deba@2440: /* -*- C++ -*-
deba@2440:  *
deba@2440:  * This file is a part of LEMON, a generic C++ optimization library
deba@2440:  *
deba@2440:  * Copyright (C) 2003-2007
deba@2440:  * Egervary Jeno Kombinatorikus Optimalizalasi Kutatocsoport
deba@2440:  * (Egervary Research Group on Combinatorial Optimization, EGRES).
deba@2440:  *
deba@2440:  * Permission to use, modify and distribute this software is granted
deba@2440:  * provided that this copyright notice appears in all copies. For
deba@2440:  * precise terms see the accompanying LICENSE file.
deba@2440:  *
deba@2440:  * This software is provided "AS IS" with no warranty of any kind,
deba@2440:  * express or implied, and with no claim as to its suitability for any
deba@2440:  * purpose.
deba@2440:  *
deba@2440:  */
deba@2440: 
deba@2440: #ifndef LEMON_NETWORK_SIMPLEX_H
deba@2440: #define LEMON_NETWORK_SIMPLEX_H
deba@2440: 
deba@2440: /// \ingroup min_cost_flow
deba@2440: ///
deba@2440: /// \file
deba@2440: /// \brief The network simplex algorithm for finding a minimum cost
deba@2440: /// flow.
deba@2440: 
deba@2440: #include <limits>
deba@2440: #include <lemon/smart_graph.h>
deba@2440: #include <lemon/graph_utils.h>
deba@2440: 
deba@2440: /// \brief The pivot rule used in the algorithm.
deba@2440: //#define FIRST_ELIGIBLE_PIVOT
deba@2440: //#define BEST_ELIGIBLE_PIVOT
deba@2444: #define EDGE_BLOCK_PIVOT
deba@2440: //#define CANDIDATE_LIST_PIVOT
deba@2440: //#define SORTED_LIST_PIVOT
deba@2440: 
deba@2444: //#define _DEBUG_ITER_
deba@2444: 
deba@2444: 
deba@2440: /// \brief State constant for edges at their lower bounds.
deba@2440: #define LOWER	1
deba@2440: /// \brief State constant for edges in the spanning tree.
deba@2440: #define TREE	0
deba@2440: /// \brief State constant for edges at their upper bounds.
deba@2440: #define UPPER	-1
deba@2440: 
deba@2440: #ifdef EDGE_BLOCK_PIVOT
deba@2440:   /// \brief Number of blocks for the "Edge Block" pivot rule.
deba@2444:   #define BLOCK_NUM		100
deba@2444:   /// \brief Lower bound for the size of blocks.
deba@2444:   #define MIN_BLOCK_SIZE	10
deba@2440: #endif
deba@2440: 
deba@2440: #ifdef CANDIDATE_LIST_PIVOT
deba@2440:   #include <list>
deba@2440:   /// \brief The maximum length of the edge list for the
deba@2440:   /// "Candidate List" pivot rule.
deba@2444:   #define LIST_LENGTH		100
deba@2440:   /// \brief The maximum number of minor iterations between two major
deba@2440:   /// itarations.
deba@2444:   #define MINOR_LIMIT		10
deba@2440: #endif
deba@2440: 
deba@2440: #ifdef SORTED_LIST_PIVOT
deba@2440:   #include <deque>
deba@2440:   #include <algorithm>
deba@2440:   /// \brief The maximum length of the edge list for the
deba@2440:   /// "Sorted List" pivot rule.
deba@2444:   #define LIST_LENGTH		500
deba@2444:   #define LOWER_DIV		3
deba@2440: #endif
deba@2440: 
deba@2440: namespace lemon {
deba@2440: 
deba@2440:   /// \addtogroup min_cost_flow
deba@2440:   /// @{
deba@2440: 
deba@2440:   /// \brief Implementation of the network simplex algorithm for
deba@2440:   /// finding a minimum cost flow.
deba@2440:   ///
deba@2440:   /// \ref lemon::NetworkSimplex "NetworkSimplex" implements the
deba@2440:   /// network simplex algorithm for finding a minimum cost flow.
deba@2440:   ///
deba@2440:   /// \param Graph The directed graph type the algorithm runs on.
deba@2440:   /// \param LowerMap The type of the lower bound map.
deba@2440:   /// \param CapacityMap The type of the capacity (upper bound) map.
deba@2440:   /// \param CostMap The type of the cost (length) map.
deba@2440:   /// \param SupplyMap The type of the supply map.
deba@2440:   ///
deba@2440:   /// \warning
deba@2440:   /// - Edge capacities and costs should be nonnegative integers.
deba@2440:   ///	However \c CostMap::Value should be signed type.
deba@2440:   /// - Supply values should be integers.
deba@2440:   /// - \c LowerMap::Value must be convertible to
deba@2440:   ///	\c CapacityMap::Value and \c CapacityMap::Value must be
deba@2440:   ///	convertible to \c SupplyMap::Value.
