RhodeCode

/* -*- mode: C++; indent-tabs-mode: nil; -*-

 *

 * This file is a part of LEMON, a generic C++ optimization library.

 *

 * Copyright (C) 2003-2009

 * Egervary Jeno Kombinatorikus Optimalizalasi Kutatocsoport

 * (Egervary Research Group on Combinatorial Optimization, EGRES).

 *

 * Permission to use, modify and distribute this software is granted

 * provided that this copyright notice appears in all copies. For

 * precise terms see the accompanying LICENSE file.

 *

 * This software is provided "AS IS" with no warranty of any kind,

 * express or implied, and with no claim as to its suitability for any

 * purpose.

 *

 */

#ifndef LEMON_NETWORK_SIMPLEX_H

#define LEMON_NETWORK_SIMPLEX_H

/// \ingroup min_cost_flow

///

/// \file

/// \brief Network Simplex algorithm for finding a minimum cost flow.

#include <vector>

#include <limits>

#include <algorithm>

#include <lemon/core.h>

#include <lemon/math.h>

namespace lemon {

  /// \addtogroup min_cost_flow

  /// @{

  /// \brief Implementation of the primal Network Simplex algorithm

  /// for finding a \ref min_cost_flow "minimum cost flow".

  ///

  /// \ref NetworkSimplex implements the primal Network Simplex algorithm

  /// for finding a \ref min_cost_flow "minimum cost flow".

  ///

  /// \tparam GR The digraph type the algorithm runs on.

  /// \tparam V The value type used in the algorithm.

  /// By default it is \c int.

  ///

  ///

  /// \note %NetworkSimplex provides five different pivot rule

  /// implementations. For more information see \ref PivotRule.

  template <typename GR, typename V = int>

  class NetworkSimplex

  {

  public:

    /// The value type of the algorithm

    typedef V Value;

    /// The type of the flow map

    typedef typename GR::template ArcMap<Value> FlowMap;

    /// The type of the potential map

    typedef typename GR::template NodeMap<Value> PotentialMap;

  public:

    /// \brief Enum type for selecting the pivot rule.

    ///

    /// Enum type for selecting the pivot rule for the \ref run()

    /// function.

    ///

    /// \ref NetworkSimplex provides five different pivot rule

    /// implementations that significantly affect the running time

    /// of the algorithm.

    /// By default \ref BLOCK_SEARCH "Block Search" is used, which

    /// proved to be the most efficient and the most robust on various

    /// test inputs according to our benchmark tests.

    /// However another pivot rule can be selected using the \ref run()

    /// function with the proper parameter.

    enum PivotRule {

      /// The First Eligible pivot rule.

      /// The next eligible arc is selected in a wraparound fashion

      /// in every iteration.

      FIRST_ELIGIBLE,

      /// The Best Eligible pivot rule.

      /// The best eligible arc is selected in every iteration.

      BEST_ELIGIBLE,

      /// The Block 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 Candidate List pivot rule.

    /// automatically allocated map, of course.

    ///

    /// \return <tt>(*this)</tt>

    NetworkSimplex& flowMap(FlowMap& map) {

      if (_local_flow) {

        delete _flow_map;

        _local_flow = false;

      }

      _flow_map = ↦

      return *this;

    }

    /// \brief Set the potential map.

    ///

    /// This function sets the potential map, which is used for storing

    /// the dual solution.

    /// If it is not used before calling \ref run(), an instance will

    /// be allocated automatically. The destructor deallocates this

    /// automatically allocated map, of course.

    ///

    /// \return <tt>(*this)</tt>

    NetworkSimplex& potentialMap(PotentialMap& map) {

      if (_local_potential) {

        delete _potential_map;

        _local_potential = false;

      }

      _potential_map = ↦

      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 \ref lowerMap(),

    /// \ref upperMap(), \ref capacityMap(), \ref boundMaps(), 

    /// \ref costMap(), \ref supplyMap() and \ref stSupply()

    /// functions. For example,

    /// \code

    ///   NetworkSimplex<ListDigraph> ns(graph);

    ///   ns.boundMaps(lower, upper).costMap(cost)

    ///     .supplyMap(sup).run();

    /// \endcode

    ///

    /// \param pivot_rule The pivot rule that will be used during the

    /// algorithm. For more information see \ref PivotRule.

