deba@2440: /* -*- C++ -*-
deba@2440:  *
deba@2440:  * This file is a part of LEMON, a generic C++ optimization library
deba@2440:  *
alpar@2553:  * Copyright (C) 2003-2008
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_CYCLE_CANCELING_H
deba@2440: #define LEMON_CYCLE_CANCELING_H
deba@2440: 
deba@2440: /// \ingroup min_cost_flow
deba@2440: ///
deba@2440: /// \file
deba@2457: /// \brief A cycle-canceling algorithm for finding a minimum cost flow.
deba@2440: 
deba@2440: #include <vector>
kpeter@2509: #include <lemon/graph_adaptor.h>
deba@2440: #include <lemon/circulation.h>
deba@2440: 
deba@2457: /// \brief The used cycle-canceling method.
deba@2440: #define LIMITED_CYCLE_CANCELING
deba@2440: //#define MIN_MEAN_CYCLE_CANCELING
deba@2440: 
deba@2440: #ifdef LIMITED_CYCLE_CANCELING
deba@2440:   #include <lemon/bellman_ford.h>
kpeter@2556:   // The maximum number of iterations for the first execution of the
kpeter@2556:   // Bellman-Ford algorithm. It should be at least 2.
kpeter@2556:   #define STARTING_LIMIT        2
kpeter@2556:   // The iteration limit for the Bellman-Ford algorithm is multiplied by
kpeter@2556:   // <tt>ALPHA_MUL / ALPHA_DIV</tt> in every round.
kpeter@2556:   // <tt>ALPHA_MUL / ALPHA_DIV</tt> must be greater than 1.
kpeter@2556:   #define ALPHA_MUL             3
kpeter@2556:   #define ALPHA_DIV             2
deba@2440: 
deba@2440: //#define _ONLY_ONE_CYCLE_
deba@2457: //#define _NO_BACK_STEP_
deba@2440: #endif
deba@2440: 
deba@2440: #ifdef MIN_MEAN_CYCLE_CANCELING
deba@2440:   #include <lemon/min_mean_cycle.h>
deba@2440:   #include <lemon/path.h>
deba@2440: #endif
deba@2440: 
kpeter@2556: //#define _DEBUG_ITER_
kpeter@2556: 
deba@2440: namespace lemon {
deba@2440: 
deba@2440:   /// \addtogroup min_cost_flow
deba@2440:   /// @{
deba@2440: 
kpeter@2556:   /// \brief Implementation of a cycle-canceling algorithm for
kpeter@2556:   /// finding a minimum cost flow.
deba@2440:   ///
kpeter@2556:   /// \ref CycleCanceling implements a cycle-canceling algorithm for
kpeter@2556:   /// 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
kpeter@2556:   /// - Edge capacities and costs should be non-negative integers.
kpeter@2556:   ///   However \c CostMap::Value should be signed type.
kpeter@2509:   /// - Supply values should be signed integers.
deba@2440:   /// - \c LowerMap::Value must be convertible to
kpeter@2556:   ///   \c CapacityMap::Value and \c CapacityMap::Value must be
kpeter@2556:   ///   convertible to \c SupplyMap::Value.
deba@2440:   ///
deba@2440:   /// \author Peter Kovacs
deba@2440: 
kpeter@2533:   template < typename Graph,
kpeter@2533:              typename LowerMap = typename Graph::template EdgeMap<int>,
kpeter@2533:              typename CapacityMap = LowerMap,
kpeter@2533:              typename CostMap = typename Graph::template EdgeMap<int>,
kpeter@2533:              typename SupplyMap = typename Graph::template NodeMap
kpeter@2533:                                   <typename CapacityMap::Value> >
deba@2440:   class CycleCanceling
deba@2440:   {
kpeter@2556:     GRAPH_TYPEDEFS(typename Graph);
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;
kpeter@2556:     typedef typename Graph::template EdgeMap<Capacity> CapacityEdgeMap;
kpeter@2556:     typedef typename Graph::template NodeMap<Supply> SupplyNodeMap;
deba@2440: 
deba@2440:     typedef ResGraphAdaptor< const Graph, Capacity,
kpeter@2556:                              CapacityEdgeMap, CapacityEdgeMap > ResGraph;
deba@2440:     typedef typename ResGraph::Node ResNode;
deba@2440:     typedef typename ResGraph::NodeIt ResNodeIt;
deba@2440:     typedef typename ResGraph::Edge ResEdge;
deba@2440:     typedef typename ResGraph::EdgeIt ResEdgeIt;
deba@2440: 
deba@2440:   public:
deba@2440: 
kpeter@2556:     /// The type of the flow map.
