RhodeCode

      /// in a wraparound fashion and the best eligible arc is selected

      /// from this block.

      BLOCK_SEARCH,

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

      /// In a major iteration a candidate list is built from eligible arcs

      /// in a wraparound fashion and in the following minor iterations

      /// the best eligible arc is selected from this list.

      CANDIDATE_LIST,

      /// The \e Altering \e Candidate \e List pivot rule.

      /// It is a modified version of the Candidate List method.

      /// It keeps only the several best eligible arcs from the former

      /// candidate list and extends this list in every iteration.

      ALTERING_LIST

    };

  private:

    TEMPLATE_DIGRAPH_TYPEDEFS(GR);

    typedef std::vector<int> IntVector;

    typedef std::vector<Value> ValueVector;

    typedef std::vector<Cost> CostVector;

    // State constants for arcs

    enum ArcState {

      STATE_UPPER = -1,

      STATE_TREE  =  0,

      STATE_LOWER =  1

    };

  private:

    // Data related to the underlying digraph

    const GR &_graph;

    int _node_num;

    int _arc_num;

    int _all_arc_num;

    int _search_arc_num;

    // Parameters of the problem

    bool _have_lower;

    SupplyType _stype;

    Value _sum_supply;

    // Data structures for storing the digraph

    IntNodeMap _node_id;

    IntArcMap _arc_id;

    IntVector _source;

    IntVector _target;

    bool _arc_mixing;

    // Node and arc data

    ValueVector _lower;

    ValueVector _upper;

    ValueVector _cap;

    CostVector _cost;

    ValueVector _supply;

    ValueVector _flow;

    CostVector _pi;

    // Data for storing the spanning tree structure

    IntVector _parent;

    IntVector _pred;

    IntVector _thread;

    IntVector _rev_thread;

    IntVector _succ_num;

    IntVector _last_succ;

    IntVector _dirty_revs;

    int _root;

    // Temporary data used in the current pivot iteration

    int in_arc, join, u_in, v_in, u_out, v_out;

    Value delta;

    const Value MAX;

  public:

    /// \brief Constant for infinite upper bounds (capacities).

    ///

    /// Constant for infinite upper bounds (capacities).

    /// It is \c std::numeric_limits<Value>::infinity() if available,

    /// \c std::numeric_limits<Value>::max() otherwise.

    const Value INF;

  private:

    // Implementation of the First Eligible pivot rule

    class FirstEligiblePivotRule

    {

    private:

      // References to the NetworkSimplex class

      const IntVector  &_source;

      const IntVector  &_target;

      const CostVector &_cost;

      const CostVector &_pi;

      int &_in_arc;

      int _search_arc_num;

      // Pivot rule data

      int _next_arc;

    public:

      // Constructor

      FirstEligiblePivotRule(NetworkSimplex &ns) :

        _source(ns._source), _target(ns._target),

        _cost(ns._cost), _state(ns._state), _pi(ns._pi),

        _in_arc(ns.in_arc), _search_arc_num(ns._search_arc_num),

        _next_arc(0)

      {}

      // Find next entering arc

      bool findEnteringArc() {

        Cost c;

        for (int e = _next_arc; e != _search_arc_num; ++e) {

          c = _state[e] * (_cost[e] + _pi[_source[e]] - _pi[_target[e]]);

          if (c < 0) {

            _in_arc = e;

        }

        for (int e = 0; e != _next_arc; ++e) {

          c = _state[e] * (_cost[e] + _pi[_source[e]] - _pi[_target[e]]);

          if (c < 0) {

            _in_arc = e;

            _next_arc = e + 1;

            return true;

          }

        }

        return false;

      }

    }; //class FirstEligiblePivotRule

    // Implementation of the Best Eligible pivot rule

    class BestEligiblePivotRule

    {

    private:

      // References to the NetworkSimplex class

      const IntVector  &_source;

      const IntVector  &_target;

      const CostVector &_cost;

      const CostVector &_pi;

      int &_in_arc;

      int _search_arc_num;

    public:

      // Constructor

      BestEligiblePivotRule(NetworkSimplex &ns) :

        _source(ns._source), _target(ns._target),

        _cost(ns._cost), _state(ns._state), _pi(ns._pi),

        _in_arc(ns.in_arc), _search_arc_num(ns._search_arc_num)

      {}

      // Find next entering arc

      bool findEnteringArc() {

        Cost c, min = 0;

        for (int e = 0; e != _search_arc_num; ++e) {

          c = _state[e] * (_cost[e] + _pi[_source[e]] - _pi[_target[e]]);

          if (c < min) {

            min = c;

            _in_arc = e;

