# HG changeset patch
# User Peter Kovacs <kpeter@inf.elte.hu>
# Date 1258064982 -3600
# Node ID 9c428bb2b1056da486089cbcf6eee0c8e8ae4488
# Parent 78071e00de00622617c241ef612f6ba55ac2450d
Port CostScaling from SVN -r3524 (#180)
diff -r 78071e00de00 -r 9c428bb2b105 lemon/Makefile.am
--- a/lemon/Makefile.am Thu Nov 12 23:27:21 2009 +0100
+++ b/lemon/Makefile.am Thu Nov 12 23:29:42 2009 +0100
@@ -69,8 +69,9 @@
lemon/color.h \
lemon/concept_check.h \
lemon/connectivity.h \
+ lemon/core.h \
+ lemon/cost_scaling.h \
lemon/counter.h \
- lemon/core.h \
lemon/cplex.h \
lemon/dfs.h \
lemon/dijkstra.h \
diff -r 78071e00de00 -r 9c428bb2b105 lemon/cost_scaling.h
--- /dev/null Thu Jan 01 00:00:00 1970 +0000
+++ b/lemon/cost_scaling.h Thu Nov 12 23:29:42 2009 +0100
@@ -0,0 +1,850 @@
+/* -*- C++ -*-
+ *
+ * This file is a part of LEMON, a generic C++ optimization library
+ *
+ * Copyright (C) 2003-2008
+ * 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_COST_SCALING_H
+#define LEMON_COST_SCALING_H
+
+/// \ingroup min_cost_flow_algs
+/// \file
+/// \brief Cost scaling algorithm for finding a minimum cost flow.
+
+#include <vector>
+#include <deque>
+#include <limits>
+
+#include <lemon/core.h>
+#include <lemon/maps.h>
+#include <lemon/math.h>
+#include <lemon/adaptors.h>
+#include <lemon/circulation.h>
+#include <lemon/bellman_ford.h>
+
+namespace lemon {
+
+ /// \addtogroup min_cost_flow_algs
+ /// @{
+
+ /// \brief Implementation of the cost scaling algorithm for finding a
+ /// minimum cost flow.
+ ///
+ /// \ref CostScaling implements the cost scaling algorithm performing
+ /// augment/push and relabel operations for finding a minimum cost
+ /// flow.
+ ///
+ /// \tparam Digraph The digraph type the algorithm runs on.
+ /// \tparam LowerMap The type of the lower bound map.
+ /// \tparam CapacityMap The type of the capacity (upper bound) map.
+ /// \tparam CostMap The type of the cost (length) map.
+ /// \tparam SupplyMap The type of the supply map.
+ ///
+ /// \warning
+ /// - Arc capacities and costs should be \e non-negative \e integers.
+ /// - Supply values should be \e signed \e integers.
+ /// - The value types of the maps should be convertible to each other.
+ /// - \c CostMap::Value must be signed type.
+ ///
+ /// \note Arc costs are multiplied with the number of nodes during
+ /// the algorithm so overflow problems may arise more easily than with
+ /// other minimum cost flow algorithms.
+ /// If it is available, <tt>long long int</tt> type is used instead of
+ /// <tt>long int</tt> in the inside computations.
+ ///
+ /// \author Peter Kovacs
+ template < typename Digraph,
+ typename LowerMap = typename Digraph::template ArcMap<int>,
+ typename CapacityMap = typename Digraph::template ArcMap<int>,
+ typename CostMap = typename Digraph::template ArcMap<int>,
+ typename SupplyMap = typename Digraph::template NodeMap<int> >
+ class CostScaling
+ {
+ TEMPLATE_DIGRAPH_TYPEDEFS(Digraph);
+
+ typedef typename CapacityMap::Value Capacity;
+ typedef typename CostMap::Value Cost;
+ typedef typename SupplyMap::Value Supply;
+ typedef typename Digraph::template ArcMap<Capacity> CapacityArcMap;
+ typedef typename Digraph::template NodeMap<Supply> SupplyNodeMap;
+
+ typedef ResidualDigraph< const Digraph,
+ CapacityArcMap, CapacityArcMap > ResDigraph;
+ typedef typename ResDigraph::Arc ResArc;
+
+#if defined __GNUC__ && !defined __STRICT_ANSI__
+ typedef long long int LCost;
+#else
+ typedef long int LCost;
+#endif
+ typedef typename Digraph::template ArcMap<LCost> LargeCostMap;
+
+ public:
+
+ /// The type of the flow map.