deba@2440:   ///
deba@2440:   /// \author Peter Kovacs
deba@2440: 
deba@2440: template < typename Graph,
deba@2440: 	   typename LowerMap = typename Graph::template EdgeMap<int>,
deba@2440: 	   typename CapacityMap = LowerMap,
deba@2440: 	   typename CostMap = typename Graph::template EdgeMap<int>,
deba@2440: 	   typename SupplyMap = typename Graph::template NodeMap
deba@2440: 				<typename CapacityMap::Value> >
deba@2440:   class NetworkSimplex
deba@2440:   {
deba@2440:     typedef typename LowerMap::Value Lower;
deba@2440:     typedef typename CapacityMap::Value Capacity;
deba@2440:     typedef typename CostMap::Value Cost;
deba@2440:     typedef typename SupplyMap::Value Supply;
deba@2440: 
deba@2440:     typedef SmartGraph SGraph;
deba@2440:     typedef typename SGraph::Node Node;
deba@2440:     typedef typename SGraph::NodeIt NodeIt;
deba@2440:     typedef typename SGraph::Edge Edge;
deba@2440:     typedef typename SGraph::EdgeIt EdgeIt;
deba@2440:     typedef typename SGraph::InEdgeIt InEdgeIt;
deba@2440:     typedef typename SGraph::OutEdgeIt OutEdgeIt;
deba@2440: 
deba@2440:     typedef typename SGraph::template EdgeMap<Lower> SLowerMap;
deba@2440:     typedef typename SGraph::template EdgeMap<Capacity> SCapacityMap;
deba@2440:     typedef typename SGraph::template EdgeMap<Cost> SCostMap;
deba@2440:     typedef typename SGraph::template NodeMap<Supply> SSupplyMap;
deba@2440:     typedef typename SGraph::template NodeMap<Cost> SPotentialMap;
deba@2440: 
deba@2440:     typedef typename SGraph::template NodeMap<int> IntNodeMap;
deba@2440:     typedef typename SGraph::template NodeMap<bool> BoolNodeMap;
deba@2440:     typedef typename SGraph::template NodeMap<Node> NodeNodeMap;
deba@2440:     typedef typename SGraph::template NodeMap<Edge> EdgeNodeMap;
deba@2440:     typedef typename SGraph::template EdgeMap<int> IntEdgeMap;
deba@2440: 
deba@2440:     typedef typename Graph::template NodeMap<Node> NodeRefMap;
deba@2440:     typedef typename Graph::template EdgeMap<Edge> EdgeRefMap;
deba@2440: 
deba@2440:   public:
deba@2440: 
deba@2440:     /// \brief The type of the flow map.
deba@2440:     typedef typename Graph::template EdgeMap<Capacity> FlowMap;
deba@2440:     /// \brief The type of the potential map.
deba@2440:     typedef typename Graph::template NodeMap<Cost> PotentialMap;
deba@2440: 
deba@2440:   protected:
deba@2440: 
deba@2440:     /// \brief Map adaptor class for handling reduced edge costs.
deba@2440:     class ReducedCostMap : public MapBase<Edge, Cost>
deba@2440:     {
deba@2440:     private:
deba@2440: 
deba@2440:       const SGraph &gr;
deba@2440:       const SCostMap &cost_map;
deba@2440:       const SPotentialMap &pot_map;
deba@2440: 
deba@2440:     public:
deba@2440: 
deba@2440:       typedef typename MapBase<Edge, Cost>::Value Value;
deba@2440:       typedef typename MapBase<Edge, Cost>::Key Key;
deba@2440: 
deba@2440:       ReducedCostMap( const SGraph &_gr,
deba@2440: 		      const SCostMap &_cm,
deba@2440: 		      const SPotentialMap &_pm ) :
deba@2440: 	gr(_gr), cost_map(_cm), pot_map(_pm) {}
deba@2440: 
deba@2440:       Value operator[](const Key &e) const {
deba@2440: 	return cost_map[e] - pot_map[gr.source(e)] + pot_map[gr.target(e)];
deba@2440:       }
deba@2440: 
deba@2440:     }; //class ReducedCostMap
deba@2440: 
deba@2440:   protected:
deba@2440: 
deba@2440:     /// \brief The directed graph the algorithm runs on.
deba@2440:     SGraph graph;
deba@2440:     /// \brief The original graph.
deba@2440:     const Graph &graph_ref;
deba@2440:     /// \brief The original lower bound map.
deba@2440:     const LowerMap *lower;
deba@2440:     /// \brief The capacity map.
deba@2440:     SCapacityMap capacity;
deba@2440:     /// \brief The cost map.
deba@2440:     SCostMap cost;
deba@2440:     /// \brief The supply map.
deba@2440:     SSupplyMap supply;
deba@2440:     /// \brief The reduced cost map.
deba@2440:     ReducedCostMap red_cost;
deba@2440:     /// \brief The sum of supply values equals zero.
deba@2440:     bool valid_supply;
deba@2440: 
deba@2440:     /// \brief The edge map of the current flow.
deba@2440:     SCapacityMap flow;
deba@2440:     /// \brief The edge map of the found flow on the original graph.
deba@2440:     FlowMap flow_result;
deba@2440:     /// \brief The potential node map.
deba@2440:     SPotentialMap potential;
deba@2440:     /// \brief The potential node map on the original graph.
deba@2440:     PotentialMap potential_result;
deba@2440: 
deba@2440:     /// \brief Node reference for the original graph.
deba@2440:     NodeRefMap node_ref;
deba@2440:     /// \brief Edge reference for the original graph.
deba@2440:     EdgeRefMap edge_ref;
deba@2440: 
deba@2440:     /// \brief The depth node map of the spanning tree structure.
deba@2440:     IntNodeMap depth;
deba@2440:     /// \brief The parent node map of the spanning tree structure.
deba@2440:     NodeNodeMap parent;
deba@2440:     /// \brief The pred_edge node map of the spanning tree structure.
deba@2440:     EdgeNodeMap pred_edge;
deba@2440:     /// \brief The thread node map of the spanning tree structure.
deba@2440:     NodeNodeMap thread;
deba@2440:     /// \brief The forward node map of the spanning tree structure.
deba@2440:     BoolNodeMap forward;
deba@2440:     /// \brief The state edge map.
deba@2440:     IntEdgeMap state;
deba@2440: 
deba@2440: 
deba@2440: #ifdef EDGE_BLOCK_PIVOT
deba@2440:     /// \brief The size of blocks for the "Edge Block" pivot rule.
deba@2440:     int block_size;
deba@2440: #endif
deba@2440: #ifdef CANDIDATE_LIST_PIVOT
deba@2440:     /// \brief The list of candidate edges for the "Candidate List"
deba@2440:     /// pivot rule.