          }

        }

        return min < 0;

      }

    }; //class BestEligiblePivotRule

    // Implementation of the Block Search pivot rule

    class BlockSearchPivotRule

    {

    private:

      // References to the NetworkSimplex class

      const IntVector  &_source;

      const IntVector  &_target;

      const CostVector &_cost;

      const CostVector &_pi;

      int &_in_arc;

      int _search_arc_num;

      // Pivot rule data

      int _block_size;

      int _next_arc;

    public:

      // Constructor

      BlockSearchPivotRule(NetworkSimplex &ns) :

        _source(ns._source), _target(ns._target),

        _cost(ns._cost), _state(ns._state), _pi(ns._pi),

        _in_arc(ns.in_arc), _search_arc_num(ns._search_arc_num),

        _next_arc(0)

      {

        // The main parameters of the pivot rule

        const double BLOCK_SIZE_FACTOR = 1.0;

        const int MIN_BLOCK_SIZE = 10;

        _block_size = std::max( int(BLOCK_SIZE_FACTOR *

                                    std::sqrt(double(_search_arc_num))),

                                MIN_BLOCK_SIZE );

          if (--cnt == 0) {

            if (min < 0) goto search_end;

            cnt = _block_size;

          }

        }

        if (min >= 0) return false;

      search_end:

        _next_arc = e;

        return true;

      }

    }; //class BlockSearchPivotRule

    // Implementation of the Candidate List pivot rule

    class CandidateListPivotRule

    {

    private:

      // References to the NetworkSimplex class

      const IntVector  &_source;

      const IntVector  &_target;

      const CostVector &_cost;

      const CostVector &_pi;

      int &_in_arc;

      int _search_arc_num;

      // Pivot rule data

      IntVector _candidates;

      int _list_length, _minor_limit;

      int _curr_length, _minor_count;

      int _next_arc;

    public:

      /// Constructor

      CandidateListPivotRule(NetworkSimplex &ns) :

        _source(ns._source), _target(ns._target),

        _cost(ns._cost), _state(ns._state), _pi(ns._pi),

        _in_arc(ns.in_arc), _search_arc_num(ns._search_arc_num),

        _next_arc(0)

      {

        // The main parameters of the pivot rule

        const double LIST_LENGTH_FACTOR = 0.25;

        const int MIN_LIST_LENGTH = 10;

        const double MINOR_LIMIT_FACTOR = 0.1;

        const int MIN_MINOR_LIMIT = 3;

            }

            if (_curr_length == _list_length) goto search_end;

          }

        }

        if (_curr_length == 0) return false;

      search_end:

        _minor_count = 1;

        _next_arc = e;

        return true;

      }

    }; //class CandidateListPivotRule

    // Implementation of the Altering Candidate List pivot rule

    class AlteringListPivotRule

    {

    private:

      // References to the NetworkSimplex class

      const IntVector  &_source;

      const IntVector  &_target;

      const CostVector &_cost;

      const CostVector &_pi;

      int &_in_arc;

      int _search_arc_num;

      // Pivot rule data

      int _block_size, _head_length, _curr_length;

      int _next_arc;

      IntVector _candidates;

      CostVector _cand_cost;

      // Functor class to compare arcs during sort of the candidate list

      class SortFunc

      {

      private:

        const CostVector &_map;

      public:

        SortFunc(const CostVector &map) : _map(map) {}

        bool operator()(int left, int right) {

          return _map[left] > _map[right];

        }

      };

      SortFunc _sort_func;

        _source(ns._source), _target(ns._target),

        _cost(ns._cost), _state(ns._state), _pi(ns._pi),

        _in_arc(ns.in_arc), _search_arc_num(ns._search_arc_num),

        _next_arc(0), _cand_cost(ns._search_arc_num), _sort_func(_cand_cost)

      {

        // The main parameters of the pivot rule

        const double BLOCK_SIZE_FACTOR = 1.0;

        const int MIN_BLOCK_SIZE = 10;

        const double HEAD_LENGTH_FACTOR = 0.1;

        const int MIN_HEAD_LENGTH = 3;

        _block_size = std::max( int(BLOCK_SIZE_FACTOR *

                                    std::sqrt(double(_search_arc_num))),

                                MIN_BLOCK_SIZE );

        _head_length = std::max( int(HEAD_LENGTH_FACTOR * _block_size),

                                 MIN_HEAD_LENGTH );

        _candidates.resize(_head_length + _block_size);

        _curr_length = 0;

      }

      // Find next entering arc

      bool findEnteringArc() {

        // Check the current candidate list

        int e;

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

          e = _candidates[i];

            _candidates[i--] = _candidates[--_curr_length];

