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				/* -- mode: C++; indent-tabs-mode: nil; --
				*
				* This file is a part of LEMON, a generic C++ optimization library.
				*
				* Copyright (C) 2003-2013
				* 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_algs
				///
				/// \file
				/// \brief Network Simplex algorithm for finding a minimum cost flow.

				#include <vector>
				#include <limits>
				#include <algorithm>

				#include <lemon/core.h>
				#include <lemon/math.h>

				namespace lemon {

				/// \addtogroup min_cost_flow_algs
				/// @{

				/// \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"
				/// \cite amo93networkflows, \cite dantzig63linearprog,
				/// \cite kellyoneill91netsimplex.
				/// This algorithm is a highly efficient specialized version of the
				/// linear programming simplex method directly for the minimum cost
				/// flow problem.
				///
				/// In general, \ref NetworkSimplex and \ref CostScaling are the fastest
				/// implementations available in LEMON for solving this problem.
				/// (For more information, see \ref min_cost_flow_algs "the module page".)
				/// Furthermore, this class supports both directions of the supply/demand
				/// inequality constraints. For more information, see \ref SupplyType.
				///
				/// Most of the parameters of the problem (except for the digraph)
				/// can be given using separate functions, and the algorithm can be
				/// executed using the \ref run() function. If some parameters are not
				/// specified, then default values will be used.
				///
				/// \tparam GR The digraph type the algorithm runs on.
				/// \tparam V The number type used for flow amounts, capacity bounds
				/// and supply values in the algorithm. By default, it is \c int.
				/// \tparam C The number type used for costs and potentials in the
				/// algorithm. By default, it is the same as \c V.
				///
				/// \warning Both \c V and \c C must be signed number types.
				/// \warning All input data (capacities, supply values, and costs) must
				/// be integer.
				///
				/// \note %NetworkSimplex provides five different pivot rule
				/// implementations, from which the most efficient one is used
				/// by default. For more information, see \ref PivotRule.
				template <typename GR, typename V = int, typename C = V>
				class NetworkSimplex
				{
				public:

				/// The type of the flow amounts, capacity bounds and supply values
				typedef V Value;
				/// The type of the arc costs
				typedef C Cost;

				public:

				/// \brief Problem type constants for the \c run() function.
				///
				/// Enum type containing the problem type constants that can be
				/// returned by the \ref run() function of the algorithm.
				enum ProblemType {
				/// The problem has no feasible solution (flow).
				INFEASIBLE,
				/// The problem has optimal solution (i.e. it is feasible and
				/// bounded), and the algorithm has found optimal flow and node
				/// potentials (primal and dual solutions).
				OPTIMAL,
				/// The objective function of the problem is unbounded, i.e.
				/// there is a directed cycle having negative total cost and
				/// infinite upper bound.
				UNBOUNDED
				};

				/// \brief Constants for selecting the type of the supply constraints.
				///
				/// Enum type containing constants for selecting the supply type,
				/// i.e. the direction of the inequalities in the supply/demand
				/// constraints of the \ref min_cost_flow "minimum cost flow problem".
				///
				/// The default supply type is \c GEQ, the \c LEQ type can be
				/// selected using \ref supplyType().
				/// The equality form is a special case of both supply types.
				enum SupplyType {
				/// This option means that there are <em>"greater or equal"</em>
				/// supply/demand constraints in the definition of the problem.
				GEQ,
				/// This option means that there are <em>"less or equal"</em>
				/// supply/demand constraints in the definition of the problem.
				LEQ
				};

				/// \brief Constants for selecting the pivot rule.
				///
				/// Enum type containing constants for selecting the pivot rule for
				/// the \ref run() function.
				///
				/// \ref NetworkSimplex provides five different implementations for
				/// the pivot strategy that significantly affects the running time
				/// of the algorithm.
				/// According to experimental tests conducted on various problem
				/// instances, \ref BLOCK_SEARCH "Block Search" and
				/// \ref ALTERING_LIST "Altering Candidate List" rules turned out
				/// to be the most efficient.
				/// Since \ref BLOCK_SEARCH "Block Search" is a simpler strategy that
				/// seemed to be slightly more robust, it is used by default.
				/// However, another pivot rule can easily be selected using the
				/// \ref run() function with the proper parameter.
				enum PivotRule {

				/// The \e First \e Eligible pivot rule.
				/// The next eligible arc is selected in a wraparound fashion
				/// in every iteration.
				FIRST_ELIGIBLE,

				/// The \e Best \e Eligible pivot rule.
				/// The best eligible arc is selected in every iteration.
				BEST_ELIGIBLE,

				/// The \e Block \e Search pivot rule.
				/// A specified number of arcs are examined in every iteration
				/// in a wraparound fashion and the best eligible arc is selected
				/// from this block.
				BLOCK_SEARCH,

				/// The \e Candidate \e List pivot rule.
				/// 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.
				CANDIDATE_LIST,

				/// The \e Altering \e Candidate \e List pivot rule.
				/// It is a modified version of the Candidate List method.
				/// It keeps only a few of the best eligible arcs from the former
				/// candidate list and extends this list in every iteration.
				ALTERING_LIST
				};

				private:

				TEMPLATE_DIGRAPH_TYPEDEFS(GR);

				typedef std::vector<int> IntVector;
				typedef std::vector<Value> ValueVector;
				typedef std::vector<Cost> CostVector;
				typedef std::vector<signed char> CharVector;
				// Note: vector<signed char> is used instead of vector<ArcState> and
				// vector<ArcDirection> for efficiency reasons

				// State constants for arcs
				enum ArcState {
				STATE_UPPER = -1,
				STATE_TREE = 0,
				STATE_LOWER = 1
				};

				// Direction constants for tree arcs
				enum ArcDirection {
				DIR_DOWN = -1,
				DIR_UP = 1
				};

				private:

				// Data related to the underlying digraph
				const GR &_graph;
				int _node_num;
				int _arc_num;
				int _all_arc_num;
				int _search_arc_num;