    ///

    /// \return \c true if a feasible flow can be found.

    bool run(PivotRule pivot_rule = BLOCK_SEARCH) {

      return init() && start(pivot_rule);

    }

    /// @}

    /// \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.

    /// The complexity of the function is \f$ O(e) \f$.

    ///

    /// \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 Value

    /// 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 Num>

    Num totalCost() const {

      Num c = 0;

      if (_pcost) {

        for (ArcIt e(_graph); e != INVALID; ++e)

          c += (*_flow_map)[e] * (*_pcost)[e];

      } else {

        for (ArcIt e(_graph); e != INVALID; ++e)

          c += (*_flow_map)[e];

      }

      return c;

    }

#ifndef DOXYGEN

    Value totalCost() const {

      return totalCost<Value>();

    }

#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.

    ///

    /// \pre \ref run() must be called before using this function.

    Value potential(const Node& n) const {

      return (*_potential_map)[n];

    }

    /// \brief Return a const reference to the potential map

    /// (the dual solution).

    ///

    /// This function returns a const reference to a node map storing

    /// the found potentials, which form the dual solution of the

    /// \ref min_cost_flow "minimum cost flow" problem.

    ///

    /// \pre \ref run() must be called before using this function.

    const PotentialMap& potentialMap() const {

      return *_potential_map;

    }

    /// @}

  private:

    // Initialize internal data structures

    bool init() {

      // Initialize result maps

      if (!_flow_map) {

        _flow_map = new FlowMap(_graph);

        _local_flow = true;

      }

      if (!_potential_map) {

        _potential_map = new PotentialMap(_graph);

        _local_potential = true;

      }

      // Initialize vectors

      _node_num = countNodes(_graph);

      _arc_num = countArcs(_graph);

      int all_node_num = _node_num + 1;

      int all_arc_num = _arc_num + _node_num;

      if (_node_num == 0) return false;

      _arc_ref.resize(_arc_num);

      _source.resize(all_arc_num);

      _target.resize(all_arc_num);

      _cap.resize(all_arc_num);

      _cost.resize(all_arc_num);

      _supply.resize(all_node_num);

      _parent.resize(all_node_num);

      _pred.resize(all_node_num);

      _forward.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);

      // Initialize node related data

      bool valid_supply = true;

      if (!_pstsup && !_psupply) {

        _pstsup = true;

        _psource = _ptarget = NodeIt(_graph);

        _pstflow = 0;

      }

      if (_psupply) {

        Value sum = 0;

        int i = 0;

        for (NodeIt n(_graph); n != INVALID; ++n, ++i) {

          _node_id[n] = i;

          _supply[i] = (*_psupply)[n];

          sum += _supply[i];

        }

        valid_supply = (sum == 0);

      } else {

        int i = 0;

        for (NodeIt n(_graph); n != INVALID; ++n, ++i) {

          _node_id[n] = i;

          _supply[i] = 0;

        }

        _supply[_node_id[_psource]] =  _pstflow;

        _supply[_node_id[_ptarget]]   = -_pstflow;

      }

      if (!valid_supply) return false;

      // 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] = all_node_num;

      _last_succ[_root] = _root - 1;

      _supply[_root] = 0;

      _pi[_root] = 0;

      // Store the arcs in a mixed order

      int k = std::max(int(sqrt(_arc_num)), 10);

      int i = 0;

      for (ArcIt e(_graph); e != INVALID; ++e) {

        _arc_ref[i] = e;

        if ((i += k) >= _arc_num) i = (i % k) + 1;

      }

      // Initialize arc maps

      if (_pupper && _pcost) {

        for (int i = 0; i != _arc_num; ++i) {

          Arc e = _arc_ref[i];