+ typedef typename Digraph::template ArcMap<Capacity> FlowMap;
+ /// The type of the potential map.
+ typedef typename Digraph::template NodeMap<LCost> PotentialMap;
+
+ private:
+
+ /// \brief Map adaptor class for handling residual arc costs.
+ ///
+ /// Map adaptor class for handling residual arc costs.
+ template <typename Map>
+ class ResidualCostMap : public MapBase<ResArc, typename Map::Value>
+ {
+ private:
+
+ const Map &_cost_map;
+
+ public:
+
+ ///\e
+ ResidualCostMap(const Map &cost_map) :
+ _cost_map(cost_map) {}
+
+ ///\e
+ inline typename Map::Value operator[](const ResArc &e) const {
+ return ResDigraph::forward(e) ? _cost_map[e] : -_cost_map[e];
+ }
+
+ }; //class ResidualCostMap
+
+ /// \brief Map adaptor class for handling reduced arc costs.
+ ///
+ /// Map adaptor class for handling reduced arc costs.
+ class ReducedCostMap : public MapBase<Arc, LCost>
+ {
+ private:
+
+ const Digraph &_gr;
+ const LargeCostMap &_cost_map;
+ const PotentialMap &_pot_map;
+
+ public:
+
+ ///\e
+ ReducedCostMap( const Digraph &gr,
+ const LargeCostMap &cost_map,
+ const PotentialMap &pot_map ) :
+ _gr(gr), _cost_map(cost_map), _pot_map(pot_map) {}
+
+ ///\e
+ inline LCost operator[](const Arc &e) const {
+ return _cost_map[e] + _pot_map[_gr.source(e)]
+ - _pot_map[_gr.target(e)];
+ }
+
+ }; //class ReducedCostMap
+
+ private:
+
+ // The digraph the algorithm runs on
+ const Digraph &_graph;
+ // The original lower bound map
+ const LowerMap *_lower;
+ // The modified capacity map
+ CapacityArcMap _capacity;
+ // The original cost map
+ const CostMap &_orig_cost;
+ // The scaled cost map
+ LargeCostMap _cost;
+ // The modified supply map
+ SupplyNodeMap _supply;
+ bool _valid_supply;
+
+ // Arc map of the current flow
+ FlowMap *_flow;
+ bool _local_flow;
+ // Node map of the current potentials
+ PotentialMap *_potential;
+ bool _local_potential;
+
+ // The residual cost map
+ ResidualCostMap<LargeCostMap> _res_cost;
+ // The residual digraph
+ ResDigraph *_res_graph;
+ // The reduced cost map
+ ReducedCostMap *_red_cost;
+ // The excess map
+ SupplyNodeMap _excess;
+ // The epsilon parameter used for cost scaling
+ LCost _epsilon;
+ // The scaling factor
+ int _alpha;
+
+ public:
+
+ /// \brief General constructor (with lower bounds).
+ ///
+ /// General constructor (with lower bounds).
+ ///
+ /// \param digraph The digraph the algorithm runs on.
+ /// \param lower The lower bounds of the arcs.
+ /// \param capacity The capacities (upper bounds) of the arcs.
+ /// \param cost The cost (length) values of the arcs.
+ /// \param supply The supply values of the nodes (signed).