deba@2440:     std::list<Edge> candidates;
deba@2440:     /// \brief The number of minor iterations.
deba@2440:     int minor_count;
deba@2440: #endif
deba@2440: #ifdef SORTED_LIST_PIVOT
deba@2440:     /// \brief The list of candidate edges for the "Sorted List"
deba@2440:     /// pivot rule.
deba@2440:     std::deque<Edge> candidates;
deba@2440: #endif
deba@2440: 
deba@2440:     // Root node of the starting spanning tree.
deba@2440:     Node root;
deba@2440:     // The entering edge of the current pivot iteration.
deba@2440:     Edge in_edge;
deba@2440:     // Temporary nodes used in the current pivot iteration.
deba@2440:     Node join, u_in, v_in, u_out, v_out;
deba@2440:     Node right, first, second, last;
deba@2440:     Node stem, par_stem, new_stem;
deba@2440:     // The maximum augment amount along the cycle in the current pivot
deba@2440:     // iteration.
deba@2440:     Capacity delta;
deba@2440: 
deba@2440:   public :
deba@2440: 
deba@2440:     /// \brief General constructor of the class (with lower bounds).
deba@2440:     ///
deba@2440:     /// General constructor of the class (with lower bounds).
deba@2440:     ///
deba@2440:     /// \param _graph The directed graph the algorithm runs on.
deba@2440:     /// \param _lower The lower bounds of the edges.
deba@2440:     /// \param _capacity The capacities (upper bounds) of the edges.
deba@2440:     /// \param _cost The cost (length) values of the edges.
deba@2440:     /// \param _supply The supply values of the nodes (signed).
deba@2440:     NetworkSimplex( const Graph &_graph,
deba@2440: 		    const LowerMap &_lower,
deba@2440: 		    const CapacityMap &_capacity,
deba@2440: 		    const CostMap &_cost,
deba@2440: 		    const SupplyMap &_supply ) :
deba@2440:       graph_ref(_graph), lower(&_lower), capacity(graph), cost(graph),
deba@2440:       supply(graph), flow(graph), flow_result(_graph), potential(graph),
deba@2440:       potential_result(_graph), depth(graph), parent(graph),
deba@2440:       pred_edge(graph), thread(graph), forward(graph), state(graph),
deba@2440:       node_ref(graph_ref), edge_ref(graph_ref),
deba@2440:       red_cost(graph, cost, potential)
deba@2440:     {
deba@2440:       // Checking the sum of supply values
deba@2440:       Supply sum = 0;
deba@2440:       for (typename Graph::NodeIt n(graph_ref); n != INVALID; ++n)
deba@2440: 	sum += _supply[n];
deba@2440:       if (!(valid_supply = sum == 0)) return;
deba@2440: 
deba@2440:       // Copying graph_ref to graph
deba@2457:       graph.reserveNode(countNodes(graph_ref) + 1);
deba@2457:       graph.reserveEdge(countEdges(graph_ref) + countNodes(graph_ref));
deba@2440:       copyGraph(graph, graph_ref)
deba@2440: 	.edgeMap(cost, _cost)
deba@2440: 	.nodeRef(node_ref)
deba@2440: 	.edgeRef(edge_ref)
deba@2440: 	.run();
deba@2440: 
deba@2440:       // Removing nonzero lower bounds
deba@2440:       for (typename Graph::EdgeIt e(graph_ref); e != INVALID; ++e) {
deba@2440: 	capacity[edge_ref[e]] = _capacity[e] - _lower[e];
deba@2440:       }
deba@2440:       for (typename Graph::NodeIt n(graph_ref); n != INVALID; ++n) {
deba@2440: 	Supply s = _supply[n];
deba@2440: 	for (typename Graph::InEdgeIt e(graph_ref, n); e != INVALID; ++e)
deba@2440: 	  s += _lower[e];
deba@2440: 	for (typename Graph::OutEdgeIt e(graph_ref, n); e != INVALID; ++e)
deba@2440: 	  s -= _lower[e];
deba@2440: 	supply[node_ref[n]] = s;
deba@2440:       }
deba@2440:     }
deba@2440: 
deba@2440:     /// \brief General constructor of the class (without lower bounds).
deba@2440:     ///
deba@2440:     /// General constructor of the class (without lower bounds).
deba@2440:     ///
deba@2440:     /// \param _graph The directed graph the algorithm runs on.
deba@2440:     /// \param _capacity The capacities (upper bounds) of the edges.
deba@2440:     /// \param _cost The cost (length) values of the edges.
deba@2440:     /// \param _supply The supply values of the nodes (signed).
deba@2440:     NetworkSimplex( const Graph &_graph,
deba@2440: 		    const CapacityMap &_capacity,
deba@2440: 		    const CostMap &_cost,
deba@2440: 		    const SupplyMap &_supply ) :
deba@2440:       graph_ref(_graph), lower(NULL), capacity(graph), cost(graph),
deba@2440:       supply(graph), flow(graph), flow_result(_graph), potential(graph),
deba@2440:       potential_result(_graph), depth(graph), parent(graph),
deba@2440:       pred_edge(graph), thread(graph), forward(graph), state(graph),
deba@2440:       node_ref(graph_ref), edge_ref(graph_ref),
deba@2440:       red_cost(graph, cost, potential)
deba@2440:     {
deba@2440:       // Checking the sum of supply values
deba@2440:       Supply sum = 0;
deba@2440:       for (typename Graph::NodeIt n(graph_ref); n != INVALID; ++n)
deba@2440: 	sum += _supply[n];
deba@2440:       if (!(valid_supply = sum == 0)) return;
deba@2440: 
deba@2440:       // Copying graph_ref to graph
deba@2440:       copyGraph(graph, graph_ref)
deba@2440: 	.edgeMap(capacity, _capacity)
deba@2440: 	.edgeMap(cost, _cost)
deba@2440: 	.nodeMap(supply, _supply)
deba@2440: 	.nodeRef(node_ref)
deba@2440: 	.edgeRef(edge_ref)
deba@2440: 	.run();
deba@2440:     }
deba@2440: 
deba@2440:     /// \brief Simple constructor of the class (with lower bounds).