kpeter@2556:     typedef typename Graph::template EdgeMap<Capacity> FlowMap;
deba@2440: 
deba@2440:   protected:
deba@2440: 
kpeter@2556:     /// Map adaptor class for handling residual edge costs.
deba@2440:     class ResCostMap : public MapBase<ResEdge, Cost>
deba@2440:     {
deba@2440:     private:
deba@2440: 
deba@2440:       const CostMap &cost_map;
deba@2440: 
deba@2440:     public:
deba@2440: 
deba@2440:       ResCostMap(const CostMap &_cost) : cost_map(_cost) {}
deba@2440: 
kpeter@2509:       Cost operator[](const ResEdge &e) const {
kpeter@2556:         return ResGraph::forward(e) ? cost_map[e] : -cost_map[e];
deba@2440:       }
deba@2440: 
deba@2440:     }; //class ResCostMap
deba@2440: 
deba@2440:   protected:
deba@2440: 
kpeter@2556:     /// The directed graph the algorithm runs on.
deba@2440:     const Graph &graph;
kpeter@2556:     /// The original lower bound map.
deba@2440:     const LowerMap *lower;
kpeter@2556:     /// The modified capacity map.
kpeter@2556:     CapacityEdgeMap capacity;
kpeter@2556:     /// The cost map.
deba@2440:     const CostMap &cost;
kpeter@2556:     /// The modified supply map.
kpeter@2556:     SupplyNodeMap supply;
deba@2440:     bool valid_supply;
deba@2440: 
kpeter@2556:     /// The current flow.
deba@2440:     FlowMap flow;
kpeter@2556:     /// The residual graph.
deba@2440:     ResGraph res_graph;
kpeter@2556:     /// The residual cost map.
deba@2440:     ResCostMap res_cost;
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:     CycleCanceling( const Graph &_graph,
kpeter@2556:                     const LowerMap &_lower,
kpeter@2556:                     const CapacityMap &_capacity,
kpeter@2556:                     const CostMap &_cost,
kpeter@2556:                     const SupplyMap &_supply ) :
deba@2440:       graph(_graph), lower(&_lower), capacity(_graph), cost(_cost),
deba@2457:       supply(_graph), flow(_graph, 0),
deba@2440:       res_graph(_graph, capacity, flow), res_cost(cost)
deba@2440:     {
kpeter@2556:       // Removing non-zero lower bounds
deba@2440:       capacity = subMap(_capacity, _lower);
deba@2440:       Supply sum = 0;
deba@2440:       for (NodeIt n(graph); n != INVALID; ++n) {
kpeter@2556:         Supply s = _supply[n];
kpeter@2556:         for (InEdgeIt e(graph, n); e != INVALID; ++e)
kpeter@2556:           s += _lower[e];
kpeter@2556:         for (OutEdgeIt e(graph, n); e != INVALID; ++e)
kpeter@2556:           s -= _lower[e];
kpeter@2556:         sum += (supply[n] = s);
deba@2440:       }
deba@2440:       valid_supply = sum == 0;
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:     CycleCanceling( const Graph &_graph,
kpeter@2556:                     const CapacityMap &_capacity,
kpeter@2556:                     const CostMap &_cost,
kpeter@2556:                     const SupplyMap &_supply ) :
deba@2440:       graph(_graph), lower(NULL), capacity(_capacity), cost(_cost),
deba@2457:       supply(_supply), flow(_graph, 0),
deba@2440:       res_graph(_graph, capacity, flow), res_cost(cost)
deba@2440:     {
deba@2440:       // Checking the sum of supply values
deba@2440:       Supply sum = 0;
deba@2440:       for (NodeIt n(graph); n != INVALID; ++n) sum += supply[n];
deba@2440:       valid_supply = sum == 0;
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
kpeter@2556:     /// to node \c _t (i.e. the supply of \c _s and the demand of \c _t).