+ CostScaling( const Digraph &digraph,
+ const LowerMap &lower,
+ const CapacityMap &capacity,
+ const CostMap &cost,
+ const SupplyMap &supply ) :
+ _graph(digraph), _lower(&lower), _capacity(digraph), _orig_cost(cost),
+ _cost(digraph), _supply(digraph), _flow(NULL), _local_flow(false),
+ _potential(NULL), _local_potential(false), _res_cost(_cost),
+ _res_graph(NULL), _red_cost(NULL), _excess(digraph, 0)
+ {
+ // Check the sum of supply values
+ Supply sum = 0;
+ for (NodeIt n(_graph); n != INVALID; ++n) sum += _supply[n];
+ _valid_supply = sum == 0;
+
+ for (ArcIt e(_graph); e != INVALID; ++e) _capacity[e] = capacity[e];
+ for (NodeIt n(_graph); n != INVALID; ++n) _supply[n] = supply[n];
+
+ // Remove non-zero lower bounds
+ for (ArcIt e(_graph); e != INVALID; ++e) {
+ if (lower[e] != 0) {
+ _capacity[e] -= lower[e];
+ _supply[_graph.source(e)] -= lower[e];
+ _supply[_graph.target(e)] += lower[e];
+ }
+ }
+ }
+/*
+ /// \brief General constructor (without lower bounds).
+ ///
+ /// General constructor (without lower bounds).
+ ///
+ /// \param digraph The digraph the algorithm runs on.
+ /// \param capacity The capacities (upper bounds) of the arcs.
+ /// \param cost The cost (length) values of the arcs.
+ /// \param supply The supply values of the nodes (signed).
+ CostScaling( const Digraph &digraph,
+ const CapacityMap &capacity,
+ const CostMap &cost,
+ const SupplyMap &supply ) :
+ _graph(digraph), _lower(NULL), _capacity(capacity), _orig_cost(cost),
+ _cost(digraph), _supply(supply), _flow(NULL), _local_flow(false),
+ _potential(NULL), _local_potential(false), _res_cost(_cost),
+ _res_graph(NULL), _red_cost(NULL), _excess(digraph, 0)
+ {
+ // Check the sum of supply values
+ Supply sum = 0;
+ for (NodeIt n(_graph); n != INVALID; ++n) sum += _supply[n];
+ _valid_supply = sum == 0;
+ }
+
+ /// \brief Simple constructor (with lower bounds).
+ ///
+ /// Simple constructor (with lower bounds).
+ ///
+ /// \param digraph The digraph the algorithm runs on.
+ /// \param lower The lower bounds of the arcs.
+ /// \param capacity The capacities (upper bounds) of the arcs.
+ /// \param cost The cost (length) values of the arcs.
+ /// \param s The source node.
+ /// \param t The target node.
+ /// \param flow_value 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).
+ CostScaling( const Digraph &digraph,
+ const LowerMap &lower,
+ const CapacityMap &capacity,
+ const CostMap &cost,
+ Node s, Node t,
+ Supply flow_value ) :
+ _graph(digraph), _lower(&lower), _capacity(capacity), _orig_cost(cost),
+ _cost(digraph), _supply(digraph, 0), _flow(NULL), _local_flow(false),
+ _potential(NULL), _local_potential(false), _res_cost(_cost),
+ _res_graph(NULL), _red_cost(NULL), _excess(digraph, 0)
+ {
+ // Remove non-zero lower bounds
+ _supply[s] = flow_value;
+ _supply[t] = -flow_value;
+ for (ArcIt e(_graph); e != INVALID; ++e) {
+ if (lower[e] != 0) {
+ _capacity[e] -= lower[e];
+ _supply[_graph.source(e)] -= lower[e];
+ _supply[_graph.target(e)] += lower[e];
+ }
+ }
+ _valid_supply = true;
+ }
+
+ /// \brief Simple constructor (without lower bounds).
+ ///
+ /// Simple constructor (without lower bounds).
+ ///
+ /// \param digraph The digraph the algorithm runs on.
+ /// \param capacity The capacities (upper bounds) of the arcs.
+ /// \param cost The cost (length) values of the arcs.
+ /// \param s The source node.
+ /// \param t The target node.
+ /// \param flow_value 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).
+ CostScaling( const Digraph &digraph,
+ const CapacityMap &capacity,
+ const CostMap &cost,
+ Node s, Node t,
+ Supply flow_value ) :
+ _graph(digraph), _lower(NULL), _capacity(capacity), _orig_cost(cost),
+ _cost(digraph), _supply(digraph, 0), _flow(NULL), _local_flow(false),
+ _potential(NULL), _local_potential(false), _res_cost(_cost),
+ _res_graph(NULL), _red_cost(NULL), _excess(digraph, 0)
+ {
+ _supply[s] = flow_value;
+ _supply[t] = -flow_value;
+ _valid_supply = true;
+ }
+*/
+ /// Destructor.
