1660 lines
52 KiB
C++
Executable File
1660 lines
52 KiB
C++
Executable File
/* -*- mode: C++; indent-tabs-mode: nil; -*-
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*
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* This file is a part of LEMON, a generic C++ optimization library.
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*
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* Copyright (C) 2003-2013
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* Egervary Jeno Kombinatorikus Optimalizalasi Kutatocsoport
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* (Egervary Research Group on Combinatorial Optimization, EGRES).
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*
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* Permission to use, modify and distribute this software is granted
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* provided that this copyright notice appears in all copies. For
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* precise terms see the accompanying LICENSE file.
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*
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* This software is provided "AS IS" with no warranty of any kind,
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* express or implied, and with no claim as to its suitability for any
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* purpose.
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*
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*/
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#ifndef LEMON_NETWORK_SIMPLEX_H
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#define LEMON_NETWORK_SIMPLEX_H
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/// \ingroup min_cost_flow_algs
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///
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/// \file
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/// \brief Network Simplex algorithm for finding a minimum cost flow.
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#include <vector>
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#include <limits>
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#include <algorithm>
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#include <lemon/core.h>
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#include <lemon/math.h>
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namespace lemon {
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/// \addtogroup min_cost_flow_algs
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/// @{
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/// \brief Implementation of the primal Network Simplex algorithm
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/// for finding a \ref min_cost_flow "minimum cost flow".
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///
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/// \ref NetworkSimplex implements the primal Network Simplex algorithm
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/// for finding a \ref min_cost_flow "minimum cost flow"
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/// \cite amo93networkflows, \cite dantzig63linearprog,
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/// \cite kellyoneill91netsimplex.
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/// This algorithm is a highly efficient specialized version of the
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/// linear programming simplex method directly for the minimum cost
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/// flow problem.
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///
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/// In general, \ref NetworkSimplex and \ref CostScaling are the fastest
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/// implementations available in LEMON for solving this problem.
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/// (For more information, see \ref min_cost_flow_algs "the module page".)
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/// Furthermore, this class supports both directions of the supply/demand
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/// inequality constraints. For more information, see \ref SupplyType.
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///
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/// Most of the parameters of the problem (except for the digraph)
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/// can be given using separate functions, and the algorithm can be
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/// executed using the \ref run() function. If some parameters are not
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/// specified, then default values will be used.
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///
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/// \tparam GR The digraph type the algorithm runs on.
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/// \tparam V The number type used for flow amounts, capacity bounds
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/// and supply values in the algorithm. By default, it is \c int.
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/// \tparam C The number type used for costs and potentials in the
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/// algorithm. By default, it is the same as \c V.
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///
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/// \warning Both \c V and \c C must be signed number types.
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/// \warning All input data (capacities, supply values, and costs) must
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/// be integer.
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///
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/// \note %NetworkSimplex provides five different pivot rule
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/// implementations, from which the most efficient one is used
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/// by default. For more information, see \ref PivotRule.
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template <typename GR, typename V = int, typename C = V>
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class NetworkSimplex
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{
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public:
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/// The type of the flow amounts, capacity bounds and supply values
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typedef V Value;
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/// The type of the arc costs
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typedef C Cost;
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public:
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/// \brief Problem type constants for the \c run() function.
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///
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/// Enum type containing the problem type constants that can be
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/// returned by the \ref run() function of the algorithm.
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enum ProblemType {
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/// The problem has no feasible solution (flow).
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INFEASIBLE,
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/// The problem has optimal solution (i.e. it is feasible and
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/// bounded), and the algorithm has found optimal flow and node
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/// potentials (primal and dual solutions).
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OPTIMAL,
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/// The objective function of the problem is unbounded, i.e.
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/// there is a directed cycle having negative total cost and
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/// infinite upper bound.
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UNBOUNDED
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};
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/// \brief Constants for selecting the type of the supply constraints.
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///
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/// Enum type containing constants for selecting the supply type,
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/// i.e. the direction of the inequalities in the supply/demand
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/// constraints of the \ref min_cost_flow "minimum cost flow problem".
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///
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/// The default supply type is \c GEQ, the \c LEQ type can be
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/// selected using \ref supplyType().
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/// The equality form is a special case of both supply types.
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enum SupplyType {
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/// This option means that there are <em>"greater or equal"</em>
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/// supply/demand constraints in the definition of the problem.
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GEQ,
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/// This option means that there are <em>"less or equal"</em>
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/// supply/demand constraints in the definition of the problem.
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LEQ
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};
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/// \brief Constants for selecting the pivot rule.
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///
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/// Enum type containing constants for selecting the pivot rule for
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/// the \ref run() function.
