# HG changeset patch
# User Peter Kovacs <kpeter@inf.elte.hu>
# Date 1235465162 -3600
# Node ID e8349c6f12ca30c0a54b36825969cdaca81f933c
# Parent 6a17a722b50e1b22187f5a4cb99a7de28aada418
Port NetworkSimplex from SVN -r3520 (#234)
diff -r 6a17a722b50e -r e8349c6f12ca lemon/Makefile.am
--- a/lemon/Makefile.am Mon Feb 23 18:01:14 2009 +0000
+++ b/lemon/Makefile.am Tue Feb 24 09:46:02 2009 +0100
@@ -85,6 +85,7 @@
lemon/max_matching.h \
lemon/min_cost_arborescence.h \
lemon/nauty_reader.h \
+ lemon/network_simplex.h \
lemon/path.h \
lemon/preflow.h \
lemon/radix_sort.h \
diff -r 6a17a722b50e -r e8349c6f12ca lemon/network_simplex.h
--- /dev/null Thu Jan 01 00:00:00 1970 +0000
+++ b/lemon/network_simplex.h Tue Feb 24 09:46:02 2009 +0100
@@ -0,0 +1,1191 @@
+/* -*- mode: C++; indent-tabs-mode: nil; -*-
+ *
+ * This file is a part of LEMON, a generic C++ optimization library.
+ *
+ * Copyright (C) 2003-2009
+ * 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_NETWORK_SIMPLEX_H
+#define LEMON_NETWORK_SIMPLEX_H
+
+/// \ingroup min_cost_flow
+///
+/// \file
+/// \brief Network simplex algorithm for finding a minimum cost flow.
+
+#include <vector>
+#include <limits>
+#include <algorithm>
+
+#include <lemon/math.h>
+
+namespace lemon {
+
+ /// \addtogroup min_cost_flow
+ /// @{
+
+ /// \brief Implementation of the primal network simplex algorithm
+ /// for finding a \ref min_cost_flow "minimum cost flow".
+ ///
+ /// \ref NetworkSimplex implements the primal network simplex algorithm
+ /// for finding a \ref min_cost_flow "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 \ref NetworkSimplex provides five different pivot rule
+ /// implementations that significantly affect the efficiency of the
+ /// algorithm.
+ /// By default "Block Search" pivot rule is used, which proved to be
+ /// by far the most efficient according to our benchmark tests.
+ /// However another pivot rule can be selected using \ref run()
+ /// function with the proper parameter.
+#ifdef DOXYGEN
+ template < typename Digraph,
+ typename LowerMap,
+ typename CapacityMap,
+ typename CostMap,
+ typename SupplyMap >
+
+#else
+ 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> >
+#endif
+ class NetworkSimplex
+ {
+ TEMPLATE_DIGRAPH_TYPEDEFS(Digraph);
+
+ typedef typename CapacityMap::Value Capacity;
+ typedef typename CostMap::Value Cost;
+ typedef typename SupplyMap::Value Supply;
+
+ typedef std::vector<Arc> ArcVector;
+ typedef std::vector<Node> NodeVector;
+ typedef std::vector<int> IntVector;
+ typedef std::vector<bool> BoolVector;
+ typedef std::vector<Capacity> CapacityVector;
+ typedef std::vector<Cost> CostVector;
+ typedef std::vector<Supply> SupplyVector;
+
+ 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;
+
+ public:
+
+ /// Enum type for selecting the pivot rule used by \ref run()
+ enum PivotRuleEnum {
+ FIRST_ELIGIBLE_PIVOT,
+ BEST_ELIGIBLE_PIVOT,
+ BLOCK_SEARCH_PIVOT,
+ CANDIDATE_LIST_PIVOT,
+ ALTERING_LIST_PIVOT
+ };
+
+ private:
+
+ // State constants for arcs
+ enum ArcStateEnum {
+ STATE_UPPER = -1,
+ STATE_TREE = 0,
+ STATE_LOWER = 1
+ };
+
+ private:
+
+ // References for the original data
+ const Digraph &_orig_graph;
+ const LowerMap *_orig_lower;
+ const CapacityMap &_orig_cap;
+ const CostMap &_orig_cost;
+ const SupplyMap *_orig_supply;
+ Node _orig_source;
+ Node _orig_target;
+ Capacity _orig_flow_value;
+
+ // Result maps
+ FlowMap *_flow_result;
+ PotentialMap *_potential_result;
+ bool _local_flow;
+ bool _local_potential;
+
+ // Data structures for storing the graph
+ ArcVector _arc;
+ NodeVector _node;
+ IntNodeMap _node_id;
+ IntVector _source;
+ IntVector _target;
+
+ // The number of nodes and arcs in the original graph
+ int _node_num;
+ int _arc_num;
+
+ // Node and arc maps
+ CapacityVector _cap;
+ CostVector _cost;
+ CostVector _supply;
+ CapacityVector _flow;
+ CostVector _pi;
+
+ // Node and arc maps for the spanning tree structure
+ IntVector _depth;
+ IntVector _parent;
+ IntVector _pred;
+ IntVector _thread;
+ BoolVector _forward;
+ IntVector _state;
+
+ // The root node
+ int _root;
+
+ // The entering arc in the current pivot iteration
+ int _in_arc;
+
+ // Temporary data used in the current pivot iteration
+ int join, u_in, v_in, u_out, v_out;
+ int right, first, second, last;
+ int stem, par_stem, new_stem;
+ Capacity delta;
+
+ private:
+
+ /// \brief Implementation of the "First Eligible" pivot rule for the
+ /// \ref NetworkSimplex "network simplex" algorithm.
+ ///
+ /// This class implements the "First Eligible" pivot rule
+ /// for the \ref NetworkSimplex "network simplex" algorithm.
+ ///
+ /// For more information see \ref NetworkSimplex::run().
+ class FirstEligiblePivotRule
+ {
+ private:
+
+ // References to the NetworkSimplex class
+ const ArcVector &_arc;
+ const IntVector &_source;
+ const IntVector &_target;
+ const CostVector &_cost;
+ const IntVector &_state;
+ const CostVector &_pi;
+ int &_in_arc;
+ int _arc_num;
+
+ // Pivot rule data
+ int _next_arc;
+
+ public:
+
+ /// Constructor
+ FirstEligiblePivotRule(NetworkSimplex &ns) :
+ _arc(ns._arc), _source(ns._source), _target(ns._target),
+ _cost(ns._cost), _state(ns._state), _pi(ns._pi),
+ _in_arc(ns._in_arc), _arc_num(ns._arc_num), _next_arc(0)
+ {}
+
+ /// Find next entering arc
+ bool findEnteringArc() {
+ Cost c;
+ for (int e = _next_arc; e < _arc_num; ++e) {
+ c = _state[e] * (_cost[e] + _pi[_source[e]] - _pi[_target[e]]);
+ if (c < 0) {
+ _in_arc = e;
+ _next_arc = e + 1;
+ return true;
+ }
+ }
+ for (int e = 0; e < _next_arc; ++e) {
+ c = _state[e] * (_cost[e] + _pi[_source[e]] - _pi[_target[e]]);
+ if (c < 0) {
+ _in_arc = e;
+ _next_arc = e + 1;
+ return true;
+ }
+ }
+ return false;
+ }
+
+ }; //class FirstEligiblePivotRule
+
+
+ /// \brief Implementation of the "Best Eligible" pivot rule for the
+ /// \ref NetworkSimplex "network simplex" algorithm.
+ ///
+ /// This class implements the "Best Eligible" pivot rule
+ /// for the \ref NetworkSimplex "network simplex" algorithm.
+ ///
+ /// For more information see \ref NetworkSimplex::run().