          }

        }

        // Extend the list

        int cnt = _block_size;

        int limit = _head_length;

        for (e = _next_arc; e != _search_arc_num; ++e) {

            _candidates[_curr_length++] = e;

          }

          if (--cnt == 0) {

            if (_curr_length > limit) goto search_end;

            limit = 0;

            cnt = _block_size;

          }

        }

        for (e = 0; e != _next_arc; ++e) {

          _cand_cost[e] = _state[e] *

            (_cost[e] + _pi[_source[e]] - _pi[_target[e]]);

          if (_cand_cost[e] < 0) {

            _candidates[_curr_length++] = e;

          }

          if (--cnt == 0) {

            if (_curr_length > limit) goto search_end;

            limit = 0;

            cnt = _block_size;

          }

        }

        if (_curr_length == 0) return false;

      search_end:

    ///

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

    ///

    /// \see resetParams(), run()

    NetworkSimplex& reset() {

      // Resize vectors

      _node_num = countNodes(_graph);

      _arc_num = countArcs(_graph);

      int all_node_num = _node_num + 1;

      int max_arc_num = _arc_num + 2 * _node_num;

      _source.resize(max_arc_num);

      _target.resize(max_arc_num);

      _lower.resize(_arc_num);

      _upper.resize(_arc_num);

      _cap.resize(max_arc_num);

      _cost.resize(max_arc_num);

      _supply.resize(all_node_num);

      _flow.resize(max_arc_num);

      _pi.resize(all_node_num);

      _parent.resize(all_node_num);

      _pred.resize(all_node_num);

      _thread.resize(all_node_num);

      _rev_thread.resize(all_node_num);

      _succ_num.resize(all_node_num);

      _last_succ.resize(all_node_num);

      _state.resize(max_arc_num);

      // Copy the graph

      int i = 0;

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

        _node_id[n] = i;

      }

      if (_arc_mixing) {

        // Store the arcs in a mixed order

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

        int i = 0, j = 0;

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

          _arc_id[a] = i;

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

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

          if ((i += k) >= _arc_num) i = ++j;

        }

      } else {

        // Store the arcs in the original order

        int i = 0;

      _parent[_root] = -1;

      _pred[_root] = -1;

      _thread[_root] = 0;

      _rev_thread[0] = _root;

      _succ_num[_root] = _node_num + 1;

      _last_succ[_root] = _root - 1;

      _supply[_root] = -_sum_supply;

      _pi[_root] = 0;

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

      if (_sum_supply == 0) {

        // EQ supply constraints

        _search_arc_num = _arc_num;

        _all_arc_num = _arc_num + _node_num;

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

          _parent[u] = _root;

          _pred[u] = e;

          _thread[u] = u + 1;

          _rev_thread[u + 1] = u;

          _succ_num[u] = 1;

          _last_succ[u] = u;

          _cap[e] = INF;

          _state[e] = STATE_TREE;

          if (_supply[u] >= 0) {

            _pi[u] = 0;

            _source[e] = u;

            _target[e] = _root;

            _flow[e] = _supply[u];

            _cost[e] = 0;

          } else {

            _pi[u] = ART_COST;

            _source[e] = _root;

            _target[e] = u;

            _flow[e] = -_supply[u];

            _cost[e] = ART_COST;

          }

        }

      }

      else if (_sum_supply > 0) {

        // LEQ supply constraints

        _search_arc_num = _arc_num + _node_num;

        int f = _arc_num + _node_num;

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

          _parent[u] = _root;

          _thread[u] = u + 1;

          _rev_thread[u + 1] = u;

          _succ_num[u] = 1;

          _last_succ[u] = u;

          if (_supply[u] >= 0) {

            _pi[u] = 0;

            _pred[u] = e;

            _source[e] = u;

            _target[e] = _root;

            _cap[e] = INF;

            _flow[e] = _supply[u];

            _cost[e] = 0;

            _state[e] = STATE_TREE;

          } else {

            _pi[u] = ART_COST;

            _pred[u] = f;

            _source[f] = _root;

            _target[f] = u;

            _cap[f] = INF;

            _flow[f] = -_supply[u];

            _cost[f] = ART_COST;

            _state[f] = STATE_TREE;

            _source[e] = u;

            _target[e] = _root;

            _cap[e] = INF;

            _flow[e] = 0;

            _cost[e] = 0;

            _state[e] = STATE_LOWER;

            ++f;

          }

        }

        _all_arc_num = f;

      }

      else {

        // GEQ supply constraints

        _search_arc_num = _arc_num + _node_num;

        int f = _arc_num + _node_num;

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

          _parent[u] = _root;