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///
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/// \ref NetworkSimplex provides five different implementations for
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/// the pivot strategy that significantly affects the running time
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/// of the algorithm.
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/// According to experimental tests conducted on various problem
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/// instances, \ref BLOCK_SEARCH "Block Search" and
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/// \ref ALTERING_LIST "Altering Candidate List" rules turned out
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/// to be the most efficient.
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/// Since \ref BLOCK_SEARCH "Block Search" is a simpler strategy that
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/// seemed to be slightly more robust, it is used by default.
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/// However, another pivot rule can easily be selected using the
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/// \ref run() function with the proper parameter.
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enum PivotRule {
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/// The \e First \e Eligible pivot rule.
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/// The next eligible arc is selected in a wraparound fashion
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/// in every iteration.
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FIRST_ELIGIBLE,
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/// The \e Best \e Eligible pivot rule.
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/// The best eligible arc is selected in every iteration.
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BEST_ELIGIBLE,
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/// The \e Block \e Search pivot rule.
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/// A specified number of arcs are examined in every iteration
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/// in a wraparound fashion and the best eligible arc is selected
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/// from this block.
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BLOCK_SEARCH,
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/// The \e Candidate \e List pivot rule.
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/// In a major iteration a candidate list is built from eligible arcs
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/// in a wraparound fashion and in the following minor iterations
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/// the best eligible arc is selected from this list.
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CANDIDATE_LIST,
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/// The \e Altering \e Candidate \e List pivot rule.
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/// It is a modified version of the Candidate List method.
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/// It keeps only a few of the best eligible arcs from the former
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/// candidate list and extends this list in every iteration.
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ALTERING_LIST
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};
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private:
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TEMPLATE_DIGRAPH_TYPEDEFS(GR);
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typedef std::vector<int> IntVector;
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typedef std::vector<Value> ValueVector;
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typedef std::vector<Cost> CostVector;
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typedef std::vector<signed char> CharVector;
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// Note: vector<signed char> is used instead of vector<ArcState> and
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// vector<ArcDirection> for efficiency reasons
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// State constants for arcs
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enum ArcState {
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STATE_UPPER = -1,
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STATE_TREE = 0,
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STATE_LOWER = 1
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};
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// Direction constants for tree arcs
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enum ArcDirection {
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DIR_DOWN = -1,
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DIR_UP = 1
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};
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private:
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// Data related to the underlying digraph
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const GR &_graph;
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int _node_num;
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int _arc_num;
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int _all_arc_num;
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int _search_arc_num;
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// Parameters of the problem
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bool _has_lower;
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SupplyType _stype;
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Value _sum_supply;
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// Data structures for storing the digraph
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IntNodeMap _node_id;
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IntArcMap _arc_id;
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IntVector _source;
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IntVector _target;
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bool _arc_mixing;
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// Node and arc data
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ValueVector _lower;
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ValueVector _upper;
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ValueVector _cap;
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CostVector _cost;
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ValueVector _supply;
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ValueVector _flow;
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CostVector _pi;
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// Data for storing the spanning tree structure
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IntVector _parent;
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IntVector _pred;
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IntVector _thread;
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IntVector _rev_thread;
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IntVector _succ_num;
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IntVector _last_succ;
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CharVector _pred_dir;
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CharVector _state;
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IntVector _dirty_revs;
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int _root;
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// Temporary data used in the current pivot iteration
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int in_arc, join, u_in, v_in, u_out, v_out;
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Value delta;
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const Value MAX;
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public:
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/// \brief Constant for infinite upper bounds (capacities).
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///
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/// Constant for infinite upper bounds (capacities).
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/// It is \c std::numeric_limits<Value>::infinity() if available,
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/// \c std::numeric_limits<Value>::max() otherwise.