+ ~CostScaling() {
+ if (_local_flow) delete _flow;
+ if (_local_potential) delete _potential;
+ delete _res_graph;
+ delete _red_cost;
+ }
+
+ /// \brief Set the flow map.
+ ///
+ /// Set the flow map.
+ ///
+ /// \return \c (*this)
+ CostScaling& flowMap(FlowMap &map) {
+ if (_local_flow) {
+ delete _flow;
+ _local_flow = false;
+ }
+ _flow = ↦
+ return *this;
+ }
+
+ /// \brief Set the potential map.
+ ///
+ /// Set the potential map.
+ ///
+ /// \return \c (*this)
+ CostScaling& potentialMap(PotentialMap &map) {
+ if (_local_potential) {
+ delete _potential;
+ _local_potential = false;
+ }
+ _potential = ↦
+ return *this;
+ }
+
+ /// \name Execution control
+
+ /// @{
+
+ /// \brief Run the algorithm.
+ ///
+ /// Run the algorithm.
+ ///
+ /// \param partial_augment By default the algorithm performs
+ /// partial augment and relabel operations in the cost scaling
+ /// phases. Set this parameter to \c false for using local push and
+ /// relabel operations instead.
+ ///
+ /// \return \c true if a feasible flow can be found.
+ bool run(bool partial_augment = true) {
+ if (partial_augment) {
+ return init() && startPartialAugment();
+ } else {
+ return init() && startPushRelabel();
+ }
+ }
+
+ /// @}
+
+ /// \name Query Functions
+ /// The result of the algorithm can be obtained using these
+ /// functions.\n
+ /// \ref lemon::CostScaling::run() "run()" must be called before
+ /// using them.
+
+ /// @{
+
+ /// \brief Return a const reference to the arc map storing the
+ /// found flow.
+ ///
+ /// Return a const reference to the arc map storing the found flow.
+ ///
+ /// \pre \ref run() must be called before using this function.
+ const FlowMap& flowMap() const {
+ return *_flow;
+ }
+
+ /// \brief Return a const reference to the node map storing the
+ /// found potentials (the dual solution).
+ ///
+ /// Return a const reference to the node map storing the found
+ /// potentials (the dual solution).
+ ///
+ /// \pre \ref run() must be called before using this function.
+ const PotentialMap& potentialMap() const {
+ return *_potential;
+ }
+
+ /// \brief Return the flow on the given arc.
+ ///
+ /// Return the flow on the given arc.
+ ///
+ /// \pre \ref run() must be called before using this function.
+ Capacity flow(const Arc& arc) const {
+ return (*_flow)[arc];
+ }
+
+ /// \brief Return the potential of the given node.
+ ///
+ /// Return the potential of the given node.
+ ///
+ /// \pre \ref run() must be called before using this function.
+ Cost potential(const Node& node) const {
+ return (*_potential)[node];
+ }
+
+ /// \brief Return the total cost of the found flow.
+ ///
+ /// Return the total cost of the found flow. The complexity of the
+ /// function is \f$ O(e) \f$.
+ ///
+ /// \pre \ref run() must be called before using this function.
+ Cost totalCost() const {
+ Cost c = 0;
+ for (ArcIt e(_graph); e != INVALID; ++e)
+ c += (*_flow)[e] * _orig_cost[e];
+ return c;
+ }
+
+ /// @}
+
+ private:
+
+ /// Initialize the algorithm.