deba@2440:     ///
deba@2440:     /// Simple constructor of the class (with lower bounds).
deba@2440:     ///
deba@2440:     /// \param _graph The directed graph the algorithm runs on.
deba@2440:     /// \param _lower The lower bounds of the edges.
deba@2440:     /// \param _capacity The capacities (upper bounds) of the edges.
deba@2440:     /// \param _cost The cost (length) values of the edges.
deba@2440:     /// \param _s The source node.
deba@2440:     /// \param _t The target node.
deba@2440:     /// \param _flow_value The required amount of flow from node \c _s
deba@2440:     /// to node \c _t (i.e. the supply of \c _s and the demand of
deba@2440:     /// \c _t).
deba@2440:     NetworkSimplex( const Graph &_graph,
deba@2440: 		    const LowerMap &_lower,
deba@2440: 		    const CapacityMap &_capacity,
deba@2440: 		    const CostMap &_cost,
deba@2440: 		    typename Graph::Node _s,
deba@2440: 		    typename Graph::Node _t,
deba@2440: 		    typename SupplyMap::Value _flow_value ) :
deba@2440:       graph_ref(_graph), lower(&_lower), capacity(graph), cost(graph),
deba@2440:       supply(graph), flow(graph), flow_result(_graph), potential(graph),
deba@2440:       potential_result(_graph), depth(graph), parent(graph),
deba@2440:       pred_edge(graph), thread(graph), forward(graph), state(graph),
deba@2440:       node_ref(graph_ref), edge_ref(graph_ref),
deba@2440:       red_cost(graph, cost, potential)
deba@2440:     {
deba@2440:       // Copying graph_ref to graph
deba@2440:       copyGraph(graph, graph_ref)
deba@2440: 	.edgeMap(cost, _cost)
deba@2440: 	.nodeRef(node_ref)
deba@2440: 	.edgeRef(edge_ref)
deba@2440: 	.run();
deba@2440: 
deba@2440:       // Removing nonzero lower bounds
deba@2440:       for (typename Graph::EdgeIt e(graph_ref); e != INVALID; ++e) {
deba@2440: 	capacity[edge_ref[e]] = _capacity[e] - _lower[e];
deba@2440:       }
deba@2440:       for (typename Graph::NodeIt n(graph_ref); n != INVALID; ++n) {
deba@2440: 	Supply s = 0;
deba@2440: 	if (n == _s) s =  _flow_value;
deba@2440: 	if (n == _t) s = -_flow_value;
deba@2440: 	for (typename Graph::InEdgeIt e(graph_ref, n); e != INVALID; ++e)
deba@2440: 	  s += _lower[e];
deba@2440: 	for (typename Graph::OutEdgeIt e(graph_ref, n); e != INVALID; ++e)
deba@2440: 	  s -= _lower[e];
deba@2440: 	supply[node_ref[n]] = s;
deba@2440:       }
deba@2440:       valid_supply = true;
deba@2440:     }
deba@2440: 
deba@2440:     /// \brief Simple constructor of the class (without lower bounds).
deba@2440:     ///
deba@2440:     /// Simple constructor of the class (without lower bounds).
deba@2440:     ///
deba@2440:     /// \param _graph The directed graph the algorithm runs on.
deba@2440:     /// \param _capacity The capacities (upper bounds) of the edges.
deba@2440:     /// \param _cost The cost (length) values of the edges.
deba@2440:     /// \param _s The source node.
deba@2440:     /// \param _t The target node.
deba@2440:     /// \param _flow_value The required amount of flow from node \c _s
deba@2440:     /// to node \c _t (i.e. the supply of \c _s and the demand of
deba@2440:     /// \c _t).
deba@2440:     NetworkSimplex( const Graph &_graph,
deba@2440: 		    const CapacityMap &_capacity,
deba@2440: 		    const CostMap &_cost,
deba@2440: 		    typename Graph::Node _s,
deba@2440: 		    typename Graph::Node _t,
deba@2440: 		    typename SupplyMap::Value _flow_value ) :
deba@2440:       graph_ref(_graph), lower(NULL), capacity(graph), cost(graph),
deba@2440:       supply(graph, 0), flow(graph), flow_result(_graph), potential(graph),
deba@2440:       potential_result(_graph), depth(graph), parent(graph),
deba@2440:       pred_edge(graph), thread(graph), forward(graph), state(graph),
deba@2440:       node_ref(graph_ref), edge_ref(graph_ref),
deba@2440:       red_cost(graph, cost, potential)
deba@2440:     {
deba@2440:       // Copying graph_ref to graph
deba@2440:       copyGraph(graph, graph_ref)
deba@2440: 	.edgeMap(capacity, _capacity)
deba@2440: 	.edgeMap(cost, _cost)
deba@2440: 	.nodeRef(node_ref)
deba@2440: 	.edgeRef(edge_ref)
deba@2440: 	.run();
deba@2440:       supply[node_ref[_s]] =  _flow_value;
deba@2440:       supply[node_ref[_t]] = -_flow_value;
deba@2440:       valid_supply = true;
deba@2440:     }
deba@2440: 
deba@2440:     /// \brief Returns a const reference to the flow map.
deba@2440:     ///
deba@2440:     /// Returns a const reference to the flow map.
deba@2440:     ///
deba@2440:     /// \pre \ref run() must be called before using this function.
deba@2440:     const FlowMap& flowMap() const {
deba@2440:       return flow_result;
deba@2440:     }
deba@2440: 
deba@2440:     /// \brief Returns a const reference to the potential map (the dual
deba@2440:     /// solution).
