RhodeCode

      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().

    /// For example,

    /// \code

    ///   CapacityScaling<ListDigraph> cs(graph);

    ///   cs.lowerMap(lower).upperMap(upper).costMap(cost)

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

    /// \endcode

    ///

    /// This function can be called more than once. All the parameters

    /// that have been given are kept for the next call, unless

    /// \ref reset() is called, thus only the modified parameters

    /// have to be set again. See \ref reset() for examples.

    /// However, the underlying digraph must not be modified after this

    /// class have been constructed, since it copies and extends the graph.

    ///

    /// \param factor The capacity scaling factor. It must be larger than

    /// one to use scaling. If it is less or equal to one, then scaling

    /// will be disabled.

    ///

    /// \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 digraph contains an arc of negative cost

    /// and infinite upper bound. It means that the objective function

    /// is unbounded on that arc, however, note that it could actually be

    /// bounded over the feasible flows, but this algroithm cannot handle

    /// these cases.

    ///

    /// \see ProblemType

    ProblemType run(int factor = 4) {

      _factor = factor;

      ProblemType pt = init();

      if (pt != OPTIMAL) return pt;

      return start();

    }

    /// \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().

    ///

    /// It is useful for multiple run() calls. If this function is not

    /// used, all the parameters given before are kept for the next

    /// \ref run() call.

    /// However, the underlying digraph must not be modified after this

    /// class have been constructed, since it copies and extends the graph.

    ///

    /// For example,

    /// \code

    ///   CapacityScaling<ListDigraph> cs(graph);

    ///

    ///   // First run

    ///   cs.lowerMap(lower).upperMap(upper).costMap(cost)

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

    ///

    ///   // Run again with modified cost map (reset() is not called,

    ///   // so only the cost map have to be set again)

    ///   cost[e] += 100;

    ///   cs.costMap(cost).run();

    ///

    ///   // Run again from scratch using reset()

    ///   // (the lower bounds will be set to zero on all arcs)

    ///   cs.reset();

    ///   cs.upperMap(capacity).costMap(cost)

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

    /// \endcode

    ///

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

    CapacityScaling& reset() {

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

        _supply[i] = 0;

      }

      for (int j = 0; j != _res_arc_num; ++j) {

        _lower[j] = 0;

        _upper[j] = INF;

        _cost[j] = _forward[j] ? 1 : -1;

      }

      _have_lower = false;

      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(e).

    ///

    /// \note The return type of the function can be specified as a

    /// template parameter. For example,

    /// \code

    ///   cs.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_idb[a];

        c += static_cast<Number>(_res_cap[i]) *

             (-static_cast<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 _res_cap[_arc_idb[a]];

    }

    /// \brief Return the flow map (the primal solution).

    ///

    /// 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, _res_cap[_arc_idb[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 Return the potential map (the dual solution).

    ///

    /// 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 the algorithm

    ProblemType init() {

      // Check the sum of supply values

      _sum_supply = 0;

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

        _sum_supply += _supply[i];

      }

      if (_sum_supply > 0) return INFEASIBLE;

      // Initialize vectors

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

        _pi[i] = 0;

        _excess[i] = _supply[i];

      }

      // Remove non-zero lower bounds

      const Value MAX = std::numeric_limits<Value>::max();

      int last_out;

      if (_have_lower) {

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

          last_out = _first_out[i+1];

          for (int j = _first_out[i]; j != last_out; ++j) {

            if (_forward[j]) {

              Value c = _lower[j];

              if (c >= 0) {

                _res_cap[j] = _upper[j] < MAX ? _upper[j] - c : INF;

              } else {

                _res_cap[j] = _upper[j] < MAX + c ? _upper[j] - c : INF;

              }

              _excess[i] -= c;

              _excess[_target[j]] += c;

            } else {

              _res_cap[j] = 0;

            }

          }

        }

      } else {

        for (int j = 0; j != _res_arc_num; ++j) {

          _res_cap[j] = _forward[j] ? _upper[j] : 0;

        }

      }

      // Handle negative costs

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

        last_out = _first_out[i+1] - 1;

        for (int j = _first_out[i]; j != last_out; ++j) {

          Value rc = _res_cap[j];

          if (_cost[j] < 0 && rc > 0) {

            if (rc >= MAX) return UNBOUNDED;

            _excess[i] -= rc;

            _excess[_target[j]] += rc;

            _res_cap[j] = 0;

            _res_cap[_reverse[j]] += rc;

          }

        }

      }

      // Handle GEQ supply type

      if (_sum_supply < 0) {

        _pi[_root] = 0;