+ class BestEligiblePivotRule
+ {
+ private:
+
+ // References to the NetworkSimplex class
+ const ArcVector &_arc;
+ const IntVector &_source;
+ const IntVector &_target;
+ const CostVector &_cost;
+ const IntVector &_state;
+ const CostVector &_pi;
+ int &_in_arc;
+ int _arc_num;
+
+ public:
+
+ /// Constructor
+ BestEligiblePivotRule(NetworkSimplex &ns) :
+ _arc(ns._arc), _source(ns._source), _target(ns._target),
+ _cost(ns._cost), _state(ns._state), _pi(ns._pi),
+ _in_arc(ns._in_arc), _arc_num(ns._arc_num)
+ {}
+
+ /// Find next entering arc
+ bool findEnteringArc() {
+ Cost c, min = 0;
+ for (int e = 0; e < _arc_num; ++e) {
+ c = _state[e] * (_cost[e] + _pi[_source[e]] - _pi[_target[e]]);
+ if (c < min) {
+ min = c;
+ _in_arc = e;
+ }
+ }
+ return min < 0;
+ }
+
+ }; //class BestEligiblePivotRule
+
+
+ /// \brief Implementation of the "Block Search" pivot rule for the
+ /// \ref NetworkSimplex "network simplex" algorithm.
+ ///
+ /// This class implements the "Block Search" pivot rule
+ /// for the \ref NetworkSimplex "network simplex" algorithm.
+ ///
+ /// For more information see \ref NetworkSimplex::run().
+ class BlockSearchPivotRule
+ {
+ private:
+
+ // References to the NetworkSimplex class
+ const ArcVector &_arc;
+ const IntVector &_source;
+ const IntVector &_target;
+ const CostVector &_cost;
+ const IntVector &_state;
+ const CostVector &_pi;
+ int &_in_arc;
+ int _arc_num;
+
+ // Pivot rule data
+ int _block_size;
+ int _next_arc;
+
+ public:
+
+ /// Constructor
+ BlockSearchPivotRule(NetworkSimplex &ns) :
+ _arc(ns._arc), _source(ns._source), _target(ns._target),
+ _cost(ns._cost), _state(ns._state), _pi(ns._pi),
+ _in_arc(ns._in_arc), _arc_num(ns._arc_num), _next_arc(0)
+ {
+ // The main parameters of the pivot rule
+ const double BLOCK_SIZE_FACTOR = 2.0;
+ const int MIN_BLOCK_SIZE = 10;
+
+ _block_size = std::max( int(BLOCK_SIZE_FACTOR * sqrt(_arc_num)),
+ MIN_BLOCK_SIZE );
+ }
+
+ /// Find next entering arc
+ bool findEnteringArc() {
+ Cost c, min = 0;
+ int cnt = _block_size;
+ int e, min_arc = _next_arc;
+ for (e = _next_arc; e < _arc_num; ++e) {
+ c = _state[e] * (_cost[e] + _pi[_source[e]] - _pi[_target[e]]);
+ if (c < min) {
+ min = c;
+ min_arc = e;
+ }
+ if (--cnt == 0) {
+ if (min < 0) break;
+ cnt = _block_size;
+ }
+ }
+ if (min == 0 || cnt > 0) {
+ for (e = 0; e < _next_arc; ++e) {
+ c = _state[e] * (_cost[e] + _pi[_source[e]] - _pi[_target[e]]);
+ if (c < min) {
+ min = c;
+ min_arc = e;
+ }
+ if (--cnt == 0) {
+ if (min < 0) break;
+ cnt = _block_size;
+ }
+ }
+ }
+ if (min >= 0) return false;
+ _in_arc = min_arc;
+ _next_arc = e;
+ return true;
+ }
+
+ }; //class BlockSearchPivotRule
+
+
+ /// \brief Implementation of the "Candidate List" pivot rule for the
+ /// \ref NetworkSimplex "network simplex" algorithm.
+ ///
+ /// This class implements the "Candidate List" pivot rule
+ /// for the \ref NetworkSimplex "network simplex" algorithm.
+ ///
+ /// For more information see \ref NetworkSimplex::run().
+ class CandidateListPivotRule
+ {
+ private:
+
+ // References to the NetworkSimplex class
+ const ArcVector &_arc;
+ const IntVector &_source;
+ const IntVector &_target;
+ const CostVector &_cost;
+ const IntVector &_state;
+ const CostVector &_pi;
+ int &_in_arc;
+ int _arc_num;
+
+ // Pivot rule data
+ IntVector _candidates;
+ int _list_length, _minor_limit;
+ int _curr_length, _minor_count;
+ int _next_arc;
+
+ public:
+
+ /// Constructor
+ CandidateListPivotRule(NetworkSimplex &ns) :
+ _arc(ns._arc), _source(ns._source), _target(ns._target),
+ _cost(ns._cost), _state(ns._state), _pi(ns._pi),
+ _in_arc(ns._in_arc), _arc_num(ns._arc_num), _next_arc(0)
+ {
+ // The main parameters of the pivot rule
+ const double LIST_LENGTH_FACTOR = 1.0;
+ const int MIN_LIST_LENGTH = 10;
+ const double MINOR_LIMIT_FACTOR = 0.1;
+ const int MIN_MINOR_LIMIT = 3;
+
+ _list_length = std::max( int(LIST_LENGTH_FACTOR * sqrt(_arc_num)),
+ MIN_LIST_LENGTH );
+ _minor_limit = std::max( int(MINOR_LIMIT_FACTOR * _list_length),
+ MIN_MINOR_LIMIT );
+ _curr_length = _minor_count = 0;
+ _candidates.resize(_list_length);
+ }
+
+ /// Find next entering arc
+ bool findEnteringArc() {
+ Cost min, c;
+ int e, min_arc = _next_arc;
+ if (_curr_length > 0 && _minor_count < _minor_limit) {
+ // Minor iteration: select the best eligible arc from the
+ // current candidate list
+ ++_minor_count;
+ min = 0;
+ for (int i = 0; i < _curr_length; ++i) {
+ e = _candidates[i];
+ c = _state[e] * (_cost[e] + _pi[_source[e]] - _pi[_target[e]]);
+ if (c < min) {
+ min = c;
+ min_arc = e;
+ }
+ if (c >= 0) {
+ _candidates[i--] = _candidates[--_curr_length];
+ }
+ }
+ if (min < 0) {
+ _in_arc = min_arc;
+ return true;
+ }
+ }
+
+ // Major iteration: build a new candidate list
+ min = 0;
+ _curr_length = 0;
+ for (e = _next_arc; e < _arc_num; ++e) {
+ c = _state[e] * (_cost[e] + _pi[_source[e]] - _pi[_target[e]]);
+ if (c < 0) {
+ _candidates[_curr_length++] = e;
+ if (c < min) {
+ min = c;
+ min_arc = e;
+ }
+ if (_curr_length == _list_length) break;
+ }
+ }
+ if (_curr_length < _list_length) {
+ for (e = 0; e < _next_arc; ++e) {
+ c = _state[e] * (_cost[e] + _pi[_source[e]] - _pi[_target[e]]);
+ if (c < 0) {
+ _candidates[_curr_length++] = e;
+ if (c < min) {
+ min = c;
+ min_arc = e;
+ }
+ if (_curr_length == _list_length) break;
+ }
+ }
+ }
+ if (_curr_length == 0) return false;
+ _minor_count = 1;
+ _in_arc = min_arc;
+ _next_arc = e;
+ return true;
+ }
+
+ }; //class CandidateListPivotRule
+
+
+ /// \brief Implementation of the "Altering Candidate List" pivot rule
+ /// for the \ref NetworkSimplex "network simplex" algorithm.
+ ///
+ /// This class implements the "Altering Candidate List" pivot rule
+ /// for the \ref NetworkSimplex "network simplex" algorithm.
+ ///
+ /// For more information see \ref NetworkSimplex::run().