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const Value INF;
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private:
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// Implementation of the First Eligible pivot rule
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class FirstEligiblePivotRule
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{
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private:
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// References to the NetworkSimplex class
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const IntVector &_source;
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const IntVector &_target;
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const CostVector &_cost;
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const CharVector &_state;
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const CostVector &_pi;
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int &_in_arc;
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int _search_arc_num;
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// Pivot rule data
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int _next_arc;
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public:
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// Constructor
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FirstEligiblePivotRule(NetworkSimplex &ns) :
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_source(ns._source), _target(ns._target),
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_cost(ns._cost), _state(ns._state), _pi(ns._pi),
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_in_arc(ns.in_arc), _search_arc_num(ns._search_arc_num),
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_next_arc(0)
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{}
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// Find next entering arc
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bool findEnteringArc() {
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Cost c;
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for (int e = _next_arc; e != _search_arc_num; ++e) {
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c = _state[e] * (_cost[e] + _pi[_source[e]] - _pi[_target[e]]);
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if (c < 0) {
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_in_arc = e;
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_next_arc = e + 1;
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return true;
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}
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}
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for (int e = 0; e != _next_arc; ++e) {
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c = _state[e] * (_cost[e] + _pi[_source[e]] - _pi[_target[e]]);
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if (c < 0) {
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_in_arc = e;
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_next_arc = e + 1;
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return true;
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}
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}
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return false;
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}
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}; //class FirstEligiblePivotRule
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// Implementation of the Best Eligible pivot rule
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class BestEligiblePivotRule
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{
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private:
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// References to the NetworkSimplex class
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const IntVector &_source;
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const IntVector &_target;
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const CostVector &_cost;
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const CharVector &_state;
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const CostVector &_pi;
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int &_in_arc;
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int _search_arc_num;
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public:
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// Constructor
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BestEligiblePivotRule(NetworkSimplex &ns) :
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_source(ns._source), _target(ns._target),
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_cost(ns._cost), _state(ns._state), _pi(ns._pi),
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_in_arc(ns.in_arc), _search_arc_num(ns._search_arc_num)
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{}
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// Find next entering arc
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bool findEnteringArc() {
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Cost c, min = 0;
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for (int e = 0; e != _search_arc_num; ++e) {
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c = _state[e] * (_cost[e] + _pi[_source[e]] - _pi[_target[e]]);
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if (c < min) {
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min = c;
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_in_arc = e;
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}
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}
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return min < 0;
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}
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}; //class BestEligiblePivotRule
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// Implementation of the Block Search pivot rule
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class BlockSearchPivotRule
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{
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private:
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// References to the NetworkSimplex class
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const IntVector &_source;
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const IntVector &_target;
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const CostVector &_cost;
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const CharVector &_state;
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const CostVector &_pi;
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int &_in_arc;
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int _search_arc_num;
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// Pivot rule data
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int _block_size;
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int _next_arc;
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public:
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// Constructor
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BlockSearchPivotRule(NetworkSimplex &ns) :
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_source(ns._source), _target(ns._target),
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_cost(ns._cost), _state(ns._state), _pi(ns._pi),
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_in_arc(ns.in_arc), _search_arc_num(ns._search_arc_num),
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_next_arc(0)
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{
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// The main parameters of the pivot rule
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const double BLOCK_SIZE_FACTOR = 1.0;
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const int MIN_BLOCK_SIZE = 10;
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_block_size = std::max( int(BLOCK_SIZE_FACTOR *
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std::sqrt(double(_search_arc_num))),
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MIN_BLOCK_SIZE );
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}
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// Find next entering arc
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bool findEnteringArc() {
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Cost c, min = 0;
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int cnt = _block_size;
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int e;
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for (e = _next_arc; e != _search_arc_num; ++e) {
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c = _state[e] * (_cost[e] + _pi[_source[e]] - _pi[_target[e]]);
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if (c < min) {
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min = c;
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_in_arc = e;
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}
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if (--cnt == 0) {
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if (min < 0) goto search_end;
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cnt = _block_size;
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}
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}
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for (e = 0; e != _next_arc; ++e) {
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c = _state[e] * (_cost[e] + _pi[_source[e]] - _pi[_target[e]]);
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if (c < min) {
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min = c;
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_in_arc = e;
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}
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if (--cnt == 0) {
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if (min < 0) goto search_end;
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cnt = _block_size;
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}
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}