+ bool init() {
+ if (!_valid_supply) return false;
+ // The scaling factor
+ _alpha = 8;
+
+ // Initialize flow and potential maps
+ if (!_flow) {
+ _flow = new FlowMap(_graph);
+ _local_flow = true;
+ }
+ if (!_potential) {
+ _potential = new PotentialMap(_graph);
+ _local_potential = true;
+ }
+
+ _red_cost = new ReducedCostMap(_graph, _cost, *_potential);
+ _res_graph = new ResDigraph(_graph, _capacity, *_flow);
+
+ // Initialize the scaled cost map and the epsilon parameter
+ Cost max_cost = 0;
+ int node_num = countNodes(_graph);
+ for (ArcIt e(_graph); e != INVALID; ++e) {
+ _cost[e] = LCost(_orig_cost[e]) * node_num * _alpha;
+ if (_orig_cost[e] > max_cost) max_cost = _orig_cost[e];
+ }
+ _epsilon = max_cost * node_num;
+
+ // Find a feasible flow using Circulation
+ Circulation< Digraph, ConstMap<Arc, Capacity>, CapacityArcMap,
+ SupplyMap >
+ circulation( _graph, constMap<Arc>(Capacity(0)), _capacity,
+ _supply );
+ return circulation.flowMap(*_flow).run();
+ }
+
+ /// Execute the algorithm performing partial augmentation and
+ /// relabel operations.
+ bool startPartialAugment() {
+ // Paramters for heuristics
+// const int BF_HEURISTIC_EPSILON_BOUND = 1000;
+// const int BF_HEURISTIC_BOUND_FACTOR = 3;
+ // Maximum augment path length
+ const int MAX_PATH_LENGTH = 4;
+
+ // Variables
+ typename Digraph::template NodeMap<Arc> pred_arc(_graph);
+ typename Digraph::template NodeMap<bool> forward(_graph);
+ typename Digraph::template NodeMap<OutArcIt> next_out(_graph);
+ typename Digraph::template NodeMap<InArcIt> next_in(_graph);
+ typename Digraph::template NodeMap<bool> next_dir(_graph);
+ std::deque<Node> active_nodes;
+ std::vector<Node> path_nodes;
+
+// int node_num = countNodes(_graph);
+ for ( ; _epsilon >= 1; _epsilon = _epsilon < _alpha && _epsilon > 1 ?
+ 1 : _epsilon / _alpha )
+ {
+/*
+ // "Early Termination" heuristic: use Bellman-Ford algorithm
+ // to check if the current flow is optimal
+ if (_epsilon <= BF_HEURISTIC_EPSILON_BOUND) {
+ typedef ShiftMap< ResidualCostMap<LargeCostMap> > ShiftCostMap;
+ ShiftCostMap shift_cost(_res_cost, 1);
+ BellmanFord<ResDigraph, ShiftCostMap> bf(*_res_graph, shift_cost);
+ bf.init(0);
+ bool done = false;
+ int K = int(BF_HEURISTIC_BOUND_FACTOR * sqrt(node_num));
+ for (int i = 0; i < K && !done; ++i)
+ done = bf.processNextWeakRound();
+ if (done) break;
+ }
+*/
+ // Saturate arcs not satisfying the optimality condition
+ Capacity delta;
+ for (ArcIt e(_graph); e != INVALID; ++e) {
+ if (_capacity[e] - (*_flow)[e] > 0 && (*_red_cost)[e] < 0) {
+ delta = _capacity[e] - (*_flow)[e];
+ _excess[_graph.source(e)] -= delta;
+ _excess[_graph.target(e)] += delta;
+ (*_flow)[e] = _capacity[e];
+ }
+ if ((*_flow)[e] > 0 && -(*_red_cost)[e] < 0) {
+ _excess[_graph.target(e)] -= (*_flow)[e];
+ _excess[_graph.source(e)] += (*_flow)[e];
+ (*_flow)[e] = 0;
+ }
+ }
+
+ // Find active nodes (i.e. nodes with positive excess)
+ for (NodeIt n(_graph); n != INVALID; ++n) {
+ if (_excess[n] > 0) active_nodes.push_back(n);