+ class AlteringListPivotRule
+ {
+ private:
+
+ // References to the NetworkSimplex class
+ const ArcVector &_arc;
+ const IntVector &_source;
+ const IntVector &_target;
+ const CostVector &_cost;
+ const IntVector &_state;
+ const CostVector &_pi;
+ int &_in_arc;
+ int _arc_num;
+
+ // Pivot rule data
+ int _block_size, _head_length, _curr_length;
+ int _next_arc;
+ IntVector _candidates;
+ CostVector _cand_cost;
+
+ // Functor class to compare arcs during sort of the candidate list
+ class SortFunc
+ {
+ private:
+ const CostVector &_map;
+ public:
+ SortFunc(const CostVector &map) : _map(map) {}
+ bool operator()(int left, int right) {
+ return _map[left] > _map[right];
+ }
+ };
+
+ SortFunc _sort_func;
+
+ public:
+
+ /// Constructor
+ AlteringListPivotRule(NetworkSimplex &ns) :
+ _arc(ns._arc), _source(ns._source), _target(ns._target),
+ _cost(ns._cost), _state(ns._state), _pi(ns._pi),
+ _in_arc(ns._in_arc), _arc_num(ns._arc_num),
+ _next_arc(0), _cand_cost(ns._arc_num), _sort_func(_cand_cost)
+ {
+ // The main parameters of the pivot rule
+ const double BLOCK_SIZE_FACTOR = 1.5;
+ const int MIN_BLOCK_SIZE = 10;
+ const double HEAD_LENGTH_FACTOR = 0.1;
+ const int MIN_HEAD_LENGTH = 3;
+
+ _block_size = std::max( int(BLOCK_SIZE_FACTOR * sqrt(_arc_num)),
+ MIN_BLOCK_SIZE );
+ _head_length = std::max( int(HEAD_LENGTH_FACTOR * _block_size),
+ MIN_HEAD_LENGTH );
+ _candidates.resize(_head_length + _block_size);
+ _curr_length = 0;
+ }
+
+ /// Find next entering arc
+ bool findEnteringArc() {
+ // Check the current candidate list
+ int e;
+ for (int i = 0; i < _curr_length; ++i) {
+ e = _candidates[i];
+ _cand_cost[e] = _state[e] *
+ (_cost[e] + _pi[_source[e]] - _pi[_target[e]]);
+ if (_cand_cost[e] >= 0) {
+ _candidates[i--] = _candidates[--_curr_length];
+ }
+ }
+
+ // Extend the list
+ int cnt = _block_size;
+ int last_edge = 0;
+ int limit = _head_length;
+
+ for (int e = _next_arc; e < _arc_num; ++e) {
+ _cand_cost[e] = _state[e] *
+ (_cost[e] + _pi[_source[e]] - _pi[_target[e]]);
+ if (_cand_cost[e] < 0) {
+ _candidates[_curr_length++] = e;
+ last_edge = e;
+ }
+ if (--cnt == 0) {
+ if (_curr_length > limit) break;
+ limit = 0;
+ cnt = _block_size;
+ }
+ }
+ if (_curr_length <= limit) {
+ for (int e = 0; e < _next_arc; ++e) {
+ _cand_cost[e] = _state[e] *
+ (_cost[e] + _pi[_source[e]] - _pi[_target[e]]);
+ if (_cand_cost[e] < 0) {
+ _candidates[_curr_length++] = e;
+ last_edge = e;
+ }
+ if (--cnt == 0) {
+ if (_curr_length > limit) break;
+ limit = 0;
+ cnt = _block_size;
+ }
+ }
+ }
+ if (_curr_length == 0) return false;
+ _next_arc = last_edge + 1;
+
+ // Make heap of the candidate list (approximating a partial sort)
+ make_heap( _candidates.begin(), _candidates.begin() + _curr_length,
+ _sort_func );
+
+ // Pop the first element of the heap
+ _in_arc = _candidates[0];
+ pop_heap( _candidates.begin(), _candidates.begin() + _curr_length,
+ _sort_func );
+ _curr_length = std::min(_head_length, _curr_length - 1);
+ return true;
+ }
+
+ }; //class AlteringListPivotRule
+
+ 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).
+ NetworkSimplex( const Digraph &digraph,
+ const LowerMap &lower,
+ const CapacityMap &capacity,
+ const CostMap &cost,
+ const SupplyMap &supply ) :
+ _orig_graph(digraph), _orig_lower(&lower), _orig_cap(capacity),
+ _orig_cost(cost), _orig_supply(&supply),
+ _flow_result(NULL), _potential_result(NULL),
+ _local_flow(false), _local_potential(false),
+ _node_id(digraph)
+ {}
+
+ /// \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).
+ NetworkSimplex( const Digraph &digraph,
+ const CapacityMap &capacity,
+ const CostMap &cost,
+ const SupplyMap &supply ) :
+ _orig_graph(digraph), _orig_lower(NULL), _orig_cap(capacity),
+ _orig_cost(cost), _orig_supply(&supply),
+ _flow_result(NULL), _potential_result(NULL),
+ _local_flow(false), _local_potential(false),
+ _node_id(digraph)
+ {}
+
+ /// \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).
+ NetworkSimplex( const Digraph &digraph,
+ const LowerMap &lower,
+ const CapacityMap &capacity,
+ const CostMap &cost,
+ Node s, Node t,
+ Capacity flow_value ) :
+ _orig_graph(digraph), _orig_lower(&lower), _orig_cap(capacity),
+ _orig_cost(cost), _orig_supply(NULL),
+ _orig_source(s), _orig_target(t), _orig_flow_value(flow_value),
+ _flow_result(NULL), _potential_result(NULL),
+ _local_flow(false), _local_potential(false),
+ _node_id(digraph)
+ {}
+
+ /// \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).
+ NetworkSimplex( const Digraph &digraph,
+ const CapacityMap &capacity,
+ const CostMap &cost,
+ Node s, Node t,
+ Capacity flow_value ) :
+ _orig_graph(digraph), _orig_lower(NULL), _orig_cap(capacity),
+ _orig_cost(cost), _orig_supply(NULL),
+ _orig_source(s), _orig_target(t), _orig_flow_value(flow_value),
+ _flow_result(NULL), _potential_result(NULL),
+ _local_flow(false), _local_potential(false),
+ _node_id(digraph)
+ {}
+
+ /// Destructor.
+ ~NetworkSimplex() {
+ if (_local_flow) delete _flow_result;
+ if (_local_potential) delete _potential_result;
+ }
+
+ /// \brief Set the flow map.
+ ///
+ /// This function sets the flow map.
+ ///
+ /// \return <tt>(*this)</tt>
+ NetworkSimplex& flowMap(FlowMap &map) {
+ if (_local_flow) {
+ delete _flow_result;
+ _local_flow = false;
+ }
+ _flow_result = ↦
+ return *this;
+ }
+
+ /// \brief Set the potential map.
+ ///
+ /// This function sets the potential map.
+ ///
+ /// \return <tt>(*this)</tt>
+ NetworkSimplex& potentialMap(PotentialMap &map) {
+ if (_local_potential) {
+ delete _potential_result;
+ _local_potential = false;
+ }
+ _potential_result = ↦
+ return *this;
+ }
+
+ /// \name Execution control
+ /// The algorithm can be executed using the
+ /// \ref lemon::NetworkSimplex::run() "run()" function.
+ /// @{
+
+ /// \brief Run the algorithm.
+ ///
+ /// This function runs the algorithm.
+ ///
+ /// \param pivot_rule The pivot rule that is used during the
+ /// algorithm.
+ ///
+ /// The available pivot rules:
+ ///
+ /// - FIRST_ELIGIBLE_PIVOT The next eligible arc is selected in
+ /// a wraparound fashion in every iteration
+ /// (\ref FirstEligiblePivotRule).
+ ///
+ /// - BEST_ELIGIBLE_PIVOT The best eligible arc is selected in
+ /// every iteration (\ref BestEligiblePivotRule).
+ ///
+ /// - BLOCK_SEARCH_PIVOT A specified number of arcs are examined in
+ /// every iteration in a wraparound fashion and the best eligible
+ /// arc is selected from this block (\ref BlockSearchPivotRule).