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if (min >= 0) return false;
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search_end:
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_next_arc = e;
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return true;
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}
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}; //class BlockSearchPivotRule
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// Implementation of the Candidate List pivot rule
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class CandidateListPivotRule
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{
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private:
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// References to the NetworkSimplex class
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const IntVector &_source;
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const IntVector &_target;
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const CostVector &_cost;
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const CharVector &_state;
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const CostVector &_pi;
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int &_in_arc;
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int _search_arc_num;
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// Pivot rule data
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IntVector _candidates;
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int _list_length, _minor_limit;
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int _curr_length, _minor_count;
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int _next_arc;
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public:
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/// Constructor
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CandidateListPivotRule(NetworkSimplex &ns) :
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_source(ns._source), _target(ns._target),
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_cost(ns._cost), _state(ns._state), _pi(ns._pi),
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_in_arc(ns.in_arc), _search_arc_num(ns._search_arc_num),
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_next_arc(0)
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{
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// The main parameters of the pivot rule
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const double LIST_LENGTH_FACTOR = 0.25;
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const int MIN_LIST_LENGTH = 10;
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const double MINOR_LIMIT_FACTOR = 0.1;
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const int MIN_MINOR_LIMIT = 3;
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_list_length = std::max( int(LIST_LENGTH_FACTOR *
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std::sqrt(double(_search_arc_num))),
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MIN_LIST_LENGTH );
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_minor_limit = std::max( int(MINOR_LIMIT_FACTOR * _list_length),
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MIN_MINOR_LIMIT );
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_curr_length = _minor_count = 0;
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_candidates.resize(_list_length);
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}
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/// Find next entering arc
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bool findEnteringArc() {
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Cost min, c;
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int e;
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if (_curr_length > 0 && _minor_count < _minor_limit) {
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// Minor iteration: select the best eligible arc from the
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// current candidate list
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++_minor_count;
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min = 0;
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for (int i = 0; i < _curr_length; ++i) {
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e = _candidates[i];
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c = _state[e] * (_cost[e] + _pi[_source[e]] - _pi[_target[e]]);
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if (c < min) {
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min = c;
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_in_arc = e;
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}
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else if (c >= 0) {
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_candidates[i--] = _candidates[--_curr_length];
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}
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}
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if (min < 0) return true;
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}
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// Major iteration: build a new candidate list
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min = 0;
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_curr_length = 0;
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for (e = _next_arc; e != _search_arc_num; ++e) {
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c = _state[e] * (_cost[e] + _pi[_source[e]] - _pi[_target[e]]);
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if (c < 0) {
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_candidates[_curr_length++] = e;
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if (c < min) {
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min = c;
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_in_arc = e;
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}
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if (_curr_length == _list_length) goto search_end;
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}
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}
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for (e = 0; e != _next_arc; ++e) {
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c = _state[e] * (_cost[e] + _pi[_source[e]] - _pi[_target[e]]);
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if (c < 0) {
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_candidates[_curr_length++] = e;
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if (c < min) {
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min = c;
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_in_arc = e;
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}
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if (_curr_length == _list_length) goto search_end;
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}
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}
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if (_curr_length == 0) return false;
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search_end:
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_minor_count = 1;
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_next_arc = e;
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return true;
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}
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}; //class CandidateListPivotRule
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|
|
|
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// Implementation of the Altering Candidate List pivot rule
|
|
class AlteringListPivotRule
|
|
{
|
|
private:
|
|
|
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// References to the NetworkSimplex class
|
|
const IntVector &_source;
|
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const IntVector &_target;
|
|
const CostVector &_cost;
|
|
const CharVector &_state;
|
|
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;
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|
|
|
// Functor class to compare arcs during sort of the candidate list
|
|
class SortFunc
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|
{
|
|
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;
|
|
|
|
public:
|
|
|
|
// Constructor
|
|
AlteringListPivotRule(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), _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 = 0.01;
|
|
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;
|
|
Cost c;
|
|
for (int i = 0; i != _curr_length; ++i) {
|
|
e = _candidates[i];
|
|
c = _state[e] * (_cost[e] + _pi[_source[e]] - _pi[_target[e]]);
|
|
if (c < 0) {
|
|
_cand_cost[e] = c;
|
|
} else {
|
|
_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) {
|
|
c = _state[e] * (_cost[e] + _pi[_source[e]] - _pi[_target[e]]);
|
|
if (c < 0) {
|
|
_cand_cost[e] = c;
|
|
_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) {
|
|
c = _state[e] * (_cost[e] + _pi[_source[e]] - _pi[_target[e]]);
|
|
if (c < 0) {
|
|
_cand_cost[e] = c;
|
|
_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:
|
|
|
|
// Perform partial sort operation on the candidate list
|
|
int new_length = std::min(_head_length + 1, _curr_length);
|
|
std::partial_sort(_candidates.begin(), _candidates.begin() + new_length,
|
|
_candidates.begin() + _curr_length, _sort_func);
|
|
|
|
// Select the entering arc and remove it from the list
|
|
_in_arc = _candidates[0];
|
|
_next_arc = e;
|
|
_candidates[0] = _candidates[new_length - 1];
|
|
_curr_length = new_length - 1;
|
|
return true;
|
|
}
|
|
|
|
}; //class AlteringListPivotRule
|
|
|
|
public:
|
|
|
|
/// \brief Constructor.
|
|
///
|
|
/// The constructor of the class.
|
|
///
|
|
/// \param graph The digraph the algorithm runs on.
|
|
/// \param arc_mixing Indicate if the arcs will be stored in a
|
|
/// mixed order in the internal data structure.
|
|
/// In general, it leads to similar performance as using the original
|
|
/// arc order, but it makes the algorithm more robust and in special
|
|
/// cases, even significantly faster. Therefore, it is enabled by default.