+ }
+
+ // Initialize the next arc maps
+ for (NodeIt n(_graph); n != INVALID; ++n) {
+ next_out[n] = OutArcIt(_graph, n);
+ next_in[n] = InArcIt(_graph, n);
+ next_dir[n] = true;
+ }
+
+ // Perform partial augment and relabel operations
+ while (active_nodes.size() > 0) {
+ // Select an active node (FIFO selection)
+ if (_excess[active_nodes[0]] <= 0) {
+ active_nodes.pop_front();
+ continue;
+ }
+ Node start = active_nodes[0];
+ path_nodes.clear();
+ path_nodes.push_back(start);
+
+ // Find an augmenting path from the start node
+ Node u, tip = start;
+ LCost min_red_cost;
+ while ( _excess[tip] >= 0 &&
+ int(path_nodes.size()) <= MAX_PATH_LENGTH )
+ {
+ if (next_dir[tip]) {
+ for (OutArcIt e = next_out[tip]; e != INVALID; ++e) {
+ if (_capacity[e] - (*_flow)[e] > 0 && (*_red_cost)[e] < 0) {
+ u = _graph.target(e);
+ pred_arc[u] = e;
+ forward[u] = true;
+ next_out[tip] = e;
+ tip = u;
+ path_nodes.push_back(tip);
+ goto next_step;
+ }
+ }
+ next_dir[tip] = false;
+ }
+ for (InArcIt e = next_in[tip]; e != INVALID; ++e) {
+ if ((*_flow)[e] > 0 && -(*_red_cost)[e] < 0) {
+ u = _graph.source(e);
+ pred_arc[u] = e;
+ forward[u] = false;
+ next_in[tip] = e;
+ tip = u;
+ path_nodes.push_back(tip);
+ goto next_step;
+ }
+ }
+
+ // Relabel tip node
+ min_red_cost = std::numeric_limits<LCost>::max() / 2;
+ for (OutArcIt oe(_graph, tip); oe != INVALID; ++oe) {
+ if ( _capacity[oe] - (*_flow)[oe] > 0 &&
+ (*_red_cost)[oe] < min_red_cost )
+ min_red_cost = (*_red_cost)[oe];
+ }
+ for (InArcIt ie(_graph, tip); ie != INVALID; ++ie) {
+ if ((*_flow)[ie] > 0 && -(*_red_cost)[ie] < min_red_cost)
+ min_red_cost = -(*_red_cost)[ie];
+ }
+ (*_potential)[tip] -= min_red_cost + _epsilon;
+
+ // Reset the next arc maps
+ next_out[tip] = OutArcIt(_graph, tip);
+ next_in[tip] = InArcIt(_graph, tip);
+ next_dir[tip] = true;
+
+ // Step back
+ if (tip != start) {
+ path_nodes.pop_back();
+ tip = path_nodes[path_nodes.size()-1];
+ }
+
+ next_step:
+ continue;
+ }
+
+ // Augment along the found path (as much flow as possible)
+ Capacity delta;
+ for (int i = 1; i < int(path_nodes.size()); ++i) {
+ u = path_nodes[i];
+ delta = forward[u] ?
+ _capacity[pred_arc[u]] - (*_flow)[pred_arc[u]] :
+ (*_flow)[pred_arc[u]];
+ delta = std::min(delta, _excess[path_nodes[i-1]]);
+ (*_flow)[pred_arc[u]] += forward[u] ? delta : -delta;
+ _excess[path_nodes[i-1]] -= delta;
+ _excess[u] += delta;
+ if (_excess[u] > 0 && _excess[u] <= delta) active_nodes.push_back(u);
+ }
+ }
+ }
+
+ // Compute node potentials for the original costs
+ ResidualCostMap<CostMap> res_cost(_orig_cost);
+ BellmanFord< ResDigraph, ResidualCostMap<CostMap> >
+ bf(*_res_graph, res_cost);
+ bf.init(0); bf.start();
+ for (NodeIt n(_graph); n != INVALID; ++n)
+ (*_potential)[n] = bf.dist(n);
+
+ // Handle non-zero lower bounds
+ if (_lower) {
+ for (ArcIt e(_graph); e != INVALID; ++e)
+ (*_flow)[e] += (*_lower)[e];
+ }
+ return true;
+ }
+
+ /// Execute the algorithm performing push and relabel operations.