				// Parameters of the problem
				bool _has_lower;
				SupplyType _stype;
				Value _sum_supply;

				// Data structures for storing the digraph
				IntNodeMap _node_id;
				IntArcMap _arc_id;
				IntVector _source;
				IntVector _target;
				bool _arc_mixing;

				// Node and arc data
				ValueVector _lower;
				ValueVector _upper;
				ValueVector _cap;
				CostVector _cost;
				ValueVector _supply;
				ValueVector _flow;
				CostVector _pi;

				// Data for storing the spanning tree structure
				IntVector _parent;
				IntVector _pred;
				IntVector _thread;
				IntVector _rev_thread;
				IntVector _succ_num;
				IntVector _last_succ;
				CharVector _pred_dir;
				CharVector _state;
				IntVector _dirty_revs;
				int _root;

				// Temporary data used in the current pivot iteration
				int in_arc, join, u_in, v_in, u_out, v_out;
				Value delta;

				const Value MAX;

				public:

				/// \brief Constant for infinite upper bounds (capacities).
				///
				/// Constant for infinite upper bounds (capacities).
				/// It is \c std::numeric_limits<Value>::infinity() if available,
				/// \c std::numeric_limits<Value>::max() otherwise.
				const Value INF;

				private:

				// Implementation of the First Eligible pivot rule
				class FirstEligiblePivotRule
				{
				private:

				// References to the NetworkSimplex class
				const IntVector &_source;
				const IntVector &_target;
				const CostVector &_cost;
				const CharVector &_state;
				const CostVector &_pi;
				int &_in_arc;
				int _search_arc_num;

				// Pivot rule data
				int _next_arc;

				public:

				// Constructor
				FirstEligiblePivotRule(NetworkSimplex &ns) :
				_source(ns._source), _target(ns._target),
				_cost(ns._cost), _state(ns._state), _pi(ns._pi),
				_in_arc(ns.in_arc), _search_arc_num(ns._search_arc_num),
				_next_arc(0)
				{}

				// Find next entering arc
				bool findEnteringArc() {
				Cost c;
				for (int e = _next_arc; e != _search_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


				// Implementation of the Best Eligible pivot rule
				class BestEligiblePivotRule
				{
				private:

				// References to the NetworkSimplex class
				const IntVector &_source;
				const IntVector &_target;
				const CostVector &_cost;
				const CharVector &_state;
				const CostVector &_pi;
				int &_in_arc;
				int _search_arc_num;

				public:

				// Constructor
				BestEligiblePivotRule(NetworkSimplex &ns) :
				_source(ns._source), _target(ns._target),
				_cost(ns._cost), _state(ns._state), _pi(ns._pi),
				_in_arc(ns.in_arc), _search_arc_num(ns._search_arc_num)
				{}

				// Find next entering arc
				bool findEnteringArc() {
				Cost c, min = 0;
				for (int e = 0; e != _search_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


				// Implementation of the Block Search pivot rule
				class BlockSearchPivotRule
				{
				private:

				// References to the NetworkSimplex class
				const IntVector &_source;
				const IntVector &_target;
				const CostVector &_cost;
				const CharVector &_state;
				const CostVector &_pi;
				int &_in_arc;
				int _search_arc_num;

				// Pivot rule data
				int _block_size;
				int _next_arc;

				public:

				// Constructor
				BlockSearchPivotRule(NetworkSimplex &ns) :
				_source(ns._source), _target(ns._target),
				_cost(ns._cost), _state(ns._state), _pi(ns._pi),
				_in_arc(ns.in_arc), _search_arc_num(ns._search_arc_num),
				_next_arc(0)
				{
				// The main parameters of the pivot rule
				const double BLOCK_SIZE_FACTOR = 1.0;
				const int MIN_BLOCK_SIZE = 10;

				_block_size = std::max( int(BLOCK_SIZE_FACTOR *
				std::sqrt(double(_search_arc_num))),
				MIN_BLOCK_SIZE );
				}

				// Find next entering arc
				bool findEnteringArc() {
				Cost c, min = 0;
				int cnt = _block_size;
				int e;
				for (e = _next_arc; e != _search_arc_num; ++e) {
				c = _state[e] * (_cost[e] + _pi[_source[e]] - _pi[_target[e]]);
				if (c < min) {
				min = c;
				_in_arc = e;
				}
				if (--cnt == 0) {
				if (min < 0) goto search_end;
				cnt = _block_size;
				}
				}
				for (e = 0; e != _next_arc; ++e) {
				c = _state[e] * (_cost[e] + _pi[_source[e]] - _pi[_target[e]]);
				if (c < min) {
				min = c;
				_in_arc = e;
				}
				if (--cnt == 0) {
				if (min < 0) goto search_end;
				cnt = _block_size;
				}
				}
				if (min >= 0) return false;

				search_end:
				_next_arc = e;
				return true;
				}

				}; //class BlockSearchPivotRule


				// Implementation of the Candidate List pivot rule
				class CandidateListPivotRule
				{
				private:

				// References to the NetworkSimplex class
				const IntVector &_source;
				const IntVector &_target;
				const CostVector &_cost;
				const CharVector &_state;
				const CostVector &_pi;
				int &_in_arc;
				int _search_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) :
				_source(ns._source), _target(ns._target),
				_cost(ns._cost), _state(ns._state), _pi(ns._pi),
				_in_arc(ns.in_arc), _search_arc_num(ns._search_arc_num),
				_next_arc(0)
				{
				// The main parameters of the pivot rule
				const double LIST_LENGTH_FACTOR = 0.25;
				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 *
				std::sqrt(double(_search_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;
				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;
				_in_arc = e;
				}
				else if (c >= 0) {
				_candidates[i--] = _candidates[--_curr_length];
				}
				}
				if (min < 0) return true;
				}