deba@2440:     CycleCanceling( const Graph &_graph,
kpeter@2556:                     const LowerMap &_lower,
kpeter@2556:                     const CapacityMap &_capacity,
kpeter@2556:                     const CostMap &_cost,
kpeter@2556:                     Node _s, Node _t,
kpeter@2556:                     Supply _flow_value ) :
deba@2440:       graph(_graph), lower(&_lower), capacity(_graph), cost(_cost),
deba@2457:       supply(_graph), flow(_graph, 0),
deba@2440:       res_graph(_graph, capacity, flow), res_cost(cost)
deba@2440:     {
kpeter@2556:       // Removing non-zero lower bounds
deba@2440:       capacity = subMap(_capacity, _lower);
deba@2440:       for (NodeIt n(graph); n != INVALID; ++n) {
kpeter@2556:         Supply s = 0;
kpeter@2556:         if (n == _s) s =  _flow_value;
kpeter@2556:         if (n == _t) s = -_flow_value;
kpeter@2556:         for (InEdgeIt e(graph, n); e != INVALID; ++e)
kpeter@2556:           s += _lower[e];
kpeter@2556:         for (OutEdgeIt e(graph, n); e != INVALID; ++e)
kpeter@2556:           s -= _lower[e];
kpeter@2556:         supply[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
kpeter@2556:     /// to node \c _t (i.e. the supply of \c _s and the demand of \c _t).
deba@2440:     CycleCanceling( const Graph &_graph,
kpeter@2556:                     const CapacityMap &_capacity,
kpeter@2556:                     const CostMap &_cost,
kpeter@2556:                     Node _s, Node _t,
kpeter@2556:                     Supply _flow_value ) :
deba@2440:       graph(_graph), lower(NULL), capacity(_capacity), cost(_cost),
deba@2457:       supply(_graph, 0), flow(_graph, 0),
deba@2440:       res_graph(_graph, capacity, flow), res_cost(cost)
deba@2440:     {
deba@2440:       supply[_s] =  _flow_value;
deba@2440:       supply[_t] = -_flow_value;
deba@2440:       valid_supply = true;
deba@2440:     }
deba@2440: 
kpeter@2556:     /// \brief Runs the algorithm.
kpeter@2556:     ///
kpeter@2556:     /// Runs the algorithm.
kpeter@2556:     ///
kpeter@2556:     /// \return \c true if a feasible flow can be found.
kpeter@2556:     bool run() {
kpeter@2556:       return init() && start();
kpeter@2556:     }
kpeter@2556: 
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;
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 (EdgeIt e(graph); e != INVALID; ++e)
kpeter@2556:         c += flow[e] * cost[e];
deba@2440:       return c;
deba@2440:     }
deba@2440: 
deba@2440:   protected:
deba@2440: 
kpeter@2556:     /// Initializes the algorithm.
deba@2440:     bool init() {
deba@2440:       // Checking the sum of supply values
deba@2440:       Supply sum = 0;
deba@2440:       for (NodeIt n(graph); n != INVALID; ++n) sum += supply[n];
deba@2440:       if (sum != 0) return false;
deba@2440: 
deba@2440:       // Finding a feasible flow
kpeter@2556:       Circulation< Graph, ConstMap<Edge, Capacity>, CapacityEdgeMap,
kpeter@2556:                    SupplyMap >
kpeter@2556:         circulation( graph, constMap<Edge>((Capacity)0), capacity,
kpeter@2556:                      supply );
kpeter@2533:       circulation.flowMap(flow);
kpeter@2544:       return circulation.run();
deba@2440:     }
deba@2440: 
deba@2440: #ifdef LIMITED_CYCLE_CANCELING
deba@2457:     /// \brief Executes a cycle-canceling algorithm using
kpeter@2556:     /// \ref Bellman-Ford algorithm with limited iteration count.