deba@2440:     ///
deba@2440:     /// Returns a const reference to the potential map (the dual
deba@2440:     /// solution).
deba@2440:     ///
deba@2440:     /// \pre \ref run() must be called before using this function.
deba@2440:     const PotentialMap& potentialMap() const {
deba@2440:       return potential_result;
deba@2440:     }
deba@2440: 
deba@2440:     /// \brief Returns the total cost of the found flow.
deba@2440:     ///
deba@2440:     /// Returns the total cost of the found flow. The complexity of the
deba@2440:     /// function is \f$ O(e) \f$.
deba@2440:     ///
deba@2440:     /// \pre \ref run() must be called before using this function.
deba@2440:     Cost totalCost() const {
deba@2440:       Cost c = 0;
deba@2440:       for (typename Graph::EdgeIt e(graph_ref); e != INVALID; ++e)
deba@2440: 	c += flow_result[e] * cost[edge_ref[e]];
deba@2440:       return c;
deba@2440:     }
deba@2440: 
deba@2440:     /// \brief Runs the algorithm.
deba@2440:     ///
deba@2440:     /// Runs the algorithm.
deba@2440:     ///
deba@2440:     /// \return \c true if a feasible flow can be found.
deba@2440:     bool run() {
deba@2440:       return init() && start();
deba@2440:     }
deba@2440: 
deba@2440:   protected:
deba@2440: 
deba@2440:     /// \brief Extends the underlaying graph and initializes all the
deba@2440:     /// node and edge maps.
deba@2440:     bool init() {
deba@2440:       if (!valid_supply) return false;
deba@2440: 
deba@2440:       // Initializing state and flow maps
deba@2440:       for (EdgeIt e(graph); e != INVALID; ++e) {
deba@2440: 	flow[e] = 0;
deba@2440: 	state[e] = LOWER;
deba@2440:       }
deba@2440: 
deba@2440:       // Adding an artificial root node to the graph
deba@2440:       root = graph.addNode();
deba@2440:       parent[root] = INVALID;
deba@2440:       pred_edge[root] = INVALID;
deba@2457:       depth[root] = 0;
deba@2457:       supply[root] = 0;
deba@2457:       potential[root] = 0;
deba@2440: 
deba@2440:       // Adding artificial edges to the graph and initializing the node
deba@2440:       // maps of the spanning tree data structure
deba@2440:       Supply sum = 0;
deba@2440:       Node last = root;
deba@2440:       Edge e;
deba@2440:       Cost max_cost = std::numeric_limits<Cost>::max() / 4;
deba@2440:       for (NodeIt u(graph); u != INVALID; ++u) {
deba@2440: 	if (u == root) continue;
deba@2440: 	thread[last] = u;
deba@2440: 	last = u;
deba@2440: 	parent[u] = root;
deba@2440: 	depth[u] = 1;
deba@2440: 	sum += supply[u];
deba@2440: 	if (supply[u] >= 0) {
deba@2440: 	  e = graph.addEdge(u, root);
deba@2440: 	  flow[e] = supply[u];
deba@2440: 	  forward[u] = true;
deba@2440: 	  potential[u] = max_cost;
deba@2440: 	} else {
deba@2440: 	  e = graph.addEdge(root, u);
deba@2440: 	  flow[e] = -supply[u];
deba@2440: 	  forward[u] = false;
deba@2440: 	  potential[u] = -max_cost;
deba@2440: 	}
deba@2440: 	cost[e] = max_cost;
deba@2440: 	capacity[e] = std::numeric_limits<Capacity>::max();
deba@2440: 	state[e] = TREE;
deba@2440: 	pred_edge[u] = e;
deba@2440:       }
deba@2440:       thread[last] = root;
deba@2440: 
deba@2440: #ifdef EDGE_BLOCK_PIVOT
deba@2440:       // Initializing block_size for the edge block pivot rule
deba@2440:       int edge_num = countEdges(graph);
deba@2457:       block_size = edge_num >= BLOCK_NUM * MIN_BLOCK_SIZE ?
deba@2444: 		   edge_num / BLOCK_NUM : MIN_BLOCK_SIZE;
deba@2440: #endif
deba@2440: #ifdef CANDIDATE_LIST_PIVOT
deba@2440:       minor_count = 0;
deba@2440: #endif
deba@2440: 
deba@2440:       return sum == 0;
deba@2440:     }
deba@2440: 
deba@2440: #ifdef FIRST_ELIGIBLE_PIVOT
deba@2440:     /// \brief Finds entering edge according to the "First Eligible"
deba@2440:     /// pivot rule.
deba@2440:     bool findEnteringEdge(EdgeIt &next_edge) {
deba@2440:       for (EdgeIt e = next_edge; e != INVALID; ++e) {
deba@2440: 	if (state[e] * red_cost[e] < 0) {
deba@2440: 	  in_edge = e;
deba@2440: 	  next_edge = ++e;
deba@2440: 	  return true;
deba@2440: 	}
deba@2440:       }
deba@2440:       for (EdgeIt e(graph); e != next_edge; ++e) {
deba@2440: 	if (state[e] * red_cost[e] < 0) {
deba@2440: 	  in_edge = e;
deba@2440: 	  next_edge = ++e;
deba@2440: 	  return true;
deba@2440: 	}
deba@2440:       }
deba@2440:       return false;
deba@2440:     }
deba@2440: #endif
deba@2440: 
deba@2440: #ifdef BEST_ELIGIBLE_PIVOT
deba@2440:     /// \brief Finds entering edge according to the "Best Eligible"
deba@2440:     /// pivot rule.
