lemon: comparison lemon/cancel_and

equal deleted inserted replaced

--1:000000000000
+:7d547fc859fc
+/* -*- 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_CANCEL_AND_TIGHTEN_H
+#define LEMON_CANCEL_AND_TIGHTEN_H
+/// \ingroup min_cost_flow
+///
+/// \file
+/// \brief Cancel and Tighten algorithm for finding a minimum cost flow.
+#include <vector>
+#include <lemon/circulation.h>
+#include <lemon/bellman_ford.h>
+#include <lemon/howard.h>
+#include <lemon/adaptors.h>
+#include <lemon/tolerance.h>
+#include <lemon/math.h>
+#include <lemon/static_graph.h>
+namespace lemon {
+/// \addtogroup min_cost_flow
+/// @{
+/// \brief Implementation of the Cancel and Tighten algorithm for
+/// finding a minimum cost flow.
+///
+/// \ref CancelAndTighten implements the Cancel and Tighten algorithm 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.
+///
+/// \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 CancelAndTighten
+{
+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;
+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<Cost> PotentialMap;
+private:
+/// \brief Map adaptor class for handling residual arc costs.
+///
+/// Map adaptor class for handling residual arc costs.
+class ResidualCostMap : public MapBase<typename ResDigraph::Arc, Cost>
+{
+typedef typename ResDigraph::Arc Arc;
+private:
+const CostMap &_cost_map;
+public:
+///\e
+ResidualCostMap(const CostMap &cost_map) : _cost_map(cost_map) {}
+///\e
+Cost operator[](const Arc &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, Cost>
+{
+private:
+const Digraph &_gr;
+const CostMap &_cost_map;
+const PotentialMap &_pot_map;
+public:
+///\e
+ReducedCostMap( const Digraph &gr,
+const CostMap &cost_map,
+const PotentialMap &pot_map ) :
+_gr(gr), _cost_map(cost_map), _pot_map(pot_map) {}
+///\e
+inline Cost operator[](const Arc &e) const {
+return _cost_map[e] + _pot_map[_gr.source(e)]
+- _pot_map[_gr.target(e)];
+}
+}; //class ReducedCostMap
+struct BFOperationTraits {
+static double zero() { return 0; }
+static double infinity() {
+return std::numeric_limits<double>::infinity();
+}
+static double plus(const double& left, const double& right) {
+return left + right;
+}
+static bool less(const double& left, const double& right) {
+return left + 1e-6 < right;
+}
+}; // class BFOperationTraits
+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 &_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 digraph
+ResDigraph *_res_graph;
+// The residual cost map
+ResidualCostMap _res_cost;
+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).
+CancelAndTighten( const Digraph &digraph,
+const LowerMap &lower,
+const CapacityMap &capacity,
+const CostMap &cost,
+const SupplyMap &supply ) :
+_graph(digraph), _lower(&lower), _capacity(digraph), _cost(cost),
+_supply(digraph), _flow(NULL), _local_flow(false),
+_potential(NULL), _local_potential(false),
+_res_graph(NULL), _res_cost(_cost)
+{
+// Check the sum of supply values
+Supply sum = 0;
+for (NodeIt n(_graph); n != INVALID; ++n) {
+_supply[n] = supply[n];
+sum += _supply[n];
+}
+_valid_supply = sum == 0;
+// Remove non-zero lower bounds
+for (ArcIt e(_graph); e != INVALID; ++e) {
+_capacity[e] = capacity[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).
+CancelAndTighten( const Digraph &digraph,
+const CapacityMap &capacity,
+const CostMap &cost,
+const SupplyMap &supply ) :
+_graph(digraph), _lower(NULL), _capacity(capacity), _cost(cost),
+_supply(supply), _flow(NULL), _local_flow(false),
+_potential(NULL), _local_potential(false),
+_res_graph(NULL), _res_cost(_cost)
+{
+// 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).