deba@2440:     bool start() {
deba@2440:       typename BellmanFord<ResGraph, ResCostMap>::PredMap pred(res_graph);
deba@2440:       typename ResGraph::template NodeMap<int> visited(res_graph);
deba@2440:       std::vector<ResEdge> cycle;
deba@2440:       int node_num = countNodes(graph);
deba@2440: 
deba@2440: #ifdef _DEBUG_ITER_
deba@2440:       int cycle_num = 0;
deba@2440: #endif
deba@2440:       int length_bound = STARTING_LIMIT;
deba@2440:       bool optimal = false;
deba@2440:       while (!optimal) {
kpeter@2556:         BellmanFord<ResGraph, ResCostMap> bf(res_graph, res_cost);
kpeter@2556:         bf.predMap(pred);
kpeter@2556:         bf.init(0);
kpeter@2556:         int iter_num = 0;
kpeter@2556:         bool cycle_found = false;
kpeter@2556:         while (!cycle_found) {
deba@2457: #ifdef _NO_BACK_STEP_
kpeter@2556:           int curr_iter_num = length_bound <= node_num ?
kpeter@2556:                               length_bound - iter_num : node_num - iter_num;
deba@2457: #else
kpeter@2556:           int curr_iter_num = iter_num + length_bound <= node_num ?
kpeter@2556:                               length_bound : node_num - iter_num;
deba@2457: #endif
kpeter@2556:           iter_num += curr_iter_num;
kpeter@2556:           int real_iter_num = curr_iter_num;
kpeter@2556:           for (int i = 0; i < curr_iter_num; ++i) {
kpeter@2556:             if (bf.processNextWeakRound()) {
kpeter@2556:               real_iter_num = i;
kpeter@2556:               break;
kpeter@2556:             }
kpeter@2556:           }
kpeter@2556:           if (real_iter_num < curr_iter_num) {
kpeter@2556:             optimal = true;
kpeter@2556:             break;
kpeter@2556:           } else {
kpeter@2556:             // Searching for node disjoint negative cycles
kpeter@2556:             for (ResNodeIt n(res_graph); n != INVALID; ++n)
kpeter@2556:               visited[n] = 0;
kpeter@2556:             int id = 0;
kpeter@2556:             for (ResNodeIt n(res_graph); n != INVALID; ++n) {
kpeter@2556:               if (visited[n] > 0) continue;
kpeter@2556:               visited[n] = ++id;
kpeter@2556:               ResNode u = pred[n] == INVALID ?
kpeter@2556:                           INVALID : res_graph.source(pred[n]);
kpeter@2556:               while (u != INVALID && visited[u] == 0) {
kpeter@2556:                 visited[u] = id;
kpeter@2556:                 u = pred[u] == INVALID ?
kpeter@2556:                     INVALID : res_graph.source(pred[u]);
kpeter@2556:               }
kpeter@2556:               if (u != INVALID && visited[u] == id) {
kpeter@2556:                 // Finding the negative cycle
kpeter@2556:                 cycle_found = true;
kpeter@2556:                 cycle.clear();
kpeter@2556:                 ResEdge e = pred[u];
kpeter@2556:                 cycle.push_back(e);
kpeter@2556:                 Capacity d = res_graph.rescap(e);
kpeter@2556:                 while (res_graph.source(e) != u) {
kpeter@2556:                   cycle.push_back(e = pred[res_graph.source(e)]);
kpeter@2556:                   if (res_graph.rescap(e) < d)
kpeter@2556:                     d = res_graph.rescap(e);
kpeter@2556:                 }
deba@2440: #ifdef _DEBUG_ITER_
kpeter@2556:                 ++cycle_num;
deba@2440: #endif
kpeter@2556:                 // Augmenting along the cycle
kpeter@2556:                 for (int i = 0; i < cycle.size(); ++i)
kpeter@2556:                   res_graph.augment(cycle[i], d);
deba@2440: #ifdef _ONLY_ONE_CYCLE_
kpeter@2556:                 break;
deba@2440: #endif
kpeter@2556:               }
kpeter@2556:             }
kpeter@2556:           }
deba@2440: 
kpeter@2556:           if (!cycle_found)
kpeter@2556:             length_bound = length_bound * ALPHA_MUL / ALPHA_DIV;
kpeter@2556:         }
deba@2440:       }
deba@2440: 
deba@2440: #ifdef _DEBUG_ITER_
deba@2457:       std::cout << "Limited cycle-canceling algorithm finished. "
kpeter@2556:                 << "Found " << cycle_num << " negative cycles."