          _source[i] = _node_id[_graph.source(e)];

          _target[i] = _node_id[_graph.target(e)];

          _cap[i] = (*_pupper)[e];

          _cost[i] = (*_pcost)[e];

        }

      } else {

        for (int i = 0; i != _arc_num; ++i) {

          Arc e = _arc_ref[i];

          _source[i] = _node_id[_graph.source(e)];

          _target[i] = _node_id[_graph.target(e)];

        }

        if (_pupper) {

          for (int i = 0; i != _arc_num; ++i)

            _cap[i] = (*_pupper)[_arc_ref[i]];

        } else {

          Value val = std::numeric_limits<Value>::max();

          for (int i = 0; i != _arc_num; ++i)

            _cap[i] = val;

        }

        if (_pcost) {

          for (int i = 0; i != _arc_num; ++i)

            _cost[i] = (*_pcost)[_arc_ref[i]];

        } else {

          for (int i = 0; i != _arc_num; ++i)

            _cost[i] = 1;

        }

      }

      // Remove non-zero lower bounds

      if (_plower) {

        for (int i = 0; i != _arc_num; ++i) {

          Value c = (*_plower)[_arc_ref[i]];

          if (c != 0) {

            _cap[i] -= c;

            _supply[_source[i]] -= c;

            _supply[_target[i]] += c;

          }

        }

      }

      // Add artificial arcs and initialize the spanning tree data structure

      Value max_cap = std::numeric_limits<Value>::max();

      Value max_cost = std::numeric_limits<Value>::max() / 4;

      for (int u = 0, e = _arc_num; u != _node_num; ++u, ++e) {

        _thread[u] = u + 1;

        _rev_thread[u + 1] = u;

        _succ_num[u] = 1;

        _last_succ[u] = u;

        _parent[u] = _root;

        _pred[u] = e;

        if (_supply[u] >= 0) {

          _flow[e] = _supply[u];

          _forward[u] = true;

          _pi[u] = -max_cost;

        } else {

          _flow[e] = -_supply[u];

          _forward[u] = false;

          _pi[u] = max_cost;

        }

      }

      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

      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 d;

      int e;

      // Search the cycle along the path form the first node to the root

      for (int u = first; u != join; u = _parent[u]) {

        e = _pred[u];

        d = _forward[u] ? _flow[e] : _cap[e] - _flow[e];

        if (d < delta) {

          delta = d;

          u_out = u;

          result = 1;

        }

      }

      // Search the cycle along the path form the second node to the root

      for (int u = second; u != join; u = _parent[u]) {

  "    8     0    0    0\n"

  "    9     3    0    0\n"

  "   10    -2    0    0\n"

  "   11     0    0    0\n"

  "   12   -20  -27    0\n"

  "\n"

  "@arcs\n"

  "       cost  cap low1 low2\n"

  " 1  2    70   11    0    8\n"

  " 1  3   150    3    0    1\n"

  " 1  4    80   15    0    2\n"

  " 2  8    80   12    0    0\n"

  " 3  5   140    5    0    3\n"

  " 4  6    60   10    0    1\n"

  " 4  7    80    2    0    0\n"

  " 4  8   110    3    0    0\n"

  " 5  7    60   14    0    0\n"

  " 5 11   120   12    0    0\n"

  " 6  3     0    3    0    0\n"

  " 6  9   140    4    0    0\n"

  " 6 10    90    8    0    0\n"

  " 7  1    30    5    0    0\n"

  " 8 12    60   16    0    4\n"

  " 9 12    50    6    0    0\n"

  "10 12    70   13    0    5\n"

  "10  2   100    7    0    0\n"

  "10  7    60   10    0    0\n"

  "11 10    20   14    0    6\n"

  "12 11    30   10    0    0\n"

  "\n"

  "@attributes\n"

  "source 1\n"

  "target 12\n";