+CancelAndTighten( 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), _cost(cost),
+_supply(digraph, 0), _flow(NULL), _local_flow(false),
+_potential(NULL), _local_potential(false),
+_res_graph(NULL), _res_cost(_cost)
+{
+// 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).
+CancelAndTighten( const Digraph &digraph,
+const CapacityMap &capacity,
+const CostMap &cost,
+Node s, Node t,
+Supply flow_value ) :
+_graph(digraph), _lower(NULL), _capacity(capacity), _cost(cost),
+_supply(digraph, 0), _flow(NULL), _local_flow(false),
+_potential(NULL), _local_potential(false),
+_res_graph(NULL), _res_cost(_cost)
+{
+_supply[s] =  flow_value;
+_supply[t] = -flow_value;
+_valid_supply = true;
+}
+*/
+/// Destructor.
+~CancelAndTighten() {
+if (_local_flow) delete _flow;
+if (_local_potential) delete _potential;
+delete _res_graph;
+}
+/// \brief Set the flow map.
+///
+/// Set the flow map.
+///
+/// \return \c (*this)
+CancelAndTighten& flowMap(FlowMap &map) {
+if (_local_flow) {
+delete _flow;
+_local_flow = false;
+}
+_flow = &map;
+return *this;
+}
+/// \brief Set the potential map.
+///
+/// Set the potential map.
+///
+/// \return \c (*this)
+CancelAndTighten& potentialMap(PotentialMap &map) {
+if (_local_potential) {
+delete _potential;
+_local_potential = false;
+}
+_potential = &map;
+return *this;
+}
+/// \name Execution control
+/// @{
+/// \brief Run the algorithm.
+///
+/// Run the algorithm.
+///
+/// \return \c true if a feasible flow can be found.
+bool run() {
+return init() && start();
+}
+/// @}
+/// \name Query Functions
+/// The result of the algorithm can be obtained using these
+/// functions.\n
+/// \ref lemon::CancelAndTighten::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] * _cost[e];
+return c;
+}
+/// @}
+private:
+/// Initialize the algorithm.
+bool init() {
+if (!_valid_supply) return false;
+// Initialize flow and potential maps
+if (!_flow) {
+_flow = new FlowMap(_graph);
+_local_flow = true;
+}
+if (!_potential) {
+_potential = new PotentialMap(_graph);
+_local_potential = true;
+}
+_res_graph = new ResDigraph(_graph, _capacity, *_flow);
+// 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();
+}
+bool start() {
+const double LIMIT_FACTOR = 0.01;
+const int MIN_LIMIT = 3;
+typedef typename Digraph::template NodeMap<double> FloatPotentialMap;
+typedef typename Digraph::template NodeMap<int> LevelMap;
+typedef typename Digraph::template NodeMap<bool> BoolNodeMap;
+typedef typename Digraph::template NodeMap<Node> PredNodeMap;
+typedef typename Digraph::template NodeMap<Arc> PredArcMap;
+typedef typename ResDigraph::template ArcMap<double> ResShiftCostMap;
+FloatPotentialMap pi(_graph);
+LevelMap level(_graph);
+BoolNodeMap reached(_graph);
+BoolNodeMap processed(_graph);
+PredNodeMap pred_node(_graph);
+PredArcMap pred_arc(_graph);
+int node_num = countNodes(_graph);