				// Major iteration: build a new candidate list
				min = 0;
				_curr_length = 0;
				for (e = _next_arc; e != _search_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;
				_in_arc = e;
				}
				if (_curr_length == _list_length) goto search_end;
				}
				}
				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;
				_in_arc = e;
				}
				if (_curr_length == _list_length) goto search_end;
				}
				}
				if (_curr_length == 0) return false;

				search_end:
				_minor_count = 1;
				_next_arc = e;
				return true;
				}

				}; //class CandidateListPivotRule


				// Implementation of the Altering Candidate List pivot rule
				class AlteringListPivotRule
				{
				private:

				// References to the NetworkSimplex class
				const IntVector &_source;
				const IntVector &_target;
				const CostVector &_cost;
				const CharVector &_state;
				const CostVector &_pi;
				int &_in_arc;
				int _search_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) :
				_source(ns._source), _target(ns._target),
				_cost(ns._cost), _state(ns._state), _pi(ns._pi),
				_in_arc(ns.in_arc), _search_arc_num(ns._search_arc_num),
				_next_arc(0), _cand_cost(ns._search_arc_num), _sort_func(_cand_cost)
				{
				// The main parameters of the pivot rule
				const double BLOCK_SIZE_FACTOR = 1.0;
				const int MIN_BLOCK_SIZE = 10;
				const double HEAD_LENGTH_FACTOR = 0.01;
				const int MIN_HEAD_LENGTH = 3;

				_block_size = std::max( int(BLOCK_SIZE_FACTOR *
				std::sqrt(double(_search_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;
				Cost c;
				for (int i = 0; i != _curr_length; ++i) {
				e = _candidates[i];
				c = _state[e] * (_cost[e] + _pi[_source[e]] - _pi[_target[e]]);
				if (c < 0) {
				_cand_cost[e] = c;
				} else {
				_candidates[i--] = _candidates[--_curr_length];
				}
				}

				// Extend the list
				int cnt = _block_size;
				int limit = _head_length;

				for (e = _next_arc; e != _search_arc_num; ++e) {
				c = _state[e] * (_cost[e] + _pi[_source[e]] - _pi[_target[e]]);
				if (c < 0) {
				_cand_cost[e] = c;
				_candidates[_curr_length++] = e;
				}
				if (--cnt == 0) {
				if (_curr_length > limit) goto search_end;
				limit = 0;
				cnt = _block_size;
				}
				}
				for (e = 0; e != _next_arc; ++e) {
				c = _state[e] * (_cost[e] + _pi[_source[e]] - _pi[_target[e]]);
				if (c < 0) {
				_cand_cost[e] = c;
				_candidates[_curr_length++] = e;
				}
				if (--cnt == 0) {
				if (_curr_length > limit) goto search_end;
				limit = 0;
				cnt = _block_size;
				}
				}
				if (_curr_length == 0) return false;

				search_end:

				// Perform partial sort operation on the candidate list
				int new_length = std::min(_head_length + 1, _curr_length);
				std::partial_sort(_candidates.begin(), _candidates.begin() + new_length,
				_candidates.begin() + _curr_length, _sort_func);

				// Select the entering arc and remove it from the list
				_in_arc = _candidates[0];
				_next_arc = e;
				_candidates[0] = _candidates[new_length - 1];
				_curr_length = new_length - 1;
				return true;
				}

				}; //class AlteringListPivotRule

				public:

				/// \brief Constructor.
				///
				/// The constructor of the class.
				///
				/// \param graph The digraph the algorithm runs on.
				/// \param arc_mixing Indicate if the arcs will be stored in a
				/// mixed order in the internal data structure.
				/// In general, it leads to similar performance as using the original
				/// arc order, but it makes the algorithm more robust and in special
				/// cases, even significantly faster. Therefore, it is enabled by default.
				NetworkSimplex(const GR& graph, bool arc_mixing = true) :
				_graph(graph), _node_id(graph), _arc_id(graph),
				_arc_mixing(arc_mixing),
				MAX(std::numeric_limits<Value>::max()),
				INF(std::numeric_limits<Value>::has_infinity ?
				std::numeric_limits<Value>::infinity() : MAX)
				{
				// Check the number types
				LEMON_ASSERT(std::numeric_limits<Value>::is_signed,
				"The flow type of NetworkSimplex must be signed");
				LEMON_ASSERT(std::numeric_limits<Cost>::is_signed,
				"The cost type of NetworkSimplex must be signed");

				// Reset data structures
				reset();
				}

				/// \name Parameters
				/// The parameters of the algorithm can be specified using these
				/// functions.

				/// @{

				/// \brief Set the lower bounds on the arcs.
				///
				/// This function sets the lower bounds on the arcs.
				/// If it is not used before calling \ref run(), the lower bounds
				/// will be set to zero on all arcs.
				///
				/// \param map An arc map storing the lower bounds.
				/// Its \c Value type must be convertible to the \c Value type
				/// of the algorithm.
				///
				/// \return <tt>(*this)</tt>
				template <typename LowerMap>
				NetworkSimplex& lowerMap(const LowerMap& map) {
				_has_lower = true;
				for (ArcIt a(_graph); a != INVALID; ++a) {
				_lower[_arc_id[a]] = map[a];
				}
				return *this;
				}

				/// \brief Set the upper bounds (capacities) on the arcs.
				///
				/// This function sets the upper bounds (capacities) on the arcs.
				/// If it is not used before calling \ref run(), the upper bounds
				/// will be set to \ref INF on all arcs (i.e. the flow value will be
				/// unbounded from above).
				///
				/// \param map An arc map storing the upper bounds.
				/// Its \c Value type must be convertible to the \c Value type
				/// of the algorithm.
				///
				/// \return <tt>(*this)</tt>
				template<typename UpperMap>
				NetworkSimplex& upperMap(const UpperMap& map) {
				for (ArcIt a(_graph); a != INVALID; ++a) {
				_upper[_arc_id[a]] = map[a];
				}
				return *this;
				}