        _excess[_root] = -_sum_supply;

        for (int a = _first_out[_root]; a != _res_arc_num; ++a) {

          int ra = _reverse[a];

          _res_cap[a] = -_sum_supply + 1;

          _res_cap[ra] = 0;

          _cost[a] = 0;

          _cost[ra] = 0;

        }

      } else {

        _pi[_root] = 0;

        _excess[_root] = 0;

        for (int a = _first_out[_root]; a != _res_arc_num; ++a) {

          int ra = _reverse[a];

          _res_cap[a] = 1;

          _res_cap[ra] = 0;

          _cost[a] = 0;

          _cost[ra] = 0;

        }

      }

      // Initialize delta value

      if (_factor > 1) {

        // With scaling

        Value max_sup = 0, max_dem = 0;

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

          Value ex = _excess[i];

          if ( ex > max_sup) max_sup =  ex;

          if (-ex > max_dem) max_dem = -ex;

        }

        Value max_cap = 0;

        for (int j = 0; j != _res_arc_num; ++j) {

          if (_res_cap[j] > max_cap) max_cap = _res_cap[j];

        }

        max_sup = std::min(std::min(max_sup, max_dem), max_cap);

        for (_delta = 1; 2 * _delta <= max_sup; _delta *= 2) ;

      } else {

        // Without scaling

        _delta = 1;

      }

      return OPTIMAL;

    }

    ProblemType start() {

      // Execute the algorithm

      ProblemType pt;

      if (_delta > 1)

        pt = startWithScaling();

      else

        pt = startWithoutScaling();

      // Handle non-zero lower bounds

      if (_have_lower) {

        int limit = _first_out[_root];

        for (int j = 0; j != limit; ++j) {

          if (!_forward[j]) _res_cap[j] += _lower[j];

        }

      }

      // Shift potentials if necessary

      Cost pr = _pi[_root];

      if (_sum_supply < 0 || pr > 0) {

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

          _pi[i] -= pr;

        }        

      }

      return pt;

    }

    // Execute the capacity scaling algorithm

    ProblemType startWithScaling() {

      // Perform capacity scaling phases

      int s, t;

      ResidualDijkstra _dijkstra(*this);

      while (true) {

        // Saturate all arcs not satisfying the optimality condition

        int last_out;

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

          last_out = _sum_supply < 0 ?

            _first_out[u+1] : _first_out[u+1] - 1;

          for (int a = _first_out[u]; a != last_out; ++a) {

            int v = _target[a];

            Cost c = _cost[a] + _pi[u] - _pi[v];

            Value rc = _res_cap[a];

            if (c < 0 && rc >= _delta) {

              _excess[u] -= rc;

              _excess[v] += rc;

              _res_cap[a] = 0;

              _res_cap[_reverse[a]] += rc;

            }

          }

        }

        // Find excess nodes and deficit nodes

        _excess_nodes.clear();

        _deficit_nodes.clear();

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

          Value ex = _excess[u];

          if (ex >=  _delta) _excess_nodes.push_back(u);

          if (ex <= -_delta) _deficit_nodes.push_back(u);

        }

        int next_node = 0, next_def_node = 0;

        // Find augmenting shortest paths

        while (next_node < int(_excess_nodes.size())) {

          // Check deficit nodes

          if (_delta > 1) {

            bool delta_deficit = false;

            for ( ; next_def_node < int(_deficit_nodes.size());

                    ++next_def_node ) {

              if (_excess[_deficit_nodes[next_def_node]] <= -_delta) {

                delta_deficit = true;

                break;

              }

            }

            if (!delta_deficit) break;

          }

          // Run Dijkstra in the residual network

          s = _excess_nodes[next_node];

          if ((t = _dijkstra.run(s, _delta)) == -1) {

            if (_delta > 1) {

              ++next_node;

              continue;

            }

            return INFEASIBLE;

          }

          // Augment along a shortest path from s to t

          Value d = std::min(_excess[s], -_excess[t]);

          int u = t;

          int a;

    /// @{

    /// \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().

    /// For example,

    /// \code

    ///   CostScaling<ListDigraph> cs(graph);

    ///   cs.lowerMap(lower).upperMap(upper).costMap(cost)

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

    /// \endcode

    ///

    /// This function can be called more than once. All the parameters

    /// that have been given are kept for the next call, unless

    /// \ref reset() is called, thus only the modified parameters

    /// have to be set again. See \ref reset() for examples.

    /// However, the underlying digraph must not be modified after this

    /// class have been constructed, since it copies and extends the graph.