+ bool startPushRelabel() {
+ // Paramters for heuristics
+// const int BF_HEURISTIC_EPSILON_BOUND = 1000;
+// const int BF_HEURISTIC_BOUND_FACTOR = 3;
+
+ typename Digraph::template NodeMap<bool> hyper(_graph, false);
+ typename Digraph::template NodeMap<Arc> pred_arc(_graph);
+ typename Digraph::template NodeMap<bool> forward(_graph);
+ typename Digraph::template NodeMap<OutArcIt> next_out(_graph);
+ typename Digraph::template NodeMap<InArcIt> next_in(_graph);
+ typename Digraph::template NodeMap<bool> next_dir(_graph);
+ std::deque<Node> active_nodes;
+
+// int node_num = countNodes(_graph);
+ for ( ; _epsilon >= 1; _epsilon = _epsilon < _alpha && _epsilon > 1 ?
+ 1 : _epsilon / _alpha )
+ {
+/*
+ // "Early Termination" heuristic: use Bellman-Ford algorithm
+ // to check if the current flow is optimal
+ if (_epsilon <= BF_HEURISTIC_EPSILON_BOUND) {
+ typedef ShiftMap< ResidualCostMap<LargeCostMap> > ShiftCostMap;
+ ShiftCostMap shift_cost(_res_cost, 1);
+ BellmanFord<ResDigraph, ShiftCostMap> bf(*_res_graph, shift_cost);
+ bf.init(0);
+ bool done = false;
+ int K = int(BF_HEURISTIC_BOUND_FACTOR * sqrt(node_num));
+ for (int i = 0; i < K && !done; ++i)
+ done = bf.processNextWeakRound();
+ if (done) break;
+ }
+*/
+
+ // Saturate arcs not satisfying the optimality condition
+ Capacity delta;
+ for (ArcIt e(_graph); e != INVALID; ++e) {
+ if (_capacity[e] - (*_flow)[e] > 0 && (*_red_cost)[e] < 0) {
+ delta = _capacity[e] - (*_flow)[e];
+ _excess[_graph.source(e)] -= delta;
+ _excess[_graph.target(e)] += delta;
+ (*_flow)[e] = _capacity[e];
+ }
+ if ((*_flow)[e] > 0 && -(*_red_cost)[e] < 0) {
+ _excess[_graph.target(e)] -= (*_flow)[e];
+ _excess[_graph.source(e)] += (*_flow)[e];
+ (*_flow)[e] = 0;
+ }
+ }
+
+ // Find active nodes (i.e. nodes with positive excess)
+ for (NodeIt n(_graph); n != INVALID; ++n) {
+ if (_excess[n] > 0) active_nodes.push_back(n);
+ }
+
+ // Initialize the next arc maps
+ for (NodeIt n(_graph); n != INVALID; ++n) {
+ next_out[n] = OutArcIt(_graph, n);
+ next_in[n] = InArcIt(_graph, n);
+ next_dir[n] = true;
+ }
+
+ // Perform push and relabel operations
+ while (active_nodes.size() > 0) {
+ // Select an active node (FIFO selection)
+ Node n = active_nodes[0], t;
+ bool relabel_enabled = true;
+
+ // Perform push operations if there are admissible arcs
+ if (_excess[n] > 0 && next_dir[n]) {
+ OutArcIt e = next_out[n];
+ for ( ; e != INVALID; ++e) {
+ if (_capacity[e] - (*_flow)[e] > 0 && (*_red_cost)[e] < 0) {
+ delta = std::min(_capacity[e] - (*_flow)[e], _excess[n]);
+ t = _graph.target(e);
+
+ // Push-look-ahead heuristic
+ Capacity ahead = -_excess[t];
+ for (OutArcIt oe(_graph, t); oe != INVALID; ++oe) {
+ if (_capacity[oe] - (*_flow)[oe] > 0 && (*_red_cost)[oe] < 0)
+ ahead += _capacity[oe] - (*_flow)[oe];
+ }
+ for (InArcIt ie(_graph, t); ie != INVALID; ++ie) {
+ if ((*_flow)[ie] > 0 && -(*_red_cost)[ie] < 0)
+ ahead += (*_flow)[ie];
+ }
+ if (ahead < 0) ahead = 0;