kpeter@2556:                 << std::endl;
deba@2440: #endif
deba@2440: 
kpeter@2556:       // Handling non-zero lower bounds
deba@2440:       if (lower) {
kpeter@2556:         for (EdgeIt e(graph); e != INVALID; ++e)
kpeter@2556:           flow[e] += (*lower)[e];
deba@2440:       }
deba@2440:       return true;
deba@2440:     }
deba@2440: #endif
deba@2440: 
deba@2440: #ifdef MIN_MEAN_CYCLE_CANCELING
deba@2457:     /// \brief Executes the minimum mean cycle-canceling algorithm
kpeter@2556:     /// using \ref MinMeanCycle.
deba@2440:     bool start() {
deba@2440:       typedef Path<ResGraph> ResPath;
deba@2440:       MinMeanCycle<ResGraph, ResCostMap> mmc(res_graph, res_cost);
deba@2440:       ResPath cycle;
deba@2440: 
deba@2440: #ifdef _DEBUG_ITER_
deba@2440:       int cycle_num = 0;
deba@2440: #endif
deba@2440:       mmc.cyclePath(cycle).init();
deba@2440:       if (mmc.findMinMean()) {
kpeter@2556:         while (mmc.cycleLength() < 0) {
deba@2440: #ifdef _DEBUG_ITER_
kpeter@2556:           ++cycle_num;
deba@2440: #endif
kpeter@2556:           // Finding the cycle
kpeter@2556:           mmc.findCycle();
deba@2440: 
kpeter@2556:           // Finding the largest flow amount that can be augmented
kpeter@2556:           // along the cycle
kpeter@2556:           Capacity delta = 0;
kpeter@2556:           for (typename ResPath::EdgeIt e(cycle); e != INVALID; ++e) {
kpeter@2556:             if (delta == 0 || res_graph.rescap(e) < delta)
kpeter@2556:               delta = res_graph.rescap(e);
kpeter@2556:           }
deba@2440: 
kpeter@2556:           // Augmenting along the cycle
kpeter@2556:           for (typename ResPath::EdgeIt e(cycle); e != INVALID; ++e)
kpeter@2556:             res_graph.augment(e, delta);
deba@2440: 
kpeter@2556:           // Finding the minimum cycle mean for the modified residual
kpeter@2556:           // graph
kpeter@2556:           mmc.reset();
kpeter@2556:           if (!mmc.findMinMean()) break;
kpeter@2556:         }
deba@2440:       }
deba@2440: 
deba@2440: #ifdef _DEBUG_ITER_
deba@2457:       std::cout << "Minimum mean cycle-canceling algorithm finished. "
kpeter@2556:                 << "Found " << cycle_num << " negative cycles."
kpeter@2556:                 << std::endl;
deba@2440: #endif
deba@2440: 
kpeter@2556:       // Handling non-zero lower bounds
deba@2440:       if (lower) {
kpeter@2556:         for (EdgeIt e(graph); e != INVALID; ++e)
kpeter@2556:           flow[e] += (*lower)[e];
deba@2440:       }
deba@2440:       return true;
deba@2440:     }
deba@2440: #endif
deba@2440: 
deba@2440:   }; //class CycleCanceling
deba@2440: 
deba@2440:   ///@}
deba@2440: 
deba@2440: } //namespace lemon
deba@2440: 
deba@2440: #endif //LEMON_CYCLE_CANCELING_H