    ///

    /// \param method The internal method that will be used in the

    /// algorithm. For more information, see \ref Method.

    /// \param factor The cost scaling factor. It must be larger than one.

    ///

    /// \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 digraph contains an arc of negative cost

    /// and infinite upper bound. It means that the objective function

    /// is unbounded on that arc, however, note that it could actually be

    /// bounded over the feasible flows, but this algroithm cannot handle

    /// these cases.

    ///

    /// \see ProblemType, Method

    ProblemType run(Method method = PARTIAL_AUGMENT, int factor = 8) {

      _alpha = factor;

      ProblemType pt = init();

      if (pt != OPTIMAL) return pt;

      start(method);

      return OPTIMAL;

    }

    /// \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().

    ///

    /// It is useful for multiple run() calls. If this function is not

    /// used, all the parameters given before are kept for the next

    /// \ref run() call.

    /// However, the underlying digraph must not be modified after this

    /// class have been constructed, since it copies and extends the graph.

    ///

    /// For example,

    /// \code

    ///   CostScaling<ListDigraph> cs(graph);

    ///

    ///   // First run

    ///   cs.lowerMap(lower).upperMap(upper).costMap(cost)

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

    ///

    ///   // Run again with modified cost map (reset() is not called,

    ///   // so only the cost map have to be set again)

    ///   cost[e] += 100;

    ///   cs.costMap(cost).run();

    ///

    ///   // Run again from scratch using reset()

    ///   // (the lower bounds will be set to zero on all arcs)

    ///   cs.reset();

    ///   cs.upperMap(capacity).costMap(cost)

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

    /// \endcode

    ///

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

    CostScaling& reset() {

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

        _supply[i] = 0;

      }

      int limit = _first_out[_root];

      for (int j = 0; j != limit; ++j) {

        _lower[j] = 0;

        _upper[j] = INF;

        _scost[j] = _forward[j] ? 1 : -1;

      }

      for (int j = limit; j != _res_arc_num; ++j) {

        _lower[j] = 0;

        _upper[j] = INF;

        _scost[j] = 0;

        _scost[_reverse[j]] = 0;

      }      

      _have_lower = false;

      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(e).

    ///

    /// \note The return type of the function can be specified as a

    /// template parameter. For example,

    /// \code

    ///   cs.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_idb[a];

        c += static_cast<Number>(_res_cap[i]) *

             (-static_cast<Number>(_scost[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 _res_cap[_arc_idb[a]];

    }

    /// \brief Return the flow map (the primal solution).

    ///

    /// 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, _res_cap[_arc_idb[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 static_cast<Cost>(_pi[_node_id[n]]);

    }

    /// \brief Return the potential map (the dual solution).

    ///

    /// 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, static_cast<Cost>(_pi[_node_id[n]]));

      }

    }

    /// @}

  private:

    // Initialize the algorithm

    ProblemType init() {

      // Check the sum of supply values

      _sum_supply = 0;

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

        _sum_supply += _supply[i];

      }

      if (_sum_supply > 0) return INFEASIBLE;

      // Initialize vectors

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

        _pi[i] = 0;

        _excess[i] = _supply[i];

      }

      // Remove infinite upper bounds and check negative arcs

      const Value MAX = std::numeric_limits<Value>::max();

      int last_out;

      if (_have_lower) {

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

          last_out = _first_out[i+1];

          for (int j = _first_out[i]; j != last_out; ++j) {

            if (_forward[j]) {

              Value c = _scost[j] < 0 ? _upper[j] : _lower[j];

              if (c >= MAX) return UNBOUNDED;

              _excess[i] -= c;

              _excess[_target[j]] += c;

            }

          }

        }

      } else {

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

          last_out = _first_out[i+1];

          for (int j = _first_out[i]; j != last_out; ++j) {

            if (_forward[j] && _scost[j] < 0) {

              Value c = _upper[j];

              if (c >= MAX) return UNBOUNDED;

              _excess[i] -= c;

              _excess[_target[j]] += c;

            }

          }

        }

      }

      Value ex, max_cap = 0;

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

        ex = _excess[i];

        _excess[i] = 0;

        if (ex < 0) max_cap -= ex;

      }

      for (int j = 0; j != _res_arc_num; ++j) {

        if (_upper[j] >= MAX) _upper[j] = max_cap;

      }

      // Initialize the large cost vector and the epsilon parameter

      _epsilon = 0;

      LargeCost lc;

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

        last_out = _first_out[i+1];

        for (int j = _first_out[i]; j != last_out; ++j) {

          lc = static_cast<LargeCost>(_scost[j]) * _res_node_num * _alpha;