+ ///
+ /// - CANDIDATE_LIST_PIVOT In a major iteration a candidate list is
+ /// built from eligible arcs in a wraparound fashion and in the
+ /// following minor iterations the best eligible arc is selected
+ /// from this list (\ref CandidateListPivotRule).
+ ///
+ /// - ALTERING_LIST_PIVOT It is a modified version of the
+ /// "Candidate List" pivot rule. It keeps only the several best
+ /// eligible arcs from the former candidate list and extends this
+ /// list in every iteration (\ref AlteringListPivotRule).
+ ///
+ /// According to our comprehensive benchmark tests the "Block Search"
+ /// pivot rule proved to be the fastest and the most robust on
+ /// various test inputs. Thus it is the default option.
+ ///
+ /// \return \c true if a feasible flow can be found.
+ bool run(PivotRuleEnum pivot_rule = BLOCK_SEARCH_PIVOT) {
+ return init() && start(pivot_rule);
+ }
+
+ /// @}
+
+ /// \name Query Functions
+ /// The results of the algorithm can be obtained using these
+ /// functions.\n
+ /// \ref lemon::NetworkSimplex::run() "run()" must be called before
+ /// using them.
+ /// @{
+
+ /// \brief Return a const reference to the flow map.
+ ///
+ /// This function returns a const reference to an arc map storing
+ /// the found flow.
+ ///
+ /// \pre \ref run() must be called before using this function.
+ const FlowMap& flowMap() const {
+ return *_flow_result;
+ }
+
+ /// \brief Return a const reference to the potential map
+ /// (the dual solution).
+ ///
+ /// This function returns a const reference to a 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_result;
+ }
+
+ /// \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.
+ Capacity flow(const Arc& arc) const {
+ return (*_flow_result)[arc];
+ }
+
+ /// \brief Return the potential of the given node.
+ ///
+ /// This function returns the potential of the given node.
+ ///
+ /// \pre \ref run() must be called before using this function.
+ Cost potential(const Node& node) const {
+ return (*_potential_result)[node];
+ }
+
+ /// \brief Return the total cost of the found flow.
+ ///
+ /// This function returns 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(_orig_graph); e != INVALID; ++e)
+ c += (*_flow_result)[e] * _orig_cost[e];
+ return c;
+ }
+
+ /// @}
+
+ private:
+
+ // Initialize internal data structures
+ bool init() {
+ // Initialize result maps
+ if (!_flow_result) {
+ _flow_result = new FlowMap(_orig_graph);
+ _local_flow = true;
+ }
+ if (!_potential_result) {
+ _potential_result = new PotentialMap(_orig_graph);
+ _local_potential = true;
+ }
+
+ // Initialize vectors
+ _node_num = countNodes(_orig_graph);
+ _arc_num = countArcs(_orig_graph);
+ int all_node_num = _node_num + 1;
+ int all_edge_num = _arc_num + _node_num;
+
+ _arc.resize(_arc_num);
+ _node.reserve(_node_num);
+ _source.resize(all_edge_num);
+ _target.resize(all_edge_num);
+
+ _cap.resize(all_edge_num);
+ _cost.resize(all_edge_num);
+ _supply.resize(all_node_num);
+ _flow.resize(all_edge_num, 0);
+ _pi.resize(all_node_num, 0);
+
+ _depth.resize(all_node_num);
+ _parent.resize(all_node_num);
+ _pred.resize(all_node_num);
+ _thread.resize(all_node_num);
+ _forward.resize(all_node_num);
+ _state.resize(all_edge_num, STATE_LOWER);
+
+ // Initialize node related data
+ bool valid_supply = true;
+ if (_orig_supply) {
+ Supply sum = 0;
+ int i = 0;
+ for (NodeIt n(_orig_graph); n != INVALID; ++n, ++i) {
+ _node.push_back(n);
+ _node_id[n] = i;
+ _supply[i] = (*_orig_supply)[n];
+ sum += _supply[i];
+ }
+ valid_supply = (sum == 0);
+ } else {
+ int i = 0;
+ for (NodeIt n(_orig_graph); n != INVALID; ++n, ++i) {
+ _node.push_back(n);
+ _node_id[n] = i;
+ _supply[i] = 0;
+ }
+ _supply[_node_id[_orig_source]] = _orig_flow_value;
+ _supply[_node_id[_orig_target]] = -_orig_flow_value;
+ }
+ if (!valid_supply) return false;
+
+ // Set data for the artificial root node
+ _root = _node_num;
+ _depth[_root] = 0;
+ _parent[_root] = -1;
+ _pred[_root] = -1;
+ _thread[_root] = 0;
+ _supply[_root] = 0;
+ _pi[_root] = 0;
+
+ // Store the arcs in a mixed order
+ int k = std::max(int(sqrt(_arc_num)), 10);
+ int i = 0;
+ for (ArcIt e(_orig_graph); e != INVALID; ++e) {
+ _arc[i] = e;
+ if ((i += k) >= _arc_num) i = (i % k) + 1;
+ }
+
+ // Initialize arc maps
+ for (int i = 0; i != _arc_num; ++i) {
+ Arc e = _arc[i];
+ _source[i] = _node_id[_orig_graph.source(e)];
+ _target[i] = _node_id[_orig_graph.target(e)];
+ _cost[i] = _orig_cost[e];
+ _cap[i] = _orig_cap[e];
+ }
+
+ // Remove non-zero lower bounds
+ if (_orig_lower) {
+ for (int i = 0; i != _arc_num; ++i) {
+ Capacity c = (*_orig_lower)[_arc[i]];
+ if (c != 0) {
+ _cap[i] -= c;
+ _supply[_source[i]] -= c;
+ _supply[_target[i]] += c;
+ }
+ }
+ }
+
+ // Add artificial arcs and initialize the spanning tree data structure
+ Cost max_cost = std::numeric_limits<Cost>::max() / 4;
+ Capacity max_cap = std::numeric_limits<Capacity>::max();
+ for (int u = 0, e = _arc_num; u != _node_num; ++u, ++e) {
+ _thread[u] = u + 1;
+ _depth[u] = 1;
+ _parent[u] = _root;
+ _pred[u] = e;
+ if (_supply[u] >= 0) {
+ _flow[e] = _supply[u];
+ _forward[u] = true;
+ _pi[u] = -max_cost;
+ } else {
+ _flow[e] = -_supply[u];
+ _forward[u] = false;
+ _pi[u] = max_cost;
+ }
+ _cost[e] = max_cost;
+ _cap[e] = max_cap;
+ _state[e] = STATE_TREE;
+ }
+
+ return true;
+ }
+
+ // Find the join node
+ void findJoinNode() {
+ int u = _source[_in_arc];
+ int v = _target[_in_arc];
+ while (_depth[u] > _depth[v]) u = _parent[u];
+ while (_depth[v] > _depth[u]) v = _parent[v];
+ while (u != v) {
+ u = _parent[u];
+ v = _parent[v];
+ }
+ join = u;
+ }
+
+ // Find the leaving arc of the cycle and returns true if the
+ // leaving arc is not the same as the entering arc
+ bool findLeavingArc() {
+ // Initialize first and second nodes according to the direction
+ // of the cycle
+ if (_state[_in_arc] == STATE_LOWER) {
+ first = _source[_in_arc];
+ second = _target[_in_arc];
+ } else {
+ first = _target[_in_arc];
+ second = _source[_in_arc];
+ }
+ delta = _cap[_in_arc];
+ int result = 0;
+ Capacity d;
+ int e;
+
+ // Search the cycle along the path form the first node to the root
+ for (int u = first; u != join; u = _parent[u]) {
+ e = _pred[u];
+ d = _forward[u] ? _flow[e] : _cap[e] - _flow[e];
+ if (d < delta) {
+ delta = d;
+ u_out = u;
+ result = 1;
+ }
+ }