deba@2440:     bool findEnteringEdge() {
deba@2440:       Cost min = 0;
deba@2440:       for (EdgeIt e(graph); e != INVALID; ++e) {
deba@2440: 	if (state[e] * red_cost[e] < min) {
deba@2440: 	  min = state[e] * red_cost[e];
deba@2440: 	  in_edge = e;
deba@2440: 	}
deba@2440:       }
deba@2440:       return min < 0;
deba@2440:     }
deba@2440: #endif
deba@2440: 
deba@2440: #ifdef EDGE_BLOCK_PIVOT
deba@2440:     /// \brief Finds entering edge according to the "Edge Block"
deba@2440:     /// pivot rule.
deba@2440:     bool findEnteringEdge(EdgeIt &next_edge) {
deba@2444:       // Performing edge block selection
deba@2444:       Cost curr, min = 0;
deba@2444:       EdgeIt min_edge(graph);
deba@2444:       int cnt = 0;
deba@2444:       for (EdgeIt e = next_edge; e != INVALID; ++e) {
deba@2444: 	if ((curr = state[e] * red_cost[e]) < min) {
deba@2444: 	  min = curr;
deba@2444: 	  min_edge = e;
deba@2440: 	}
deba@2444: 	if (++cnt == block_size) {
deba@2444: 	  if (min < 0) break;
deba@2444: 	  cnt = 0;
deba@2444: 	}
deba@2444:       }
deba@2444:       if (!(min < 0)) {
deba@2440: 	for (EdgeIt e(graph); e != next_edge; ++e) {
deba@2440: 	  if ((curr = state[e] * red_cost[e]) < min) {
deba@2440: 	    min = curr;
deba@2440: 	    min_edge = e;
deba@2440: 	  }
deba@2440: 	  if (++cnt == block_size) {
deba@2440: 	    if (min < 0) break;
deba@2440: 	    cnt = 0;
deba@2440: 	  }
deba@2440: 	}
deba@2440:       }
deba@2444:       in_edge = min_edge;
deba@2444:       if ((next_edge = ++min_edge) == INVALID)
deba@2444: 	next_edge = EdgeIt(graph);
deba@2444:       return min < 0;
deba@2440:     }
deba@2440: #endif
deba@2440: 
deba@2440: #ifdef CANDIDATE_LIST_PIVOT
deba@2440:     /// \brief Functor class for removing non-eligible edges from the
deba@2440:     /// candidate list.
deba@2440:     class RemoveFunc
deba@2440:     {
deba@2440:     private:
deba@2440:       const IntEdgeMap &st;
deba@2440:       const ReducedCostMap &rc;
deba@2440:     public:
deba@2440:       RemoveFunc(const IntEdgeMap &_st, const ReducedCostMap &_rc) :
deba@2440: 	st(_st), rc(_rc) {}
deba@2440:       bool operator()(const Edge &e) {
deba@2440: 	return st[e] * rc[e] >= 0;
deba@2440:       }
deba@2440:     };
deba@2440: 
deba@2440:     /// \brief Finds entering edge according to the "Candidate List"
deba@2440:     /// pivot rule.
deba@2440:     bool findEnteringEdge() {
deba@2440:       static RemoveFunc remove_func(state, red_cost);
deba@2440:       typedef typename std::list<Edge>::iterator ListIt;
deba@2440: 
deba@2440:       candidates.remove_if(remove_func);
deba@2440:       if (minor_count >= MINOR_LIMIT || candidates.size() == 0) {
deba@2440: 	// Major iteration
deba@2440: 	for (EdgeIt e(graph); e != INVALID; ++e) {
deba@2440: 	  if (state[e] * red_cost[e] < 0) {
deba@2440: 	    candidates.push_back(e);
deba@2440: 	    if (candidates.size() == LIST_LENGTH) break;
deba@2440: 	  }
deba@2440: 	}
deba@2440: 	if (candidates.size() == 0) return false;
deba@2440:       }
deba@2440: 
deba@2440:       // Minor iteration
deba@2440:       ++minor_count;
deba@2440:       Cost min = 0;
deba@2440:       for (ListIt it = candidates.begin(); it != candidates.end(); ++it) {
deba@2440: 	if (state[*it] * red_cost[*it] < min) {
deba@2440: 	  min = state[*it] * red_cost[*it];
deba@2440: 	  in_edge = *it;
deba@2440: 	}
deba@2440:       }
deba@2440:       return true;
deba@2440:     }
deba@2440: #endif
deba@2440: 
deba@2440: #ifdef SORTED_LIST_PIVOT
deba@2440:     /// \brief Functor class to compare edges during sort of the
deba@2440:     /// candidate list.
deba@2440:     class SortFunc
deba@2440:     {
deba@2440:     private:
deba@2440:       const IntEdgeMap &st;
deba@2440:       const ReducedCostMap &rc;
deba@2440:     public:
deba@2440:       SortFunc(const IntEdgeMap &_st, const ReducedCostMap &_rc) :
deba@2440: 	st(_st), rc(_rc) {}
deba@2440:       bool operator()(const Edge &e1, const Edge &e2) {
deba@2440: 	return st[e1] * rc[e1] < st[e2] * rc[e2];
deba@2440:       }
deba@2440:     };
deba@2440: 
deba@2440:     /// \brief Finds entering edge according to the "Sorted List"
deba@2440:     /// pivot rule.
deba@2440:     bool findEnteringEdge() {
deba@2440:       static SortFunc sort_func(state, red_cost);
deba@2440: 
deba@2440:       // Minor iteration
deba@2440:       while (candidates.size() > 0) {
deba@2440: 	in_edge = candidates.front();
deba@2440: 	candidates.pop_front();
deba@2440: 	if (state[in_edge] * red_cost[in_edge] < 0) return true;
deba@2440:       }
deba@2440: 
deba@2440:       // Major iteration
deba@2440:       Cost curr, min = 0;
deba@2440:       for (EdgeIt e(graph); e != INVALID; ++e) {
deba@2440: 	if ((curr = state[e] * red_cost[e]) < min / LOWER_DIV) {
deba@2440: 	  candidates.push_back(e);
deba@2440: 	  if (curr < min) min = curr;
deba@2444: 	  if (candidates.size() == LIST_LENGTH) break;
deba@2440: 	}
deba@2440:       }
deba@2440:       if (candidates.size() == 0) return false;
deba@2440:       sort(candidates.begin(), candidates.end(), sort_func);
deba@2444:       in_edge = candidates.front();
deba@2444:       candidates.pop_front();
deba@2440:       return true;
deba@2440:     }
deba@2440: #endif
deba@2440: 
deba@2440:     /// \brief Finds the join node.