				/// \brief Set the costs of the arcs.
				///
				/// This function sets the costs of the arcs.
				/// If it is not used before calling \ref run(), the costs
				/// will be set to \c 1 on all arcs.
				///
				/// \param map An arc map storing the costs.
				/// Its \c Value type must be convertible to the \c Cost type
				/// of the algorithm.
				///
				/// \return <tt>(*this)</tt>
				template<typename CostMap>
				NetworkSimplex& costMap(const CostMap& map) {
				for (ArcIt a(_graph); a != INVALID; ++a) {
				_cost[_arc_id[a]] = map[a];
				}
				return *this;
				}

				/// \brief Set the supply values of the nodes.
				///
				/// This function sets the supply values of the nodes.
				/// If neither this function nor \ref stSupply() is used before
				/// calling \ref run(), the supply of each node will be set to zero.
				///
				/// \param map A node map storing the supply values.
				/// Its \c Value type must be convertible to the \c Value type
				/// of the algorithm.
				///
				/// \return <tt>(*this)</tt>
				///
				/// \sa supplyType()
				template<typename SupplyMap>
				NetworkSimplex& supplyMap(const SupplyMap& map) {
				for (NodeIt n(_graph); n != INVALID; ++n) {
				_supply[_node_id[n]] = map[n];
				}
				return *this;
				}

				/// \brief Set single source and target nodes and a supply value.
				///
				/// This function sets a single source node and a single target node
				/// and the required flow value.
				/// If neither this function nor \ref supplyMap() is used before
				/// calling \ref run(), the supply of each node will be set to zero.
				///
				/// Using this function has the same effect as using \ref supplyMap()
				/// with a map in which \c k is assigned to \c s, \c -k is
				/// assigned to \c t and all other nodes have zero supply value.
				///
				/// \param s The source node.
				/// \param t The target node.
				/// \param k The required amount of flow from node \c s to node \c t
				/// (i.e. the supply of \c s and the demand of \c t).
				///
				/// \return <tt>(*this)</tt>
				NetworkSimplex& stSupply(const Node& s, const Node& t, Value k) {
				for (int i = 0; i != _node_num; ++i) {
				_supply[i] = 0;
				}
				_supply[_node_id[s]] = k;
				_supply[_node_id[t]] = -k;
				return *this;
				}

				/// \brief Set the type of the supply constraints.
				///
				/// This function sets the type of the supply/demand constraints.
				/// If it is not used before calling \ref run(), the \ref GEQ supply
				/// type will be used.
				///
				/// For more information, see \ref SupplyType.
				///
				/// \return <tt>(*this)</tt>
				NetworkSimplex& supplyType(SupplyType supply_type) {
				_stype = supply_type;
				return *this;
				}

				/// @}

				/// \name Execution Control
				/// The algorithm can be executed using \ref run().

				/// @{

				/// \brief Run the algorithm.
				///
				/// This function runs the algorithm.
				/// The paramters can be specified using functions \ref lowerMap(),
				/// \ref upperMap(), \ref costMap(), \ref supplyMap(), \ref stSupply(),
				/// \ref supplyType().
				/// For example,
				/// \code
				/// NetworkSimplex<ListDigraph> ns(graph);
				/// ns.lowerMap(lower).upperMap(upper).costMap(cost)
				/// .supplyMap(sup).run();
				/// \endcode
				///
				/// This function can be called more than once. All the given parameters
				/// are kept for the next call, unless \ref resetParams() or \ref reset()
				/// is used, thus only the modified parameters have to be set again.
				/// If the underlying digraph was also modified after the construction
				/// of the class (or the last \ref reset() call), then the \ref reset()
				/// function must be called.
				///
				/// \param pivot_rule The pivot rule that will be used during the
				/// algorithm. For more information, see \ref PivotRule.
				///
				/// \return \c INFEASIBLE if no feasible flow exists,
				/// \n \c OPTIMAL if the problem has optimal solution
				/// (i.e. it is feasible and bounded), and the algorithm has found
				/// optimal flow and node potentials (primal and dual solutions),
				/// \n \c UNBOUNDED if the objective function of the problem is
				/// unbounded, i.e. there is a directed cycle having negative total
				/// cost and infinite upper bound.
				///
				/// \see ProblemType, PivotRule
				/// \see resetParams(), reset()
				ProblemType run(PivotRule pivot_rule = BLOCK_SEARCH) {
				if (!init()) return INFEASIBLE;
				return start(pivot_rule);
				}

				/// \brief Reset all the parameters that have been given before.
				///
				/// This function resets all the paramaters that have been given
				/// before using functions \ref lowerMap(), \ref upperMap(),
				/// \ref costMap(), \ref supplyMap(), \ref stSupply(), \ref supplyType().
				///
				/// It is useful for multiple \ref run() calls. Basically, all the given
				/// parameters are kept for the next \ref run() call, unless
				/// \ref resetParams() or \ref reset() is used.
				/// If the underlying digraph was also modified after the construction
				/// of the class or the last \ref reset() call, then the \ref reset()
				/// function must be used, otherwise \ref resetParams() is sufficient.
				///
				/// For example,
				/// \code
				/// NetworkSimplex<ListDigraph> ns(graph);
				///
				/// // First run
				/// ns.lowerMap(lower).upperMap(upper).costMap(cost)
				/// .supplyMap(sup).run();
				///
				/// // Run again with modified cost map (resetParams() is not called,
				/// // so only the cost map have to be set again)
				/// cost[e] += 100;
				/// ns.costMap(cost).run();
				///
				/// // Run again from scratch using resetParams()
				/// // (the lower bounds will be set to zero on all arcs)
				/// ns.resetParams();
				/// ns.upperMap(capacity).costMap(cost)
				/// .supplyMap(sup).run();
				/// \endcode
				///
				/// \return <tt>(*this)</tt>
				///
				/// \see reset(), run()
				NetworkSimplex& resetParams() {
				for (int i = 0; i != _node_num; ++i) {
				_supply[i] = 0;
				}
				for (int i = 0; i != _arc_num; ++i) {
				_lower[i] = 0;
				_upper[i] = INF;
				_cost[i] = 1;
				}
				_has_lower = false;
				_stype = GEQ;
				return *this;
				}