+
+ // Push flow along the arc
+ if (ahead < delta) {
+ (*_flow)[e] += ahead;
+ _excess[n] -= ahead;
+ _excess[t] += ahead;
+ active_nodes.push_front(t);
+ hyper[t] = true;
+ relabel_enabled = false;
+ break;
+ } else {
+ (*_flow)[e] += delta;
+ _excess[n] -= delta;
+ _excess[t] += delta;
+ if (_excess[t] > 0 && _excess[t] <= delta)
+ active_nodes.push_back(t);
+ }
+
+ if (_excess[n] == 0) break;
+ }
+ }
+ if (e != INVALID) {
+ next_out[n] = e;
+ } else {
+ next_dir[n] = false;
+ }
+ }
+
+ if (_excess[n] > 0 && !next_dir[n]) {
+ InArcIt e = next_in[n];
+ for ( ; e != INVALID; ++e) {
+ if ((*_flow)[e] > 0 && -(*_red_cost)[e] < 0) {
+ delta = std::min((*_flow)[e], _excess[n]);
+ t = _graph.source(e);
+
+ // Push-look-ahead heuristic
+ Capacity ahead = -_excess[t];
+ for (OutArcIt oe(_graph, t); oe != INVALID; ++oe) {
+ if (_capacity[oe] - (*_flow)[oe] > 0 && (*_red_cost)[oe] < 0)
+ ahead += _capacity[oe] - (*_flow)[oe];
+ }
+ for (InArcIt ie(_graph, t); ie != INVALID; ++ie) {
+ if ((*_flow)[ie] > 0 && -(*_red_cost)[ie] < 0)
+ ahead += (*_flow)[ie];
+ }
+ if (ahead < 0) ahead = 0;
+
+ // Push flow along the arc
+ if (ahead < delta) {
+ (*_flow)[e] -= ahead;
+ _excess[n] -= ahead;
+ _excess[t] += ahead;
+ active_nodes.push_front(t);
+ hyper[t] = true;
+ relabel_enabled = false;
+ break;
+ } else {
+ (*_flow)[e] -= delta;
+ _excess[n] -= delta;
+ _excess[t] += delta;
+ if (_excess[t] > 0 && _excess[t] <= delta)
+ active_nodes.push_back(t);
+ }
+
+ if (_excess[n] == 0) break;
+ }
+ }
+ next_in[n] = e;
+ }
+
+ // Relabel the node if it is still active (or hyper)
+ if (relabel_enabled && (_excess[n] > 0 || hyper[n])) {
+ LCost min_red_cost = std::numeric_limits<LCost>::max() / 2;
+ for (OutArcIt oe(_graph, n); oe != INVALID; ++oe) {
+ if ( _capacity[oe] - (*_flow)[oe] > 0 &&
+ (*_red_cost)[oe] < min_red_cost )
+ min_red_cost = (*_red_cost)[oe];
+ }
+ for (InArcIt ie(_graph, n); ie != INVALID; ++ie) {
+ if ((*_flow)[ie] > 0 && -(*_red_cost)[ie] < min_red_cost)
+ min_red_cost = -(*_red_cost)[ie];
+ }
+ (*_potential)[n] -= min_red_cost + _epsilon;
+ hyper[n] = false;
+
+ // Reset the next arc maps
+ next_out[n] = OutArcIt(_graph, n);
+ next_in[n] = InArcIt(_graph, n);
+ next_dir[n] = true;
+ }
+
+ // Remove nodes that are not active nor hyper
+ while ( active_nodes.size() > 0 &&
+ _excess[active_nodes[0]] <= 0 &&
+ !hyper[active_nodes[0]] ) {
+ active_nodes.pop_front();
+ }
+ }
+ }
+
+ // Compute node potentials for the original costs
+ ResidualCostMap<CostMap> res_cost(_orig_cost);
+ BellmanFord< ResDigraph, ResidualCostMap<CostMap> >
+ bf(*_res_graph, res_cost);
+ bf.init(0); bf.start();
+ for (NodeIt n(_graph); n != INVALID; ++n)
+ (*_potential)[n] = bf.dist(n);
+
+ // Handle non-zero lower bounds
+ if (_lower) {
+ for (ArcIt e(_graph); e != INVALID; ++e)
+ (*_flow)[e] += (*_lower)[e];
+ }
+ return true;
+ }
+
+ }; //class CostScaling
+
+ ///@}
+
+} //namespace lemon
+
+#endif //LEMON_COST_SCALING_H