deba@2440:     Node findJoinNode() {
deba@2440:       // Finding the join node
deba@2440:       Node u = graph.source(in_edge);
deba@2440:       Node v = graph.target(in_edge);
deba@2440:       while (u != v) {
deba@2440: 	if (depth[u] == depth[v]) {
deba@2440: 	  u = parent[u];
deba@2440: 	  v = parent[v];
deba@2440: 	}
deba@2440: 	else if (depth[u] > depth[v]) u = parent[u];
deba@2440: 	else v = parent[v];
deba@2440:       }
deba@2440:       return u;
deba@2440:     }
deba@2440: 
deba@2440:     /// \brief Finds the leaving edge of the cycle. Returns \c true if
deba@2440:     /// the leaving edge is not the same as the entering edge.
deba@2440:     bool findLeavingEdge() {
deba@2440:       // Initializing first and second nodes according to the direction
deba@2440:       // of the cycle
deba@2440:       if (state[in_edge] == LOWER) {
deba@2440: 	first = graph.source(in_edge);
deba@2440: 	second	= graph.target(in_edge);
deba@2440:       } else {
deba@2440: 	first = graph.target(in_edge);
deba@2440: 	second	= graph.source(in_edge);
deba@2440:       }
deba@2440:       delta = capacity[in_edge];
deba@2440:       bool result = false;
deba@2440:       Capacity d;
deba@2440:       Edge e;
deba@2440: 
deba@2440:       // Searching the cycle along the path form the first node to the
deba@2440:       // root node
deba@2440:       for (Node u = first; u != join; u = parent[u]) {
deba@2440: 	e = pred_edge[u];
deba@2440: 	d = forward[u] ? flow[e] : capacity[e] - flow[e];
deba@2440: 	if (d < delta) {
deba@2440: 	  delta = d;
deba@2440: 	  u_out = u;
deba@2440: 	  u_in = first;
deba@2440: 	  v_in = second;
deba@2440: 	  result = true;
deba@2440: 	}
deba@2440:       }
deba@2440:       // Searching the cycle along the path form the second node to the
deba@2440:       // root node
deba@2440:       for (Node u = second; u != join; u = parent[u]) {
deba@2440: 	e = pred_edge[u];
deba@2440: 	d = forward[u] ? capacity[e] - flow[e] : flow[e];
deba@2440: 	if (d <= delta) {
deba@2440: 	  delta = d;
deba@2440: 	  u_out = u;
deba@2440: 	  u_in = second;
deba@2440: 	  v_in = first;
deba@2440: 	  result = true;
deba@2440: 	}
deba@2440:       }
deba@2440:       return result;
deba@2440:     }
deba@2440: 
deba@2440:     /// \brief Changes flow and state edge maps.
deba@2440:     void changeFlows(bool change) {
deba@2440:       // Augmenting along the cycle
deba@2440:       if (delta > 0) {
deba@2440: 	Capacity val = state[in_edge] * delta;
deba@2440: 	flow[in_edge] += val;
deba@2440: 	for (Node u = graph.source(in_edge); u != join; u = parent[u]) {
deba@2440: 	  flow[pred_edge[u]] += forward[u] ? -val : val;
deba@2440: 	}
deba@2440: 	for (Node u = graph.target(in_edge); u != join; u = parent[u]) {
deba@2440: 	  flow[pred_edge[u]] += forward[u] ? val : -val;
deba@2440: 	}
deba@2440:       }
deba@2440:       // Updating the state of the entering and leaving edges
deba@2440:       if (change) {
deba@2440: 	state[in_edge] = TREE;
deba@2440: 	state[pred_edge[u_out]] =
deba@2440: 	  (flow[pred_edge[u_out]] == 0) ? LOWER : UPPER;
deba@2440:       } else {
deba@2440: 	state[in_edge] = -state[in_edge];
deba@2440:       }
deba@2440:     }
deba@2440: 
deba@2440:     /// \brief Updates thread and parent node maps.