          _cost[j] = lc;

          if (lc > _epsilon) _epsilon = lc;

        }

      }

      _epsilon /= _alpha;

      // Initialize maps for Circulation and remove non-zero lower bounds

      ConstMap<Arc, Value> low(0);

      typedef typename Digraph::template ArcMap<Value> ValueArcMap;

      typedef typename Digraph::template NodeMap<Value> ValueNodeMap;

      ValueArcMap cap(_graph), flow(_graph);

      ValueNodeMap sup(_graph);

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

        sup[n] = _supply[_node_id[n]];

      }

      if (_have_lower) {

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

          int j = _arc_idf[a];

          Value c = _lower[j];

          cap[a] = _upper[j] - c;

          sup[_graph.source(a)] -= c;

          sup[_graph.target(a)] += c;

        }

      } else {

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

          cap[a] = _upper[_arc_idf[a]];

        }

      }

      // Find a feasible flow using Circulation

      Circulation<Digraph, ConstMap<Arc, Value>, ValueArcMap, ValueNodeMap>

        circ(_graph, low, cap, sup);

      if (!circ.flowMap(flow).run()) return INFEASIBLE;

      // Set residual capacities and handle GEQ supply type

      if (_sum_supply < 0) {

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

          Value fa = flow[a];

          _res_cap[_arc_idf[a]] = cap[a] - fa;

          _res_cap[_arc_idb[a]] = fa;

          sup[_graph.source(a)] -= fa;

          sup[_graph.target(a)] += fa;

        }

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

          _excess[_node_id[n]] = sup[n];

        }

        for (int a = _first_out[_root]; a != _res_arc_num; ++a) {

          int u = _target[a];

          int ra = _reverse[a];

          _res_cap[a] = -_sum_supply + 1;

          _res_cap[ra] = -_excess[u];

          _cost[a] = 0;

          _cost[ra] = 0;

          _excess[u] = 0;

        }

      } else {

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

          Value fa = flow[a];

          _res_cap[_arc_idf[a]] = cap[a] - fa;

          _res_cap[_arc_idb[a]] = fa;

        }

        for (int a = _first_out[_root]; a != _res_arc_num; ++a) {

          int ra = _reverse[a];

          _res_cap[a] = 1;

          _res_cap[ra] = 0;

          _cost[a] = 0;

          _cost[ra] = 0;

        }

      }

      return OPTIMAL;

    }

    // Execute the algorithm and transform the results

    void start(Method method) {

      // Maximum path length for partial augment

      const int MAX_PATH_LENGTH = 4;

      // Execute the algorithm

      switch (method) {

        case PUSH:

          startPush();

          break;

        case AUGMENT:

          startAugment();

          break;

        case PARTIAL_AUGMENT:

          startAugment(MAX_PATH_LENGTH);

          break;

      }

      // Compute node potentials for the original costs

      _arc_vec.clear();

      _cost_vec.clear();

      for (int j = 0; j != _res_arc_num; ++j) {

        if (_res_cap[j] > 0) {

          _arc_vec.push_back(IntPair(_source[j], _target[j]));

          _cost_vec.push_back(_scost[j]);

        }

      }

      _sgr.build(_res_node_num, _arc_vec.begin(), _arc_vec.end());

      typename BellmanFord<StaticDigraph, LargeCostArcMap>

        ::template SetDistMap<LargeCostNodeMap>::Create bf(_sgr, _cost_map);

      bf.distMap(_pi_map);

      bf.init(0);

      bf.start();

      // Handle non-zero lower bounds

      if (_have_lower) {

        int limit = _first_out[_root];

        for (int j = 0; j != limit; ++j) {

          if (!_forward[j]) _res_cap[j] += _lower[j];

        }

      }

    }

    /// Execute the algorithm performing augment and relabel operations

    void startAugment(int max_length = std::numeric_limits<int>::max()) {

      // Paramters for heuristics

      const int BF_HEURISTIC_EPSILON_BOUND = 1000;

      const int BF_HEURISTIC_BOUND_FACTOR  = 3;

      // Perform cost scaling phases

      IntVector pred_arc(_res_node_num);

      std::vector<int> path_nodes;

      for ( ; _epsilon >= 1; _epsilon = _epsilon < _alpha && _epsilon > 1 ?

                                        1 : _epsilon / _alpha )

      {

        // "Early Termination" heuristic: use Bellman-Ford algorithm

        // to check if the current flow is optimal

        if (_epsilon <= BF_HEURISTIC_EPSILON_BOUND) {