+typedef std::pair<Arc, bool> pair;
+std::vector<pair> stack(node_num);
+std::vector<Node> proc_vector(node_num);
+ResShiftCostMap shift_cost(*_res_graph);
+Tolerance<double> tol;
+tol.epsilon(1e-6);
+Timer t1, t2, t3;
+t1.reset();
+t2.reset();
+t3.reset();
+// Initialize epsilon and the node potentials
+double epsilon = 0;
+for (ArcIt e(_graph); e != INVALID; ++e) {
+if (_capacity[e] - (*_flow)[e] > 0 && _cost[e] < -epsilon)
+epsilon = -_cost[e];
+else if ((*_flow)[e] > 0 && _cost[e] > epsilon)
+epsilon = _cost[e];
+}
+for (NodeIt v(_graph); v != INVALID; ++v) {
+pi[v] = 0;
+}
+// Start phases
+int limit = int(LIMIT_FACTOR * node_num);
+if (limit < MIN_LIMIT) limit = MIN_LIMIT;
+int iter = limit;
+while (epsilon * node_num >= 1) {
+t1.start();
+// Find and cancel cycles in the admissible digraph using DFS
+for (NodeIt n(_graph); n != INVALID; ++n) {
+reached[n] = false;
+processed[n] = false;
+}
+int stack_head = -1;
+int proc_head = -1;
+for (NodeIt start(_graph); start != INVALID; ++start) {
+if (reached[start]) continue;
+// New start node
+reached[start] = true;
+pred_arc[start] = INVALID;
+pred_node[start] = INVALID;
+// Find the first admissible residual outgoing arc
+double p = pi[start];
+Arc e;
+_graph.firstOut(e, start);
+while ( e != INVALID && (_capacity[e] - (*_flow)[e] == 0 ||
+!tol.negative(_cost[e] + p - pi[_graph.target(e)])) )
+_graph.nextOut(e);
+if (e != INVALID) {
+stack[++stack_head] = pair(e, true);
+goto next_step_1;
+}
+_graph.firstIn(e, start);
+while ( e != INVALID && ((*_flow)[e] == 0 ||
+!tol.negative(-_cost[e] + p - pi[_graph.source(e)])) )
+_graph.nextIn(e);
+if (e != INVALID) {
+stack[++stack_head] = pair(e, false);
+goto next_step_1;
+}
+processed[start] = true;
+proc_vector[++proc_head] = start;
+continue;
+next_step_1:
+while (stack_head >= 0) {
+Arc se = stack[stack_head].first;
+bool sf = stack[stack_head].second;
+Node u, v;
+if (sf) {
+u = _graph.source(se);
+v = _graph.target(se);
+} else {
+u = _graph.target(se);
+v = _graph.source(se);
+}
+if (!reached[v]) {
+// A new node is reached
+reached[v] = true;
+pred_node[v] = u;
+pred_arc[v] = se;
+// Find the first admissible residual outgoing arc
+double p = pi[v];
+Arc e;
+_graph.firstOut(e, v);
+while ( e != INVALID && (_capacity[e] - (*_flow)[e] == 0 ||
+!tol.negative(_cost[e] + p - pi[_graph.target(e)])) )
+_graph.nextOut(e);
+if (e != INVALID) {
+stack[++stack_head] = pair(e, true);
+goto next_step_2;
+}
+_graph.firstIn(e, v);
+while ( e != INVALID && ((*_flow)[e] == 0 ||
+!tol.negative(-_cost[e] + p - pi[_graph.source(e)])) )
+_graph.nextIn(e);
+stack[++stack_head] = pair(e, false);
+next_step_2: ;
+} else {
+if (!processed[v]) {
+// A cycle is found
+Node n, w = u;
+Capacity d, delta = sf ? _capacity[se] - (*_flow)[se] :
+(*_flow)[se];
+for (n = u; n != v; n = pred_node[n]) {
+d = _graph.target(pred_arc[n]) == n ?