          _thread[u] = u + 1;

          _rev_thread[u + 1] = u;

          _succ_num[u] = 1;

          _last_succ[u] = u;

          if (_supply[u] <= 0) {

            _pi[u] = 0;

            _pred[u] = e;

            _source[e] = _root;

            _target[e] = u;

            _cap[e] = INF;

            _flow[e] = -_supply[u];

            _cost[e] = 0;

            _state[e] = STATE_TREE;

          } else {

            _pi[u] = -ART_COST;

            _pred[u] = f;

            _source[f] = u;

            _target[f] = _root;

            _cap[f] = INF;

            _flow[f] = _supply[u];

            _state[f] = STATE_TREE;

            _cost[f] = ART_COST;

            _source[e] = _root;

            _target[e] = u;

            _cap[e] = INF;

            _flow[e] = 0;

            _cost[e] = 0;

            _state[e] = STATE_LOWER;

            ++f;

          }

        }

        _all_arc_num = f;

      }

      return true;

    }

    // 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;

      int e;

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

        e = _pred[u];

        if (d < delta) {

          delta = d;

          u_out = u;

          result = 1;

        }

      }

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

        e = _pred[u];

        if (d <= delta) {

          delta = d;

          u_out = u;

          result = 2;

        }

      }

      if (result == 1) {

        u_in = first;

        v_in = second;

      } else {

        u_in = second;

        v_in = first;

      }

      return result != 0;

    }

    // Change _flow and _state vectors

    void changeFlow(bool change) {

      // Augment along the cycle

      if (delta > 0) {

        Value val = _state[in_arc] * delta;

        _flow[in_arc] += val;

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

        }

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

        }

      }

      // Update the state of the entering and leaving arcs

      if (change) {

        _state[in_arc] = STATE_TREE;

        _state[_pred[u_out]] =

          (_flow[_pred[u_out]] == 0) ? STATE_LOWER : STATE_UPPER;

      } else {

        _state[in_arc] = -_state[in_arc];

      }

    }

    // Update the tree structure

    void updateTreeStructure() {

      int old_rev_thread = _rev_thread[u_out];

      int old_succ_num = _succ_num[u_out];

      int old_last_succ = _last_succ[u_out];

      v_out = _parent[u_out];

      // Handle the case when old_rev_thread equals to v_in

      // (it also means that join and v_out coincide)

      // Update _thread and _parent along the stem nodes (i.e. the nodes

      // between u_in and u_out, whose parent have to be changed)

      _dirty_revs.clear();

      _dirty_revs.push_back(v_in);

      while (stem != u_out) {

        // Insert the next stem node into the thread list

        // Remove the subtree of stem from the thread list

        // Change the parent node and shift stem nodes

        _parent[stem] = par_stem;

        par_stem = stem;

          _rev_thread[par_stem] : _last_succ[stem];

      }

      _parent[u_out] = par_stem;

      // Remove the subtree of u_out from the thread list except for

      // the case when old_rev_thread equals to v_in

      if (old_rev_thread != v_in) {

      }

      // Update _rev_thread using the new _thread values

      for (int i = 0; i != int(_dirty_revs.size()); ++i) {

        _rev_thread[_thread[u]] = u;

      }

      // stem nodes from u_out to u_in

      int tmp_sc = 0, tmp_ls = _last_succ[u_out];

        _succ_num[u] = tmp_sc;

      }

      _pred[u_in] = in_arc;

      _succ_num[u_in] = old_succ_num;

      }

      // Update _last_succ from v_in towards the root

      }

      // Update _last_succ from v_out towards the root

      if (join != old_rev_thread && v_in != old_rev_thread) {

             u = _parent[u]) {

          _last_succ[u] = old_rev_thread;

        }

             u = _parent[u]) {

        }

      }

      // Update _succ_num from v_in to join

        _succ_num[u] += old_succ_num;

      }

      // Update _succ_num from v_out to join

        _succ_num[u] -= old_succ_num;

      }

    }

    void updatePotential() {

      int end = _thread[_last_succ[u_in]];

      for (int u = u_in; u != end; u = _thread[u]) {

        _pi[u] += sigma;

      }

    }

    // Heuristic initial pivots

    bool initialPivots() {

      Value curr, total = 0;

      std::vector<Node> supply_nodes, demand_nodes;

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

        curr = _supply[_node_id[u]];

        if (curr > 0) {

          total += curr;

          supply_nodes.push_back(u);

        }

        else if (curr < 0) {

          demand_nodes.push_back(u);

        }

      }

      if (_sum_supply > 0) total -= _sum_supply;

      if (total <= 0) return true;

      IntVector arc_vector;