+ // Search the cycle along the path form the second node to the root
+ for (int u = second; u != join; u = _parent[u]) {
+ e = _pred[u];
+ d = _forward[u] ? _cap[e] - _flow[e] : _flow[e];
+ if (d <= delta) {
+ delta = d;
+ u_out = u;
+ result = 2;
+ }
+ }
+
+ if (result == 1) {
+ u_in = first;
+ v_in = second;
+ } else {
+ u_in = second;
+ v_in = first;
+ }
+ return result != 0;
+ }
+
+ // Change _flow and _state vectors
+ void changeFlow(bool change) {
+ // Augment along the cycle
+ if (delta > 0) {
+ Capacity val = _state[_in_arc] * delta;
+ _flow[_in_arc] += val;
+ for (int u = _source[_in_arc]; u != join; u = _parent[u]) {
+ _flow[_pred[u]] += _forward[u] ? -val : val;
+ }
+ for (int u = _target[_in_arc]; u != join; u = _parent[u]) {
+ _flow[_pred[u]] += _forward[u] ? val : -val;
+ }
+ }
+ // Update the state of the entering and leaving arcs
+ if (change) {
+ _state[_in_arc] = STATE_TREE;
+ _state[_pred[u_out]] =
+ (_flow[_pred[u_out]] == 0) ? STATE_LOWER : STATE_UPPER;
+ } else {
+ _state[_in_arc] = -_state[_in_arc];
+ }
+ }
+
+ // Update _thread and _parent vectors
+ void updateThreadParent() {
+ int u;
+ v_out = _parent[u_out];
+
+ // Handle the case when join and v_out coincide
+ bool par_first = false;
+ if (join == v_out) {
+ for (u = join; u != u_in && u != v_in; u = _thread[u]) ;
+ if (u == v_in) {
+ par_first = true;
+ while (_thread[u] != u_out) u = _thread[u];
+ first = u;
+ }
+ }
+
+ // Find the last successor of u_in (u) and the node after it (right)
+ // according to the thread index
+ for (u = u_in; _depth[_thread[u]] > _depth[u_in]; u = _thread[u]) ;
+ right = _thread[u];
+ if (_thread[v_in] == u_out) {
+ for (last = u; _depth[last] > _depth[u_out]; last = _thread[last]) ;
+ if (last == u_out) last = _thread[last];
+ }
+ else last = _thread[v_in];
+
+ // Update stem nodes
+ _thread[v_in] = stem = u_in;
+ par_stem = v_in;
+ while (stem != u_out) {
+ _thread[u] = new_stem = _parent[stem];
+
+ // Find the node just before the stem node (u) according to
+ // the original thread index
+ for (u = new_stem; _thread[u] != stem; u = _thread[u]) ;
+ _thread[u] = right;
+
+ // Change the parent node of stem and shift stem and par_stem nodes
+ _parent[stem] = par_stem;
+ par_stem = stem;
+ stem = new_stem;
+
+ // Find the last successor of stem (u) and the node after it (right)
+ // according to the thread index
+ for (u = stem; _depth[_thread[u]] > _depth[stem]; u = _thread[u]) ;
+ right = _thread[u];
+ }
+ _parent[u_out] = par_stem;
+ _thread[u] = last;
+
+ if (join == v_out && par_first) {
+ if (first != v_in) _thread[first] = right;
+ } else {
+ for (u = v_out; _thread[u] != u_out; u = _thread[u]) ;
+ _thread[u] = right;
+ }
+ }
+
+ // Update _pred and _forward vectors
+ void updatePredArc() {
+ int u = u_out, v;
+ while (u != u_in) {
+ v = _parent[u];
+ _pred[u] = _pred[v];
+ _forward[u] = !_forward[v];
+ u = v;
+ }
+ _pred[u_in] = _in_arc;
+ _forward[u_in] = (u_in == _source[_in_arc]);
+ }
+
+ // Update _depth and _potential vectors
+ void updateDepthPotential() {
+ _depth[u_in] = _depth[v_in] + 1;
+ Cost sigma = _forward[u_in] ?
+ _pi[v_in] - _pi[u_in] - _cost[_pred[u_in]] :
+ _pi[v_in] - _pi[u_in] + _cost[_pred[u_in]];
+ _pi[u_in] += sigma;
+ for(int u = _thread[u_in]; _parent[u] != -1; u = _thread[u]) {
+ _depth[u] = _depth[_parent[u]] + 1;
+ if (_depth[u] <= _depth[u_in]) break;
+ _pi[u] += sigma;
+ }
+ }
+
+ // Execute the algorithm
+ bool start(PivotRuleEnum pivot_rule) {
+ // Select the pivot rule implementation
+ switch (pivot_rule) {
+ case FIRST_ELIGIBLE_PIVOT:
+ return start<FirstEligiblePivotRule>();
+ case BEST_ELIGIBLE_PIVOT:
+ return start<BestEligiblePivotRule>();
+ case BLOCK_SEARCH_PIVOT:
+ return start<BlockSearchPivotRule>();
+ case CANDIDATE_LIST_PIVOT:
+ return start<CandidateListPivotRule>();
+ case ALTERING_LIST_PIVOT:
+ return start<AlteringListPivotRule>();
+ }
+ return false;
+ }
+
+ template<class PivotRuleImplementation>
+ bool start() {
+ PivotRuleImplementation pivot(*this);
+
+ // Execute the network simplex algorithm
+ while (pivot.findEnteringArc()) {
+ findJoinNode();
+ bool change = findLeavingArc();
+ changeFlow(change);
+ if (change) {
+ updateThreadParent();
+ updatePredArc();
+ updateDepthPotential();
+ }
+ }
+
+ // Check if the flow amount equals zero on all the artificial arcs
+ for (int e = _arc_num; e != _arc_num + _node_num; ++e) {
+ if (_flow[e] > 0) return false;
+ }
+
+ // Copy flow values to _flow_result
+ if (_orig_lower) {
+ for (int i = 0; i != _arc_num; ++i) {
+ Arc e = _arc[i];
+ (*_flow_result)[e] = (*_orig_lower)[e] + _flow[i];
+ }
+ } else {
+ for (int i = 0; i != _arc_num; ++i) {
+ (*_flow_result)[_arc[i]] = _flow[i];
+ }
+ }
+ // Copy potential values to _potential_result
+ for (int i = 0; i != _node_num; ++i) {
+ (*_potential_result)[_node[i]] = _pi[i];
+ }
+
+ return true;
+ }
+
+ }; //class NetworkSimplex
+
+ ///@}
+
+} //namespace lemon
+
+#endif //LEMON_NETWORK_SIMPLEX_H
diff -r 6a17a722b50e -r e8349c6f12ca test/CMakeLists.txt
--- a/test/CMakeLists.txt Mon Feb 23 18:01:14 2009 +0000
+++ b/test/CMakeLists.txt Tue Feb 24 09:46:02 2009 +0100
@@ -30,6 +30,7 @@
maps_test
max_matching_test
min_cost_arborescence_test
+ min_cost_flow_test
path_test
preflow_test
radix_sort_test
diff -r 6a17a722b50e -r e8349c6f12ca test/Makefile.am
--- a/test/Makefile.am Mon Feb 23 18:01:14 2009 +0000
+++ b/test/Makefile.am Tue Feb 24 09:46:02 2009 +0100
@@ -26,6 +26,7 @@
test/maps_test \
test/max_matching_test \
test/min_cost_arborescence_test \
+ test/min_cost_flow_test \
test/path_test \
test/preflow_test \
test/radix_sort_test \
@@ -68,6 +69,7 @@
test_mip_test_SOURCES = test/mip_test.cc
test_max_matching_test_SOURCES = test/max_matching_test.cc
test_min_cost_arborescence_test_SOURCES = test/min_cost_arborescence_test.cc
+test_min_cost_flow_test_SOURCES = test/min_cost_flow_test.cc
test_path_test_SOURCES = test/path_test.cc
test_preflow_test_SOURCES = test/preflow_test.cc
test_radix_sort_test_SOURCES = test/radix_sort_test.cc
diff -r 6a17a722b50e -r e8349c6f12ca test/min_cost_flow_test.cc
--- /dev/null Thu Jan 01 00:00:00 1970 +0000
+++ b/test/min_cost_flow_test.cc Tue Feb 24 09:46:02 2009 +0100
@@ -0,0 +1,455 @@
+/* -*- mode: C++; indent-tabs-mode: nil; -*-
+ *
+ * This file is a part of LEMON, a generic C++ optimization library.