deba@2440:     void updateThreadParent() {
deba@2440:       Node u;
deba@2440:       v_out = parent[u_out];
deba@2440: 
deba@2440:       // Handling the case when join and v_out coincide
deba@2440:       bool par_first = false;
deba@2440:       if (join == v_out) {
deba@2440: 	for (u = join; u != u_in && u != v_in; u = thread[u]) ;
deba@2440: 	if (u == v_in) {
deba@2440: 	  par_first = true;
deba@2440: 	  while (thread[u] != u_out) u = thread[u];
deba@2440: 	  first = u;
deba@2440: 	}
deba@2440:       }
deba@2440: 
deba@2440:       // Finding the last successor of u_in (u) and the node after it
deba@2440:       // (right) according to the thread index
deba@2440:       for (u = u_in; depth[thread[u]] > depth[u_in]; u = thread[u]) ;
deba@2440:       right = thread[u];
deba@2440:       if (thread[v_in] == u_out) {
deba@2440: 	for (last = u; depth[last] > depth[u_out]; last = thread[last]) ;
deba@2440: 	if (last == u_out) last = thread[last];
deba@2440:       }
deba@2440:       else last = thread[v_in];
deba@2440: 
deba@2440:       // Updating stem nodes
deba@2440:       thread[v_in] = stem = u_in;
deba@2440:       par_stem = v_in;
deba@2440:       while (stem != u_out) {
deba@2440: 	thread[u] = new_stem = parent[stem];
deba@2440: 
deba@2440: 	// Finding the node just before the stem node (u) according to
deba@2440: 	// the original thread index
deba@2440: 	for (u = new_stem; thread[u] != stem; u = thread[u]) ;
deba@2440: 	thread[u] = right;
deba@2440: 
deba@2440: 	// Changing the parent node of stem and shifting stem and
deba@2440: 	// par_stem nodes
deba@2440: 	parent[stem] = par_stem;
deba@2440: 	par_stem = stem;
deba@2440: 	stem = new_stem;
deba@2440: 
deba@2440: 	// Finding the last successor of stem (u) and the node after it
deba@2440: 	// (right) according to the thread index
deba@2440: 	for (u = stem; depth[thread[u]] > depth[stem]; u = thread[u]) ;
deba@2440: 	right = thread[u];
deba@2440:       }
deba@2440:       parent[u_out] = par_stem;
deba@2440:       thread[u] = last;
deba@2440: 
deba@2440:       if (join == v_out && par_first) {
deba@2440: 	if (first != v_in) thread[first] = right;
deba@2440:       } else {
deba@2440: 	for (u = v_out; thread[u] != u_out; u = thread[u]) ;
deba@2440: 	thread[u] = right;
deba@2440:       }
deba@2440:     }
deba@2440: 
deba@2440:     /// \brief Updates pred_edge and forward node maps.
deba@2440:     void updatePredEdge() {
deba@2440:       Node u = u_out, v;
deba@2440:       while (u != u_in) {
deba@2440: 	v = parent[u];
deba@2440: 	pred_edge[u] = pred_edge[v];
deba@2440: 	forward[u] = !forward[v];
deba@2440: 	u = v;
deba@2440:       }
deba@2440:       pred_edge[u_in] = in_edge;
deba@2440:       forward[u_in] = (u_in == graph.source(in_edge));
deba@2440:     }
deba@2440: 
deba@2440:     /// \brief Updates depth and potential node maps.
deba@2440:     void updateDepthPotential() {
deba@2440:       depth[u_in] = depth[v_in] + 1;
deba@2440:       potential[u_in] = forward[u_in] ?
deba@2440: 	potential[v_in] + cost[pred_edge[u_in]] :
deba@2440: 	potential[v_in] - cost[pred_edge[u_in]];
deba@2440: 
deba@2440:       Node u = thread[u_in], v;
deba@2440:       while (true) {
deba@2440: 	v = parent[u];
deba@2440: 	if (v == INVALID) break;
deba@2440: 	depth[u] = depth[v] + 1;
deba@2440: 	potential[u] = forward[u] ?
deba@2440: 	  potential[v] + cost[pred_edge[u]] :
deba@2440: 	  potential[v] - cost[pred_edge[u]];
deba@2440: 	if (depth[u] <= depth[v_in]) break;
deba@2440: 	u = thread[u];
deba@2440:       }
deba@2440:     }
deba@2440: 
deba@2440:     /// \brief Executes the algorithm.
deba@2440:     bool start() {
deba@2440:       // Processing pivots
deba@2440: #ifdef _DEBUG_ITER_
deba@2440:       int iter_num = 0;
deba@2440: #endif
deba@2440: #if defined(FIRST_ELIGIBLE_PIVOT) || defined(EDGE_BLOCK_PIVOT)
deba@2440:       EdgeIt next_edge(graph);
deba@2440:       while (findEnteringEdge(next_edge))
deba@2440: #else
deba@2440:       while (findEnteringEdge())
deba@2440: #endif
deba@2440:       {
deba@2440: 	join = findJoinNode();
deba@2440: 	bool change = findLeavingEdge();
deba@2440: 	changeFlows(change);
deba@2440: 	if (change) {
deba@2440: 	  updateThreadParent();
deba@2440: 	  updatePredEdge();
deba@2440: 	  updateDepthPotential();
deba@2440: 	}
deba@2440: #ifdef _DEBUG_ITER_
deba@2440: 	++iter_num;
deba@2440: #endif
deba@2440:       }
deba@2440: 
deba@2440: #ifdef _DEBUG_ITER_
deba@2440:       std::cout << "Network Simplex algorithm finished. " << iter_num
deba@2444: 		<< " pivot iterations performed." << std::endl;
deba@2440: #endif
deba@2440: 
deba@2440:       // Checking if the flow amount equals zero on all the
deba@2440:       // artificial edges
deba@2440:       for (InEdgeIt e(graph, root); e != INVALID; ++e)
deba@2440: 	if (flow[e] > 0) return false;
deba@2440:       for (OutEdgeIt e(graph, root); e != INVALID; ++e)
deba@2440: 	if (flow[e] > 0) return false;
deba@2440: 
deba@2440:       // Copying flow values to flow_result
deba@2440:       if (lower) {
deba@2440: 	for (typename Graph::EdgeIt e(graph_ref); e != INVALID; ++e)
deba@2440: 	  flow_result[e] = (*lower)[e] + flow[edge_ref[e]];
deba@2440:       } else {
deba@2440: 	for (typename Graph::EdgeIt e(graph_ref); e != INVALID; ++e)
deba@2440: 	  flow_result[e] = flow[edge_ref[e]];
deba@2440:       }
deba@2440:       // Copying potential values to potential_result
deba@2440:       for (typename Graph::NodeIt n(graph_ref); n != INVALID; ++n)
deba@2440: 	potential_result[n] = potential[node_ref[n]];
deba@2440: 
deba@2440:       return true;
deba@2440:     }
deba@2440: 
deba@2440:   }; //class NetworkSimplex
deba@2440: 
deba@2440:   ///@}
deba@2440: 
deba@2440: } //namespace lemon
deba@2440: 
deba@2440: #endif //LEMON_NETWORK_SIMPLEX_H