// Check the interface of an MCF algorithm

template <typename GR, typename Value>

class McfClassConcept

{

public:

  template <typename MCF>

  struct Constraints {

    void constraints() {

      checkConcept<concepts::Digraph, GR>();

      MCF mcf(g);

             .upperMap(upper)

             .capacityMap(upper)

             .boundMaps(lower, upper)

             .costMap(cost)

             .supplyMap(sup)

             .stSupply(n, n, k)

             .run();

      const typename MCF::FlowMap &fm = mcf.flowMap();

      const typename MCF::PotentialMap &pm = mcf.potentialMap();

      v = mcf.totalCost();

      double x = mcf.template totalCost<double>();

      v = mcf.flow(a);

      v = mcf.potential(n);

      mcf.flowMap(flow);

      mcf.potentialMap(pot);

      ignore_unused_variable_warning(fm);

      ignore_unused_variable_warning(pm);

      ignore_unused_variable_warning(x);

    }

    typedef typename GR::Node Node;

    typedef typename GR::Arc Arc;

    typedef concepts::ReadMap<Node, Value> NM;

    typedef concepts::ReadMap<Arc, Value> AM;

    const GR &g;

    const AM &lower;

    const AM &upper;

    const AM &cost;

    const NM ⊃

    const Node &n;

    const Arc &a;

    const Value &k;

    Value v;

    bool b;

    typename MCF::FlowMap &flow;

    typename MCF::PotentialMap &pot;

  };

};

// Check the feasibility of the given flow (primal soluiton)

template < typename GR, typename LM, typename UM,

    check(mcf.totalCost() == total, "The flow is not optimal " + test_id);

    check(checkPotential(gr, lower, upper, cost, mcf.flowMap(),

                         mcf.potentialMap()),

          "Wrong potentials " + test_id);

  }

}

int main()

{

  // Check the interfaces

  {

    typedef int Value;

    // TODO: This typedef should be enabled if the standard maps are

    // reference maps in the graph concepts (See #190).

/**/

    //typedef concepts::Digraph GR;

    typedef ListDigraph GR;

/**/

    checkConcept< McfClassConcept<GR, Value>,

                  NetworkSimplex<GR, Value> >();

  }

  // Run various MCF tests

  typedef ListDigraph Digraph;

  DIGRAPH_TYPEDEFS(ListDigraph);

  // Read the test digraph

  Digraph gr;

  Digraph::ArcMap<int> c(gr), l1(gr), l2(gr), u(gr);

  Digraph::NodeMap<int> s1(gr), s2(gr), s3(gr);

  ConstMap<Arc, int> cc(1), cu(std::numeric_limits<int>::max());

  Node v, w;

  std::istringstream input(test_lgf);

  DigraphReader<Digraph>(gr, input)

    .arcMap("cost", c)

    .arcMap("cap", u)

    .arcMap("low1", l1)

    .arcMap("low2", l2)

    .nodeMap("sup1", s1)

    .nodeMap("sup2", s2)

    .nodeMap("sup3", s3)

    .node("source", v)

    .node("target", w)

    .run();

  // A. Test NetworkSimplex with the default pivot rule

  {

             gr, l1, u, c, s1, true,  5240, "#A1");

             gr, l1, u, c, s2, true,  7620, "#A2");

             gr, l2, u, c, s1, true,  5970, "#A3");

             gr, l2, u, c, s2, true,  8010, "#A4");

             gr, l1, cu, cc, s1, true,  74, "#A5");

             gr, l2, cu, cc, s2, true,  94, "#A6");

             gr, l1, cu, cc, s3, true,   0, "#A7");

             gr, l2, u, cc, s3, false,   0, "#A8");

  }

  // B. Test NetworkSimplex with each pivot rule

  {

             gr, l2, u, c, s1, true,  5970, "#B1");

             gr, l2, u, c, s1, true,  5970, "#B2");

             gr, l2, u, c, s1, true,  5970, "#B3");

             gr, l2, u, c, s1, true,  5970, "#B4");

             gr, l2, u, c, s1, true,  5970, "#B5");

  }

  return 0;

}