				/// \brief Reset the internal data structures and all the parameters
				/// that have been given before.
				///
				/// This function resets the internal data structures and all the
				/// paramaters that have been given before using functions \ref lowerMap(),
				/// \ref upperMap(), \ref costMap(), \ref supplyMap(), \ref stSupply(),
				/// \ref supplyType().
				///
				/// It is useful for multiple \ref run() calls. Basically, all the given
				/// parameters are kept for the next \ref run() call, unless
				/// \ref resetParams() or \ref reset() is used.
				/// If the underlying digraph was also modified after the construction
				/// of the class or the last \ref reset() call, then the \ref reset()
				/// function must be used, otherwise \ref resetParams() is sufficient.
				///
				/// See \ref resetParams() for examples.
				///
				/// \return <tt>(*this)</tt>
				///
				/// \see resetParams(), run()
				NetworkSimplex& reset() {
				// Resize vectors
				_node_num = countNodes(_graph);
				_arc_num = countArcs(_graph);
				int all_node_num = _node_num + 1;
				int max_arc_num = _arc_num + 2 * _node_num;

				_source.resize(max_arc_num);
				_target.resize(max_arc_num);

				_lower.resize(_arc_num);
				_upper.resize(_arc_num);
				_cap.resize(max_arc_num);
				_cost.resize(max_arc_num);
				_supply.resize(all_node_num);
				_flow.resize(max_arc_num);
				_pi.resize(all_node_num);

				_parent.resize(all_node_num);
				_pred.resize(all_node_num);
				_pred_dir.resize(all_node_num);
				_thread.resize(all_node_num);
				_rev_thread.resize(all_node_num);
				_succ_num.resize(all_node_num);
				_last_succ.resize(all_node_num);
				_state.resize(max_arc_num);

				// Copy the graph
				int i = 0;
				for (NodeIt n(_graph); n != INVALID; ++n, ++i) {
				_node_id[n] = i;
				}
				if (_arc_mixing && _node_num > 1) {
				// Store the arcs in a mixed order
				const int skip = std::max(_arc_num / _node_num, 3);
				int i = 0, j = 0;
				for (ArcIt a(_graph); a != INVALID; ++a) {
				_arc_id[a] = i;
				_source[i] = _node_id[_graph.source(a)];
				_target[i] = _node_id[_graph.target(a)];
				if ((i += skip) >= _arc_num) i = ++j;
				}
				} else {
				// Store the arcs in the original order
				int i = 0;
				for (ArcIt a(_graph); a != INVALID; ++a, ++i) {
				_arc_id[a] = i;
				_source[i] = _node_id[_graph.source(a)];
				_target[i] = _node_id[_graph.target(a)];
				}
				}

				// Reset parameters
				resetParams();
				return *this;
				}

				/// @}

				/// \name Query Functions
				/// The results of the algorithm can be obtained using these
				/// functions.\n
				/// The \ref run() function must be called before using them.

				/// @{

				/// \brief Return the total cost of the found flow.
				///
				/// This function returns the total cost of the found flow.
				/// Its complexity is O(m).
				///
				/// \note The return type of the function can be specified as a
				/// template parameter. For example,
				/// \code
				/// ns.totalCost<double>();
				/// \endcode
				/// It is useful if the total cost cannot be stored in the \c Cost
				/// type of the algorithm, which is the default return type of the
				/// function.
				///
				/// \pre \ref run() must be called before using this function.
				template <typename Number>
				Number totalCost() const {
				Number c = 0;
				for (ArcIt a(_graph); a != INVALID; ++a) {
				int i = _arc_id[a];
				c += Number(_flow[i]) * Number(_cost[i]);
				}
				return c;
				}

				#ifndef DOXYGEN
				Cost totalCost() const {
				return totalCost<Cost>();
				}
				#endif

				/// \brief Return the flow on the given arc.
				///
				/// This function returns the flow on the given arc.
				///
				/// \pre \ref run() must be called before using this function.
				Value flow(const Arc& a) const {
				return _flow[_arc_id[a]];
				}

				/// \brief Copy the flow values (the primal solution) into the
				/// given map.
				///
				/// This function copies the flow value on each arc into the given
				/// map. The \c Value type of the algorithm must be convertible to
				/// the \c Value type of the map.
				///
				/// \pre \ref run() must be called before using this function.
				template <typename FlowMap>
				void flowMap(FlowMap &map) const {
				for (ArcIt a(_graph); a != INVALID; ++a) {
				map.set(a, _flow[_arc_id[a]]);
				}
				}

				/// \brief Return the potential (dual value) of the given node.
				///
				/// This function returns the potential (dual value) of the
				/// given node.
				///
				/// \pre \ref run() must be called before using this function.
				Cost potential(const Node& n) const {
				return _pi[_node_id[n]];
				}

				/// \brief Copy the potential values (the dual solution) into the
				/// given map.
				///
				/// This function copies the potential (dual value) of each node
				/// into the given map.
				/// The \c Cost type of the algorithm must be convertible to the
				/// \c Value type of the map.
				///
				/// \pre \ref run() must be called before using this function.
				template <typename PotentialMap>
				void potentialMap(PotentialMap &map) const {
				for (NodeIt n(_graph); n != INVALID; ++n) {
				map.set(n, _pi[_node_id[n]]);
				}
				}

				/// @}

				private:

				// Initialize internal data structures
				bool init() {
				if (_node_num == 0) return false;

				// Check the sum of supply values
				_sum_supply = 0;
				for (int i = 0; i != _node_num; ++i) {
				_sum_supply += _supply[i];
				}
				if ( !((_stype == GEQ && _sum_supply <= 0) \|\|
				(_stype == LEQ && _sum_supply >= 0)) ) return false;