+ *
+ * Copyright (C) 2003-2009
+ * 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.
+ *
+ */
+
+#include <iostream>
+#include <fstream>
+
+#include <lemon/list_graph.h>
+#include <lemon/smart_graph.h>
+#include <lemon/lgf_reader.h>
+
+//#include <lemon/cycle_canceling.h>
+//#include <lemon/capacity_scaling.h>
+//#include <lemon/cost_scaling.h>
+#include <lemon/network_simplex.h>
+//#include <lemon/min_cost_flow.h>
+//#include <lemon/min_cost_max_flow.h>
+
+#include <lemon/concepts/digraph.h>
+#include <lemon/concept_check.h>
+
+#include "test_tools.h"
+
+using namespace lemon;
+
+char test_lgf[] =
+ "@nodes\n"
+ "label sup1 sup2 sup3\n"
+ " 1 20 27 0\n"
+ " 2 -4 0 0\n"
+ " 3 0 0 0\n"
+ " 4 0 0 0\n"
+ " 5 9 0 0\n"
+ " 6 -6 0 0\n"
+ " 7 0 0 0\n"
+ " 8 0 0 0\n"
+ " 9 3 0 0\n"
+ " 10 -2 0 0\n"
+ " 11 0 0 0\n"
+ " 12 -20 -27 0\n"
+ "\n"
+ "@arcs\n"
+ " cost cap low1 low2\n"
+ " 1 2 70 11 0 8\n"
+ " 1 3 150 3 0 1\n"
+ " 1 4 80 15 0 2\n"
+ " 2 8 80 12 0 0\n"
+ " 3 5 140 5 0 3\n"
+ " 4 6 60 10 0 1\n"
+ " 4 7 80 2 0 0\n"
+ " 4 8 110 3 0 0\n"
+ " 5 7 60 14 0 0\n"
+ " 5 11 120 12 0 0\n"
+ " 6 3 0 3 0 0\n"
+ " 6 9 140 4 0 0\n"
+ " 6 10 90 8 0 0\n"
+ " 7 1 30 5 0 0\n"
+ " 8 12 60 16 0 4\n"
+ " 9 12 50 6 0 0\n"
+ "10 12 70 13 0 5\n"
+ "10 2 100 7 0 0\n"
+ "10 7 60 10 0 0\n"
+ "11 10 20 14 0 6\n"
+ "12 11 30 10 0 0\n"
+ "\n"
+ "@attributes\n"
+ "source 1\n"
+ "target 12\n";
+
+
+// Check the interface of an MCF algorithm
+template <typename GR, typename Value>
+class McfClassConcept
+{
+public:
+
+ template <typename MCF>
+ struct Constraints {
+ void constraints() {
+ checkConcept<concepts::Digraph, GR>();
+
+ MCF mcf_test1(g, lower, upper, cost, sup);
+ MCF mcf_test2(g, upper, cost, sup);
+ MCF mcf_test3(g, lower, upper, cost, n, n, k);
+ MCF mcf_test4(g, upper, cost, n, n, k);
+
+ // TODO: This part should be enabled and the next part
+ // should be removed if map copying is supported
+/*
+ flow = mcf_test1.flowMap();
+ mcf_test1.flowMap(flow);
+
+ pot = mcf_test1.potentialMap();
+ mcf_test1.potentialMap(pot);
+*/
+/**/
+ const typename MCF::FlowMap &fm =
+ mcf_test1.flowMap();
+ mcf_test1.flowMap(flow);
+ const typename MCF::PotentialMap &pm =
+ mcf_test1.potentialMap();
+ mcf_test1.potentialMap(pot);
+ ignore_unused_variable_warning(fm);
+ ignore_unused_variable_warning(pm);
+/**/
+
+ mcf_test1.run();
+
+ v = mcf_test1.totalCost();
+ v = mcf_test1.flow(a);
+ v = mcf_test1.potential(n);
+ }
+
+ typedef typename GR::Node Node;
+ typedef typename GR::Arc Arc;
+ typedef concepts::ReadMap<Node, Value> NM;
+ typedef concepts::ReadMap<Arc, Value> AM;
+
+ const GR &g;
+ const AM &lower;
+ const AM &upper;
+ const AM &cost;
+ const NM ⊃
+ const Node &n;
+ const Arc &a;
+ const Value &k;
+ Value v;
+
+ typename MCF::FlowMap &flow;
+ typename MCF::PotentialMap &pot;
+ };
+
+};
+
+
+// Check the feasibility of the given flow (primal soluiton)
+template < typename GR, typename LM, typename UM,
+ typename SM, typename FM >
+bool checkFlow( const GR& gr, const LM& lower, const UM& upper,
+ const SM& supply, const FM& flow )
+{
+ TEMPLATE_DIGRAPH_TYPEDEFS(GR);
+
+ for (ArcIt e(gr); e != INVALID; ++e) {
+ if (flow[e] < lower[e] || flow[e] > upper[e]) return false;
+ }
+
+ for (NodeIt n(gr); n != INVALID; ++n) {
+ typename SM::Value sum = 0;
+ for (OutArcIt e(gr, n); e != INVALID; ++e)
+ sum += flow[e];
+ for (InArcIt e(gr, n); e != INVALID; ++e)
+ sum -= flow[e];
+ if (sum != supply[n]) return false;
+ }
+
+ return true;
+}
+
+// Check the feasibility of the given potentials (dual soluiton)
+// using the Complementary Slackness optimality condition
+template < typename GR, typename LM, typename UM,
+ typename CM, typename FM, typename PM >
+bool checkPotential( const GR& gr, const LM& lower, const UM& upper,
+ const CM& cost, const FM& flow, const PM& pi )
+{
+ TEMPLATE_DIGRAPH_TYPEDEFS(GR);
+
+ bool opt = true;
+ for (ArcIt e(gr); opt && e != INVALID; ++e) {
+ typename CM::Value red_cost =
+ cost[e] + pi[gr.source(e)] - pi[gr.target(e)];
+ opt = red_cost == 0 ||
+ (red_cost > 0 && flow[e] == lower[e]) ||
+ (red_cost < 0 && flow[e] == upper[e]);
+ }
+ return opt;
+}
+
+// Run a minimum cost flow algorithm and check the results
+template < typename MCF, typename GR,
+ typename LM, typename UM,
+ typename CM, typename SM >
+void checkMcf( const MCF& mcf, bool mcf_result,
+ const GR& gr, const LM& lower, const UM& upper,
+ const CM& cost, const SM& supply,
+ bool result, typename CM::Value total,
+ const std::string &test_id = "" )
+{
+ check(mcf_result == result, "Wrong result " + test_id);
+ if (result) {
+ check(checkFlow(gr, lower, upper, supply, mcf.flowMap()),
+ "The flow is not feasible " + test_id);
+ check(mcf.totalCost() == total, "The flow is not optimal " + test_id);
+ check(checkPotential(gr, lower, upper, cost, mcf.flowMap(),
+ mcf.potentialMap()),