+_capacity[pred_arc[n]] - (*_flow)[pred_arc[n]] :
+(*_flow)[pred_arc[n]];
+if (d <= delta) {
+delta = d;
+w = pred_node[n];
+}
+}
+/*
+std::cout << "CYCLE FOUND: ";
+if (sf)
+std::cout << _cost[se] + pi[_graph.source(se)] - pi[_graph.target(se)];
+else
+std::cout << _graph.id(se) << ":" << -(_cost[se] + pi[_graph.source(se)] - pi[_graph.target(se)]);
+for (n = u; n != v; n = pred_node[n]) {
+if (_graph.target(pred_arc[n]) == n)
+std::cout << " " << _cost[pred_arc[n]] + pi[_graph.source(pred_arc[n])] - pi[_graph.target(pred_arc[n])];
+else
+std::cout << " " << -(_cost[pred_arc[n]] + pi[_graph.source(pred_arc[n])] - pi[_graph.target(pred_arc[n])]);
+}
+std::cout << "\n";
+*/
+// Augment along the cycle
+(*_flow)[se] = sf ? (*_flow)[se] + delta :
+(*_flow)[se] - delta;
+for (n = u; n != v; n = pred_node[n]) {
+if (_graph.target(pred_arc[n]) == n)
+(*_flow)[pred_arc[n]] += delta;
+else
+(*_flow)[pred_arc[n]] -= delta;
+}
+for (n = u; stack_head > 0 && n != w; n = pred_node[n]) {
+--stack_head;
+reached[n] = false;
+}
+u = w;
+}
+v = u;
+// Find the next admissible residual outgoing arc
+double p = pi[v];
+Arc e = stack[stack_head].first;
+if (!stack[stack_head].second) {
+_graph.nextIn(e);
+goto in_arc_3;
+}
+_graph.nextOut(e);
+while ( e != INVALID && (_capacity[e] - (*_flow)[e] == 0 ||
+!tol.negative(_cost[e] + p - pi[_graph.target(e)])) )
+_graph.nextOut(e);
+if (e != INVALID) {
+stack[stack_head] = pair(e, true);
+goto next_step_3;
+}
+_graph.firstIn(e, v);
+in_arc_3:
+while ( e != INVALID && ((*_flow)[e] == 0 ||
+!tol.negative(-_cost[e] + p - pi[_graph.source(e)])) )
+_graph.nextIn(e);
+stack[stack_head] = pair(e, false);
+next_step_3: ;
+}
+while (stack_head >= 0 && stack[stack_head].first == INVALID) {
+processed[v] = true;
+proc_vector[++proc_head] = v;
+if (--stack_head >= 0) {
+v = stack[stack_head].second ?
+_graph.source(stack[stack_head].first) :
+_graph.target(stack[stack_head].first);
+// Find the next admissible residual outgoing arc
+double p = pi[v];
+Arc e = stack[stack_head].first;
+if (!stack[stack_head].second) {
+_graph.nextIn(e);
+goto in_arc_4;
+}
+_graph.nextOut(e);
+while ( e != INVALID && (_capacity[e] - (*_flow)[e] == 0 ||
+!tol.negative(_cost[e] + p - pi[_graph.target(e)])) )
+_graph.nextOut(e);
+if (e != INVALID) {
+stack[stack_head] = pair(e, true);
+goto next_step_4;
+}
+_graph.firstIn(e, v);
+in_arc_4:
+while ( e != INVALID && ((*_flow)[e] == 0 ||
+!tol.negative(-_cost[e] + p - pi[_graph.source(e)])) )
+_graph.nextIn(e);
+stack[stack_head] = pair(e, false);
+next_step_4: ;
+}
+}
+}
+}
+t1.stop();
+// Tighten potentials and epsilon
+if (--iter > 0) {
+// Compute levels
+t2.start();
+for (int i = proc_head; i >= 0; --i) {
+Node v = proc_vector[i];
+double p = pi[v];
+int l = 0;
+for (InArcIt e(_graph, v); e != INVALID; ++e) {
+Node u = _graph.source(e);
+if ( _capacity[e] - (*_flow)[e] > 0 &&
+tol.negative(_cost[e] + pi[u] - p) &&
+level[u] + 1 > l ) l = level[u] + 1;
+}
+for (OutArcIt e(_graph, v); e != INVALID; ++e) {
+Node u = _graph.target(e);
+if ( (*_flow)[e] > 0 &&
