodes.push_back(u); } int next_node = 0, next_def_node = 0; // Find augmenting shortest paths while (next_node < int(_excess_nodes.size())) { // Check deficit nodes if (_delta > 1) { bool delta_deficit = false; for ( ; next_def_node < int(_deficit_nodes.size()); ++next_def_node ) { if (_excess[_deficit_nodes[next_def_node]] <= -_delta) { delta_deficit = true; break; } } if (!delta_deficit) break; } // Run Dijkstra in the residual network s = _excess_nodes[next_node]; if ((t = _dijkstra.run(s, _delta)) == -1) { if (_delta > 1) { ++next_node; continue; } return INFEASIBLE; } // Augment along a shortest path from s to t Value d = std::min(_excess[s], -_excess[t]); int u = t; int a; if (d > _delta) { while ((a = _pred[u]) != -1) { if (_res_cap[a] < d) d = _res_cap[a]; u = _source[a]; } } u = t; while ((a = _pred[u]) != -1) { _res_cap[a] -= d; _res_cap[_reverse[a]] += d; u = _source[a]; } _excess[s] -= d; _excess[t] += d; if (_excess[s] < _delta) ++next_node; } if (_delta == 1) break; _delta = _delta <= _factor ? 1 : _delta / _factor; } return OPTIMAL; } // Execute the successive shortest path algorithm ProblemType startWithoutScaling() { // Find excess nodes _excess_nodes.clear(); for (int i = 0; i != _node_num; ++i) { if (_excess[i] > 0) _excess_nodes.push_back(i); } if (_excess_nodes.size() == 0) return OPTIMAL; int next_node = 0; // Find shortest paths int s, t; ResidualDijkstra _dijkstra(*this); while ( _excess[_excess_nodes[next_node]] > 0 || ++next_node < int(_excess_nodes.size()) ) { // Run Dijkstra in the residual network s = _excess_nodes[next_node]; if ((t = _dijkstra.run(s)) == -1) return INFEASIBLE; // Augment along a shortest path from s to t Value d = std::min(_excess[s], -_excess[t]); int u = t; int a; if (d > 1) { while ((a = _pred[u]) != -1) { if (_res_cap[a] < d) d = _res_cap[a]; u = _source[a]; } } u = t; while ((a = _pred[u]) != -1) { _res_cap[a] -= d; _res_cap[_reverse[a]] += d; u = _source[a]; } _excess[s] -= d; _excess[t] += d; } return OPTIMAL; } }; //class CapacityScaling ///@} } //namespace lemon #endif //LEMON_CAPACITY_SCALING_H