				// Check lower and upper bounds
				LEMON_DEBUG(checkBoundMaps(),
				"Upper bounds must be greater or equal to the lower bounds");

				// Remove non-zero lower bounds
				if (_has_lower) {
				for (int i = 0; i != _arc_num; ++i) {
				Value c = _lower[i];
				if (c >= 0) {
				_cap[i] = _upper[i] < MAX ? _upper[i] - c : INF;
				} else {
				_cap[i] = _upper[i] < MAX + c ? _upper[i] - c : INF;
				}
				_supply[_source[i]] -= c;
				_supply[_target[i]] += c;
				}
				} else {
				for (int i = 0; i != _arc_num; ++i) {
				_cap[i] = _upper[i];
				}
				}

				// Initialize artifical cost
				Cost ART_COST;
				if (std::numeric_limits<Cost>::is_exact) {
				ART_COST = std::numeric_limits<Cost>::max() / 2 + 1;
				} else {
				ART_COST = 0;
				for (int i = 0; i != _arc_num; ++i) {
				if (_cost[i] > ART_COST) ART_COST = _cost[i];
				}
				ART_COST = (ART_COST + 1) * _node_num;
				}

				// Initialize arc maps
				for (int i = 0; i != _arc_num; ++i) {
				_flow[i] = 0;
				_state[i] = STATE_LOWER;
				}

				// Set data for the artificial root node
				_root = _node_num;
				_parent[_root] = -1;
				_pred[_root] = -1;
				_thread[_root] = 0;
				_rev_thread[0] = _root;
				_succ_num[_root] = _node_num + 1;
				_last_succ[_root] = _root - 1;
				_supply[_root] = -_sum_supply;
				_pi[_root] = 0;

				// Add artificial arcs and initialize the spanning tree data structure
				if (_sum_supply == 0) {
				// EQ supply constraints
				_search_arc_num = _arc_num;
				_all_arc_num = _arc_num + _node_num;
				for (int u = 0, e = _arc_num; u != _node_num; ++u, ++e) {
				_parent[u] = _root;
				_pred[u] = e;
				_thread[u] = u + 1;
				_rev_thread[u + 1] = u;
				_succ_num[u] = 1;
				_last_succ[u] = u;
				_cap[e] = INF;
				_state[e] = STATE_TREE;
				if (_supply[u] >= 0) {
				_pred_dir[u] = DIR_UP;
				_pi[u] = 0;
				_source[e] = u;
				_target[e] = _root;
				_flow[e] = _supply[u];
				_cost[e] = 0;
				} else {
				_pred_dir[u] = DIR_DOWN;
				_pi[u] = ART_COST;
				_source[e] = _root;
				_target[e] = u;
				_flow[e] = -_supply[u];
				_cost[e] = ART_COST;
				}
				}
				}
				else if (_sum_supply > 0) {
				// LEQ supply constraints
				_search_arc_num = _arc_num + _node_num;
				int f = _arc_num + _node_num;
				for (int u = 0, e = _arc_num; u != _node_num; ++u, ++e) {
				_parent[u] = _root;
				_thread[u] = u + 1;
				_rev_thread[u + 1] = u;
				_succ_num[u] = 1;
				_last_succ[u] = u;
				if (_supply[u] >= 0) {
				_pred_dir[u] = DIR_UP;
				_pi[u] = 0;
				_pred[u] = e;
				_source[e] = u;
				_target[e] = _root;
				_cap[e] = INF;
				_flow[e] = _supply[u];
				_cost[e] = 0;
				_state[e] = STATE_TREE;
				} else {
				_pred_dir[u] = DIR_DOWN;
				_pi[u] = ART_COST;
				_pred[u] = f;
				_source[f] = _root;
				_target[f] = u;
				_cap[f] = INF;
				_flow[f] = -_supply[u];
				_cost[f] = ART_COST;
				_state[f] = STATE_TREE;
				_source[e] = u;
				_target[e] = _root;
				_cap[e] = INF;
				_flow[e] = 0;
				_cost[e] = 0;
				_state[e] = STATE_LOWER;
				++f;
				}
				}
				_all_arc_num = f;
				}
				else {
				// GEQ supply constraints
				_search_arc_num = _arc_num + _node_num;
				int f = _arc_num + _node_num;
				for (int u = 0, e = _arc_num; u != _node_num; ++u, ++e) {
				_parent[u] = _root;
				_thread[u] = u + 1;
				_rev_thread[u + 1] = u;
				_succ_num[u] = 1;
				_last_succ[u] = u;
				if (_supply[u] <= 0) {
				_pred_dir[u] = DIR_DOWN;
				_pi[u] = 0;
				_pred[u] = e;
				_source[e] = _root;
				_target[e] = u;
				_cap[e] = INF;
				_flow[e] = -_supply[u];
				_cost[e] = 0;
				_state[e] = STATE_TREE;
				} else {
				_pred_dir[u] = DIR_UP;
				_pi[u] = -ART_COST;
				_pred[u] = f;
				_source[f] = u;
				_target[f] = _root;
				_cap[f] = INF;
				_flow[f] = _supply[u];
				_state[f] = STATE_TREE;
				_cost[f] = ART_COST;
				_source[e] = _root;
				_target[e] = u;
				_cap[e] = INF;
				_flow[e] = 0;
				_cost[e] = 0;
				_state[e] = STATE_LOWER;
				++f;
				}
				}
				_all_arc_num = f;
				}

				return true;
				}

				// Check if the upper bound is greater than or equal to the lower bound
				// on each arc.
				bool checkBoundMaps() {
				for (int j = 0; j != _arc_num; ++j) {
				if (_upper[j] < _lower[j]) return false;
				}
				return true;
				}

				// Find the join node
				void findJoinNode() {
				int u = _source[in_arc];
				int v = _target[in_arc];
				while (u != v) {
				if (_succ_num[u] < _succ_num[v]) {
				u = _parent[u];
				} else {
				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
				int first, second;
				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;
				Value c, d;
				int e;