+ "Wrong potentials " + test_id);
+ }
+}
+
+int main()
+{
+ // Check the interfaces
+ {
+ typedef int Value;
+ // This typedef should be enabled if the standard maps are
+ // reference maps in the graph concepts
+ //typedef concepts::Digraph GR;
+ typedef ListDigraph GR;
+ typedef concepts::ReadMap<GR::Node, Value> NM;
+ typedef concepts::ReadMap<GR::Arc, Value> AM;
+
+ //checkConcept< McfClassConcept<GR, Value>,
+ // CycleCanceling<GR, AM, AM, AM, NM> >();
+ //checkConcept< McfClassConcept<GR, Value>,
+ // CapacityScaling<GR, AM, AM, AM, NM> >();
+ //checkConcept< McfClassConcept<GR, Value>,
+ // CostScaling<GR, AM, AM, AM, NM> >();
+ checkConcept< McfClassConcept<GR, Value>,
+ NetworkSimplex<GR, AM, AM, AM, NM> >();
+ //checkConcept< MinCostFlow<GR, Value>,
+ // NetworkSimplex<GR, AM, AM, AM, NM> >();
+ }
+
+ // Run various MCF tests
+ typedef ListDigraph Digraph;
+ DIGRAPH_TYPEDEFS(ListDigraph);
+
+ // Read the test digraph
+ Digraph gr;
+ Digraph::ArcMap<int> c(gr), l1(gr), l2(gr), u(gr);
+ Digraph::NodeMap<int> s1(gr), s2(gr), s3(gr);
+ Node v, w;
+
+ std::istringstream input(test_lgf);
+ DigraphReader<Digraph>(gr, input)
+ .arcMap("cost", c)
+ .arcMap("cap", u)
+ .arcMap("low1", l1)
+ .arcMap("low2", l2)
+ .nodeMap("sup1", s1)
+ .nodeMap("sup2", s2)
+ .nodeMap("sup3", s3)
+ .node("source", v)
+ .node("target", w)
+ .run();
+
+/*
+ // A. Test CapacityScaling with scaling
+ {
+ CapacityScaling<Digraph> mcf1(gr, u, c, s1);
+ CapacityScaling<Digraph> mcf2(gr, u, c, v, w, 27);
+ CapacityScaling<Digraph> mcf3(gr, u, c, s3);
+ CapacityScaling<Digraph> mcf4(gr, l2, u, c, s1);
+ CapacityScaling<Digraph> mcf5(gr, l2, u, c, v, w, 27);
+ CapacityScaling<Digraph> mcf6(gr, l2, u, c, s3);
+
+ checkMcf(mcf1, mcf1.run(), gr, l1, u, c, s1, true, 5240, "#A1");
+ checkMcf(mcf2, mcf2.run(), gr, l1, u, c, s2, true, 7620, "#A2");
+ checkMcf(mcf3, mcf3.run(), gr, l1, u, c, s3, true, 0, "#A3");
+ checkMcf(mcf4, mcf4.run(), gr, l2, u, c, s1, true, 5970, "#A4");
+ checkMcf(mcf5, mcf5.run(), gr, l2, u, c, s2, true, 8010, "#A5");
+ checkMcf(mcf6, mcf6.run(), gr, l2, u, c, s3, false, 0, "#A6");
+ }
+
+ // B. Test CapacityScaling without scaling
+ {
+ CapacityScaling<Digraph> mcf1(gr, u, c, s1);
+ CapacityScaling<Digraph> mcf2(gr, u, c, v, w, 27);
+ CapacityScaling<Digraph> mcf3(gr, u, c, s3);
+ CapacityScaling<Digraph> mcf4(gr, l2, u, c, s1);
+ CapacityScaling<Digraph> mcf5(gr, l2, u, c, v, w, 27);
+ CapacityScaling<Digraph> mcf6(gr, l2, u, c, s3);
+
+ checkMcf(mcf1, mcf1.run(false), gr, l1, u, c, s1, true, 5240, "#B1");
+ checkMcf(mcf2, mcf2.run(false), gr, l1, u, c, s2, true, 7620, "#B2");
+ checkMcf(mcf3, mcf3.run(false), gr, l1, u, c, s3, true, 0, "#B3");
+ checkMcf(mcf4, mcf4.run(false), gr, l2, u, c, s1, true, 5970, "#B4");
+ checkMcf(mcf5, mcf5.run(false), gr, l2, u, c, s2, true, 8010, "#B5");
+ checkMcf(mcf6, mcf6.run(false), gr, l2, u, c, s3, false, 0, "#B6");
+ }
+
+ // C. Test CostScaling using partial augment-relabel method
+ {
+ CostScaling<Digraph> mcf1(gr, u, c, s1);
+ CostScaling<Digraph> mcf2(gr, u, c, v, w, 27);
+ CostScaling<Digraph> mcf3(gr, u, c, s3);
+ CostScaling<Digraph> mcf4(gr, l2, u, c, s1);
+ CostScaling<Digraph> mcf5(gr, l2, u, c, v, w, 27);
+ CostScaling<Digraph> mcf6(gr, l2, u, c, s3);
+
+ checkMcf(mcf1, mcf1.run(), gr, l1, u, c, s1, true, 5240, "#C1");
+ checkMcf(mcf2, mcf2.run(), gr, l1, u, c, s2, true, 7620, "#C2");
+ checkMcf(mcf3, mcf3.run(), gr, l1, u, c, s3, true, 0, "#C3");
+ checkMcf(mcf4, mcf4.run(), gr, l2, u, c, s1, true, 5970, "#C4");
+ checkMcf(mcf5, mcf5.run(), gr, l2, u, c, s2, true, 8010, "#C5");
+ checkMcf(mcf6, mcf6.run(), gr, l2, u, c, s3, false, 0, "#C6");
+ }
+
+ // D. Test CostScaling using push-relabel method
+ {
+ CostScaling<Digraph> mcf1(gr, u, c, s1);
+ CostScaling<Digraph> mcf2(gr, u, c, v, w, 27);
+ CostScaling<Digraph> mcf3(gr, u, c, s3);
+ CostScaling<Digraph> mcf4(gr, l2, u, c, s1);
+ CostScaling<Digraph> mcf5(gr, l2, u, c, v, w, 27);
+ CostScaling<Digraph> mcf6(gr, l2, u, c, s3);
+
+ checkMcf(mcf1, mcf1.run(false), gr, l1, u, c, s1, true, 5240, "#D1");
+ checkMcf(mcf2, mcf2.run(false), gr, l1, u, c, s2, true, 7620, "#D2");
+ checkMcf(mcf3, mcf3.run(false), gr, l1, u, c, s3, true, 0, "#D3");
+ checkMcf(mcf4, mcf4.run(false), gr, l2, u, c, s1, true, 5970, "#D4");
+ checkMcf(mcf5, mcf5.run(false), gr, l2, u, c, s2, true, 8010, "#D5");
+ checkMcf(mcf6, mcf6.run(false), gr, l2, u, c, s3, false, 0, "#D6");
+ }
+*/
+
+ // E. Test NetworkSimplex with FIRST_ELIGIBLE_PIVOT
+ {
+ NetworkSimplex<Digraph>::PivotRuleEnum pr =
+ NetworkSimplex<Digraph>::FIRST_ELIGIBLE_PIVOT;
+ NetworkSimplex<Digraph> mcf1(gr, u, c, s1);
+ NetworkSimplex<Digraph> mcf2(gr, u, c, v, w, 27);
+ NetworkSimplex<Digraph> mcf3(gr, u, c, s3);
+ NetworkSimplex<Digraph> mcf4(gr, l2, u, c, s1);
+ NetworkSimplex<Digraph> mcf5(gr, l2, u, c, v, w, 27);