+tol.negative(-_cost[e] + pi[u] - p) &&
+level[u] + 1 > l ) l = level[u] + 1;
+}
+level[v] = l;
+}
+// Modify potentials
+double p, q = -1;
+for (ArcIt e(_graph); e != INVALID; ++e) {
+Node u = _graph.source(e);
+Node v = _graph.target(e);
+if (_capacity[e] - (*_flow)[e] > 0 && level[u] - level[v] > 0) {
+p = (_cost[e] + pi[u] - pi[v] + epsilon) /
+(level[u] - level[v] + 1);
+if (q < 0 || p < q) q = p;
+}
+else if ((*_flow)[e] > 0 && level[v] - level[u] > 0) {
+p = (-_cost[e] - pi[u] + pi[v] + epsilon) /
+(level[v] - level[u] + 1);
+if (q < 0 || p < q) q = p;
+}
+}
+for (NodeIt v(_graph); v != INVALID; ++v) {
+pi[v] -= q * level[v];
+}
+// Modify epsilon
+epsilon = 0;
+for (ArcIt e(_graph); e != INVALID; ++e) {
+double curr = _cost[e] + pi[_graph.source(e)]
+- pi[_graph.target(e)];
+if (_capacity[e] - (*_flow)[e] > 0 && curr < -epsilon)
+epsilon = -curr;
+else if ((*_flow)[e] > 0 && curr > epsilon)
+epsilon = curr;
+}
+t2.stop();
+} else {
+// Set epsilon to the minimum cycle mean
+t3.start();
+/**/
+StaticDigraph static_graph;
+typename ResDigraph::template NodeMap<typename StaticDigraph::Node> node_ref(*_res_graph);
+typename ResDigraph::template ArcMap<typename StaticDigraph::Arc> arc_ref(*_res_graph);
+static_graph.build(*_res_graph, node_ref, arc_ref);
+typename StaticDigraph::template NodeMap<double> static_pi(static_graph);
+typename StaticDigraph::template ArcMap<double> static_cost(static_graph);
+for (typename ResDigraph::ArcIt e(*_res_graph); e != INVALID; ++e)
+static_cost[arc_ref[e]] = _res_cost[e];
+Howard<StaticDigraph, typename StaticDigraph::template ArcMap<double> >
+mmc(static_graph, static_cost);
+mmc.findMinMean();
+epsilon = -mmc.cycleMean();
+/**/
+/*
+Howard<ResDigraph, ResidualCostMap> mmc(*_res_graph, _res_cost);
+mmc.findMinMean();
+epsilon = -mmc.cycleMean();
+*/
+// Compute feasible potentials for the current epsilon
+for (typename StaticDigraph::ArcIt e(static_graph); e != INVALID; ++e)
+static_cost[e] += epsilon;
+typename BellmanFord<StaticDigraph, typename StaticDigraph::template ArcMap<double> >::
+template SetDistMap<typename StaticDigraph::template NodeMap<double> >::
+template SetOperationTraits<BFOperationTraits>::Create
+bf(static_graph, static_cost);
+bf.distMap(static_pi).init(0);
+bf.start();
+for (NodeIt n(_graph); n != INVALID; ++n)
+pi[n] = static_pi[node_ref[n]];
+/*
+for (typename ResDigraph::ArcIt e(*_res_graph); e != INVALID; ++e)
+shift_cost[e] = _res_cost[e] + epsilon;
+typename BellmanFord<ResDigraph, ResShiftCostMap>::
+template SetDistMap<FloatPotentialMap>::
+template SetOperationTraits<BFOperationTraits>::Create
+bf(*_res_graph, shift_cost);
+bf.distMap(pi).init(0);
+bf.start();
+*/
+iter = limit;
+t3.stop();
+}
+}
+//      std::cout << t1.realTime() << " " << t2.realTime() << " " << t3.realTime() << "\n";
+// Handle non-zero lower bounds
+if (_lower) {
+for (ArcIt e(_graph); e != INVALID; ++e)
+(*_flow)[e] += (*_lower)[e];
+}
+return true;
+}
+}; //class CancelAndTighten
+///@}
+} //namespace lemon
+#endif //LEMON_CANCEL_AND_TIGHTEN_H