				// Search the cycle form the first node to the join node
				for (int u = first; u != join; u = _parent[u]) {
				e = _pred[u];
				d = _flow[e];
				if (_pred_dir[u] == DIR_DOWN) {
				c = _cap[e];
				d = c >= MAX ? INF : c - d;
				}
				if (d < delta) {
				delta = d;
				u_out = u;
				result = 1;
				}
				}

				// Search the cycle form the second node to the join node
				for (int u = second; u != join; u = _parent[u]) {
				e = _pred[u];
				d = _flow[e];
				if (_pred_dir[u] == DIR_UP) {
				c = _cap[e];
				d = c >= MAX ? INF : c - d;
				}
				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) {
				Value val = _state[in_arc] * delta;
				_flow[in_arc] += val;
				for (int u = _source[in_arc]; u != join; u = _parent[u]) {
				_flow[_pred[u]] -= _pred_dir[u] * val;
				}
				for (int u = _target[in_arc]; u != join; u = _parent[u]) {
				_flow[_pred[u]] += _pred_dir[u] * 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 the tree structure
				void updateTreeStructure() {
				int old_rev_thread = _rev_thread[u_out];
				int old_succ_num = _succ_num[u_out];
				int old_last_succ = _last_succ[u_out];
				v_out = _parent[u_out];

				// Check if u_in and u_out coincide
				if (u_in == u_out) {
				// Update _parent, _pred, _pred_dir
				_parent[u_in] = v_in;
				_pred[u_in] = in_arc;
				_pred_dir[u_in] = u_in == _source[in_arc] ? DIR_UP : DIR_DOWN;

				// Update _thread and _rev_thread
				if (_thread[v_in] != u_out) {
				int after = _thread[old_last_succ];
				_thread[old_rev_thread] = after;
				_rev_thread[after] = old_rev_thread;
				after = _thread[v_in];
				_thread[v_in] = u_out;
				_rev_thread[u_out] = v_in;
				_thread[old_last_succ] = after;
				_rev_thread[after] = old_last_succ;
				}
				} else {
				// Handle the case when old_rev_thread equals to v_in
				// (it also means that join and v_out coincide)
				int thread_continue = old_rev_thread == v_in ?
				_thread[old_last_succ] : _thread[v_in];

				// Update _thread and _parent along the stem nodes (i.e. the nodes
				// between u_in and u_out, whose parent have to be changed)
				int stem = u_in; // the current stem node
				int par_stem = v_in; // the new parent of stem
				int next_stem; // the next stem node
				int last = _last_succ[u_in]; // the last successor of stem
				int before, after = _thread[last];
				_thread[v_in] = u_in;
				_dirty_revs.clear();
				_dirty_revs.push_back(v_in);
				while (stem != u_out) {
				// Insert the next stem node into the thread list
				next_stem = _parent[stem];
				_thread[last] = next_stem;
				_dirty_revs.push_back(last);

				// Remove the subtree of stem from the thread list
				before = _rev_thread[stem];
				_thread[before] = after;
				_rev_thread[after] = before;

				// Change the parent node and shift stem nodes
				_parent[stem] = par_stem;
				par_stem = stem;
				stem = next_stem;

				// Update last and after
				last = _last_succ[stem] == _last_succ[par_stem] ?
				_rev_thread[par_stem] : _last_succ[stem];
				after = _thread[last];
				}
				_parent[u_out] = par_stem;
				_thread[last] = thread_continue;
				_rev_thread[thread_continue] = last;
				_last_succ[u_out] = last;

				// Remove the subtree of u_out from the thread list except for
				// the case when old_rev_thread equals to v_in
				if (old_rev_thread != v_in) {
				_thread[old_rev_thread] = after;
				_rev_thread[after] = old_rev_thread;
				}

				// Update _rev_thread using the new _thread values
				for (int i = 0; i != int(_dirty_revs.size()); ++i) {
				int u = _dirty_revs[i];
				_rev_thread[_thread[u]] = u;
				}

				// Update _pred, _pred_dir, _last_succ and _succ_num for the
				// stem nodes from u_out to u_in
				int tmp_sc = 0, tmp_ls = _last_succ[u_out];
				for (int u = u_out, p = _parent[u]; u != u_in; u = p, p = _parent[u]) {
				_pred[u] = _pred[p];
				_pred_dir[u] = -_pred_dir[p];
				tmp_sc += _succ_num[u] - _succ_num[p];
				_succ_num[u] = tmp_sc;
				_last_succ[p] = tmp_ls;
				}
				_pred[u_in] = in_arc;
				_pred_dir[u_in] = u_in == _source[in_arc] ? DIR_UP : DIR_DOWN;
				_succ_num[u_in] = old_succ_num;
				}

				// Update _last_succ from v_in towards the root
				int up_limit_out = _last_succ[join] == v_in ? join : -1;
				int last_succ_out = _last_succ[u_out];
				for (int u = v_in; u != -1 && _last_succ[u] == v_in; u = _parent[u]) {
				_last_succ[u] = last_succ_out;
				}

				// Update _last_succ from v_out towards the root
				if (join != old_rev_thread && v_in != old_rev_thread) {
				for (int u = v_out; u != up_limit_out && _last_succ[u] == old_last_succ;
				u = _parent[u]) {
				_last_succ[u] = old_rev_thread;
				}
				}
				else if (last_succ_out != old_last_succ) {
				for (int u = v_out; u != up_limit_out && _last_succ[u] == old_last_succ;
				u = _parent[u]) {
				_last_succ[u] = last_succ_out;
				}
				}

				// Update _succ_num from v_in to join
				for (int u = v_in; u != join; u = _parent[u]) {
				_succ_num[u] += old_succ_num;
				}
				// Update _succ_num from v_out to join
				for (int u = v_out; u != join; u = _parent[u]) {
				_succ_num[u] -= old_succ_num;
				}
				}