+ NetworkSimplex<Digraph> mcf6(gr, l2, u, c, s3);
+
+ checkMcf(mcf1, mcf1.run(pr), gr, l1, u, c, s1, true, 5240, "#E1");
+ checkMcf(mcf2, mcf2.run(pr), gr, l1, u, c, s2, true, 7620, "#E2");
+ checkMcf(mcf3, mcf3.run(pr), gr, l1, u, c, s3, true, 0, "#E3");
+ checkMcf(mcf4, mcf4.run(pr), gr, l2, u, c, s1, true, 5970, "#E4");
+ checkMcf(mcf5, mcf5.run(pr), gr, l2, u, c, s2, true, 8010, "#E5");
+ checkMcf(mcf6, mcf6.run(pr), gr, l2, u, c, s3, false, 0, "#E6");
+ }
+
+ // F. Test NetworkSimplex with BEST_ELIGIBLE_PIVOT
+ {
+ NetworkSimplex<Digraph>::PivotRuleEnum pr =
+ NetworkSimplex<Digraph>::BEST_ELIGIBLE_PIVOT;
+ NetworkSimplex<Digraph> mcf1(gr, u, c, s1);
+ NetworkSimplex<Digraph> mcf2(gr, u, c, v, w, 27);
+ NetworkSimplex<Digraph> mcf3(gr, u, c, s3);
+ NetworkSimplex<Digraph> mcf4(gr, l2, u, c, s1);
+ NetworkSimplex<Digraph> mcf5(gr, l2, u, c, v, w, 27);
+ NetworkSimplex<Digraph> mcf6(gr, l2, u, c, s3);
+
+ checkMcf(mcf1, mcf1.run(pr), gr, l1, u, c, s1, true, 5240, "#F1");
+ checkMcf(mcf2, mcf2.run(pr), gr, l1, u, c, s2, true, 7620, "#F2");
+ checkMcf(mcf3, mcf3.run(pr), gr, l1, u, c, s3, true, 0, "#F3");
+ checkMcf(mcf4, mcf4.run(pr), gr, l2, u, c, s1, true, 5970, "#F4");
+ checkMcf(mcf5, mcf5.run(pr), gr, l2, u, c, s2, true, 8010, "#F5");
+ checkMcf(mcf6, mcf6.run(pr), gr, l2, u, c, s3, false, 0, "#F6");
+ }
+
+ // G. Test NetworkSimplex with BLOCK_SEARCH_PIVOT
+ {
+ NetworkSimplex<Digraph>::PivotRuleEnum pr =
+ NetworkSimplex<Digraph>::BLOCK_SEARCH_PIVOT;
+ NetworkSimplex<Digraph> mcf1(gr, u, c, s1);
+ NetworkSimplex<Digraph> mcf2(gr, u, c, v, w, 27);
+ NetworkSimplex<Digraph> mcf3(gr, u, c, s3);
+ NetworkSimplex<Digraph> mcf4(gr, l2, u, c, s1);
+ NetworkSimplex<Digraph> mcf5(gr, l2, u, c, v, w, 27);
+ NetworkSimplex<Digraph> mcf6(gr, l2, u, c, s3);
+
+ checkMcf(mcf1, mcf1.run(pr), gr, l1, u, c, s1, true, 5240, "#G1");
+ checkMcf(mcf2, mcf2.run(pr), gr, l1, u, c, s2, true, 7620, "#G2");
+ checkMcf(mcf3, mcf3.run(pr), gr, l1, u, c, s3, true, 0, "#G3");
+ checkMcf(mcf4, mcf4.run(pr), gr, l2, u, c, s1, true, 5970, "#G4");
+ checkMcf(mcf5, mcf5.run(pr), gr, l2, u, c, s2, true, 8010, "#G5");
+ checkMcf(mcf6, mcf6.run(pr), gr, l2, u, c, s3, false, 0, "#G6");
+ }
+
+ // H. Test NetworkSimplex with CANDIDATE_LIST_PIVOT
+ {
+ NetworkSimplex<Digraph>::PivotRuleEnum pr =
+ NetworkSimplex<Digraph>::CANDIDATE_LIST_PIVOT;
+ NetworkSimplex<Digraph> mcf1(gr, u, c, s1);
+ NetworkSimplex<Digraph> mcf2(gr, u, c, v, w, 27);
+ NetworkSimplex<Digraph> mcf3(gr, u, c, s3);
+ NetworkSimplex<Digraph> mcf4(gr, l2, u, c, s1);
+ NetworkSimplex<Digraph> mcf5(gr, l2, u, c, v, w, 27);
+ NetworkSimplex<Digraph> mcf6(gr, l2, u, c, s3);
+
+ checkMcf(mcf1, mcf1.run(pr), gr, l1, u, c, s1, true, 5240, "#H1");
+ checkMcf(mcf2, mcf2.run(pr), gr, l1, u, c, s2, true, 7620, "#H2");
+ checkMcf(mcf3, mcf3.run(pr), gr, l1, u, c, s3, true, 0, "#H3");
+ checkMcf(mcf4, mcf4.run(pr), gr, l2, u, c, s1, true, 5970, "#H4");
+ checkMcf(mcf5, mcf5.run(pr), gr, l2, u, c, s2, true, 8010, "#H5");
+ checkMcf(mcf6, mcf6.run(pr), gr, l2, u, c, s3, false, 0, "#H6");
+ }
+
+ // I. Test NetworkSimplex with ALTERING_LIST_PIVOT
+ {
+ NetworkSimplex<Digraph>::PivotRuleEnum pr =
+ NetworkSimplex<Digraph>::ALTERING_LIST_PIVOT;
+ NetworkSimplex<Digraph> mcf1(gr, u, c, s1);
+ NetworkSimplex<Digraph> mcf2(gr, u, c, v, w, 27);
+ NetworkSimplex<Digraph> mcf3(gr, u, c, s3);
+ NetworkSimplex<Digraph> mcf4(gr, l2, u, c, s1);
+ NetworkSimplex<Digraph> mcf5(gr, l2, u, c, v, w, 27);
+ NetworkSimplex<Digraph> mcf6(gr, l2, u, c, s3);
+
+ checkMcf(mcf1, mcf1.run(pr), gr, l1, u, c, s1, true, 5240, "#I1");
+ checkMcf(mcf2, mcf2.run(pr), gr, l1, u, c, s2, true, 7620, "#I2");
+ checkMcf(mcf3, mcf3.run(pr), gr, l1, u, c, s3, true, 0, "#I3");
+ checkMcf(mcf4, mcf4.run(pr), gr, l2, u, c, s1, true, 5970, "#I4");
+ checkMcf(mcf5, mcf5.run(pr), gr, l2, u, c, s2, true, 8010, "#I5");
+ checkMcf(mcf6, mcf6.run(pr), gr, l2, u, c, s3, false, 0, "#I6");
+ }
+
+/*
+ // J. Test MinCostFlow
+ {
+ MinCostFlow<Digraph> mcf1(gr, u, c, s1);
+ MinCostFlow<Digraph> mcf2(gr, u, c, v, w, 27);
+ MinCostFlow<Digraph> mcf3(gr, u, c, s3);
+ MinCostFlow<Digraph> mcf4(gr, l2, u, c, s1);
+ MinCostFlow<Digraph> mcf5(gr, l2, u, c, v, w, 27);
+ MinCostFlow<Digraph> mcf6(gr, l2, u, c, s3);
+
+ checkMcf(mcf1, mcf1.run(), gr, l1, u, c, s1, true, 5240, "#J1");
+ checkMcf(mcf2, mcf2.run(), gr, l1, u, c, s2, true, 7620, "#J2");
+ checkMcf(mcf3, mcf3.run(), gr, l1, u, c, s3, true, 0, "#J3");
+ checkMcf(mcf4, mcf4.run(), gr, l2, u, c, s1, true, 5970, "#J4");
+ checkMcf(mcf5, mcf5.run(), gr, l2, u, c, s2, true, 8010, "#J5");
+ checkMcf(mcf6, mcf6.run(), gr, l2, u, c, s3, false, 0, "#J6");
+ }
+*/
+/*
+ // K. Test MinCostMaxFlow
+ {
+ MinCostMaxFlow<Digraph> mcmf(gr, u, c, v, w);
+ mcmf.run();
+ checkMcf(mcmf, true, gr, l1, u, c, s3, true, 7620, "#K1");
+ }
+*/
+
+ return 0;
+}