				// Update potentials in the subtree that has been moved
				void updatePotential() {
				Cost sigma = _pi[v_in] - _pi[u_in] -
				_pred_dir[u_in] * _cost[in_arc];
				int end = _thread[_last_succ[u_in]];
				for (int u = u_in; u != end; u = _thread[u]) {
				_pi[u] += sigma;
				}
				}

				// Heuristic initial pivots
				bool initialPivots() {
				Value curr, total = 0;
				std::vector<Node> supply_nodes, demand_nodes;
				for (NodeIt u(_graph); u != INVALID; ++u) {
				curr = _supply[_node_id[u]];
				if (curr > 0) {
				total += curr;
				supply_nodes.push_back(u);
				}
				else if (curr < 0) {
				demand_nodes.push_back(u);
				}
				}
				if (_sum_supply > 0) total -= _sum_supply;
				if (total <= 0) return true;

				IntVector arc_vector;
				if (_sum_supply >= 0) {
				if (supply_nodes.size() == 1 && demand_nodes.size() == 1) {
				// Perform a reverse graph search from the sink to the source
				typename GR::template NodeMap<bool> reached(_graph, false);
				Node s = supply_nodes[0], t = demand_nodes[0];
				std::vector<Node> stack;
				reached[t] = true;
				stack.push_back(t);
				while (!stack.empty()) {
				Node u, v = stack.back();
				stack.pop_back();
				if (v == s) break;
				for (InArcIt a(_graph, v); a != INVALID; ++a) {
				if (reached[u = _graph.source(a)]) continue;
				int j = _arc_id[a];
				if (_cap[j] >= total) {
				arc_vector.push_back(j);
				reached[u] = true;
				stack.push_back(u);
				}
				}
				}
				} else {
				// Find the min. cost incoming arc for each demand node
				for (int i = 0; i != int(demand_nodes.size()); ++i) {
				Node v = demand_nodes[i];
				Cost c, min_cost = std::numeric_limits<Cost>::max();
				Arc min_arc = INVALID;
				for (InArcIt a(_graph, v); a != INVALID; ++a) {
				c = _cost[_arc_id[a]];
				if (c < min_cost) {
				min_cost = c;
				min_arc = a;
				}
				}
				if (min_arc != INVALID) {
				arc_vector.push_back(_arc_id[min_arc]);
				}
				}
				}
				} else {
				// Find the min. cost outgoing arc for each supply node
				for (int i = 0; i != int(supply_nodes.size()); ++i) {
				Node u = supply_nodes[i];
				Cost c, min_cost = std::numeric_limits<Cost>::max();
				Arc min_arc = INVALID;
				for (OutArcIt a(_graph, u); a != INVALID; ++a) {
				c = _cost[_arc_id[a]];
				if (c < min_cost) {
				min_cost = c;
				min_arc = a;
				}
				}
				if (min_arc != INVALID) {
				arc_vector.push_back(_arc_id[min_arc]);
				}
				}
				}

				// Perform heuristic initial pivots
				for (int i = 0; i != int(arc_vector.size()); ++i) {
				in_arc = arc_vector[i];
				if (_state[in_arc] * (_cost[in_arc] + _pi[_source[in_arc]] -
				_pi[_target[in_arc]]) >= 0) continue;
				findJoinNode();
				bool change = findLeavingArc();
				if (delta >= MAX) return false;
				changeFlow(change);
				if (change) {
				updateTreeStructure();
				updatePotential();
				}
				}
				return true;
				}

				// Execute the algorithm
				ProblemType start(PivotRule pivot_rule) {
				// Select the pivot rule implementation
				switch (pivot_rule) {
				case FIRST_ELIGIBLE:
				return start<FirstEligiblePivotRule>();
				case BEST_ELIGIBLE:
				return start<BestEligiblePivotRule>();
				case BLOCK_SEARCH:
				return start<BlockSearchPivotRule>();
				case CANDIDATE_LIST:
				return start<CandidateListPivotRule>();
				case ALTERING_LIST:
				return start<AlteringListPivotRule>();
				}
				return INFEASIBLE; // avoid warning
				}

				template <typename PivotRuleImpl>
				ProblemType start() {
				PivotRuleImpl pivot(*this);

				// Perform heuristic initial pivots
				if (!initialPivots()) return UNBOUNDED;

				// Execute the Network Simplex algorithm
				while (pivot.findEnteringArc()) {
				findJoinNode();
				bool change = findLeavingArc();
				if (delta >= MAX) return UNBOUNDED;
				changeFlow(change);
				if (change) {
				updateTreeStructure();
				updatePotential();
				}
				}

				// Check feasibility
				for (int e = _search_arc_num; e != _all_arc_num; ++e) {
				if (_flow[e] != 0) return INFEASIBLE;
				}

				// Transform the solution and the supply map to the original form
				if (_has_lower) {
				for (int i = 0; i != _arc_num; ++i) {
				Value c = _lower[i];
				if (c != 0) {
				_flow[i] += c;
				_supply[_source[i]] += c;
				_supply[_target[i]] -= c;
				}
				}
				}

				// Shift potentials to meet the requirements of the GEQ/LEQ type
				// optimality conditions
				if (_sum_supply == 0) {
				if (_stype == GEQ) {
				Cost max_pot = -std::numeric_limits<Cost>::max();
				for (int i = 0; i != _node_num; ++i) {
				if (_pi[i] > max_pot) max_pot = _pi[i];
				}
				if (max_pot > 0) {
				for (int i = 0; i != _node_num; ++i)
				_pi[i] -= max_pot;
				}
				} else {
				Cost min_pot = std::numeric_limits<Cost>::max();
				for (int i = 0; i != _node_num; ++i) {
				if (_pi[i] < min_pot) min_pot = _pi[i];
				}
				if (min_pot < 0) {
				for (int i = 0; i != _node_num; ++i)
				_pi[i] -= min_pot;
				}
				}
				}

				return OPTIMAL;
				}

				}; //class NetworkSimplex

				///@}

				} //namespace lemon

				#endif //LEMON_NETWORK_SIMPLEX_H