|
|
NetworkSimplex(const GR& graph, bool arc_mixing = true) :
|
|
_graph(graph), _node_id(graph), _arc_id(graph),
|
|
_arc_mixing(arc_mixing),
|
|
MAX(std::numeric_limits<Value>::max()),
|
|
INF(std::numeric_limits<Value>::has_infinity ?
|
|
std::numeric_limits<Value>::infinity() : MAX)
|
|
{
|
|
// Check the number types
|
|
LEMON_ASSERT(std::numeric_limits<Value>::is_signed,
|
|
"The flow type of NetworkSimplex must be signed");
|
|
LEMON_ASSERT(std::numeric_limits<Cost>::is_signed,
|
|
"The cost type of NetworkSimplex must be signed");
|
|
|
|
// Reset data structures
|
|
reset();
|
|
}
|
|
|
|
/// \name Parameters
|
|
/// The parameters of the algorithm can be specified using these
|
|
/// functions.
|
|
|
|
/// @{
|
|
|
|
/// \brief Set the lower bounds on the arcs.
|
|
///
|
|
/// This function sets the lower bounds on the arcs.
|
|
/// If it is not used before calling \ref run(), the lower bounds
|
|
/// will be set to zero on all arcs.
|
|
///
|
|
/// \param map An arc map storing the lower bounds.
|
|
/// Its \c Value type must be convertible to the \c Value type
|
|
/// of the algorithm.
|
|
///
|
|
/// \return <tt>(*this)</tt>
|
|
template <typename LowerMap>
|
|
NetworkSimplex& lowerMap(const LowerMap& map) {
|
|
_has_lower = true;
|
|
for (ArcIt a(_graph); a != INVALID; ++a) {
|
|
_lower[_arc_id[a]] = map[a];
|
|
}
|
|
return *this;
|
|
}
|
|
|
|
/// \brief Set the upper bounds (capacities) on the arcs.
|
|
///
|
|
/// This function sets the upper bounds (capacities) on the arcs.
|
|
/// If it is not used before calling \ref run(), the upper bounds
|
|
/// will be set to \ref INF on all arcs (i.e. the flow value will be
|
|
/// unbounded from above).
|
|
///
|
|
/// \param map An arc map storing the upper bounds.
|
|
/// Its \c Value type must be convertible to the \c Value type
|
|
/// of the algorithm.
|
|
///
|
|
/// \return <tt>(*this)</tt>
|
|
template<typename UpperMap>
|
|
NetworkSimplex& upperMap(const UpperMap& map) {
|
|
for (ArcIt a(_graph); a != INVALID; ++a) {
|
|
_upper[_arc_id[a]] = map[a];
|
|
}
|
|
return *this;
|
|
}
|
|
|
|
/// \brief Set the costs of the arcs.
|
|
///
|
|
/// This function sets the costs of the arcs.
|
|
/// If it is not used before calling \ref run(), the costs
|
|
/// will be set to \c 1 on all arcs.
|
|
///
|
|
/// \param map An arc map storing the costs.
|
|
/// Its \c Value type must be convertible to the \c Cost type
|
|
/// of the algorithm.
|
|
///
|
|
/// \return <tt>(*this)</tt>
|
|
template<typename CostMap>
|
|
NetworkSimplex& costMap(const CostMap& map) {
|
|
for (ArcIt a(_graph); a != INVALID; ++a) {
|
|
_cost[_arc_id[a]] = map[a];
|
|
}
|
|
return *this;
|
|
}
|
|
|
|
/// \brief Set the supply values of the nodes.
|
|
///
|
|
/// This function sets the supply values of the nodes.
|
|
/// If neither this function nor \ref stSupply() is used before
|
|
/// calling \ref run(), the supply of each node will be set to zero.
|
|
///
|
|
/// \param map A node map storing the supply values.
|
|
/// Its \c Value type must be convertible to the \c Value type
|
|
/// of the algorithm.
|
|
///
|
|
/// \return <tt>(*this)</tt>
|
|
///
|
|
/// \sa supplyType()
|
|
template<typename SupplyMap>
|
|
NetworkSimplex& supplyMap(const SupplyMap& map) {
|
|
for (NodeIt n(_graph); n != INVALID; ++n) {
|
|
_supply[_node_id[n]] = map[n];
|
|
}
|
|
return *this;
|
|
}
|
|
|
|
/// \brief Set single source and target nodes and a supply value.
|
|
///
|
|
/// This function sets a single source node and a single target node
|
|
/// and the required flow value.
|
|
/// If neither this function nor \ref supplyMap() is used before
|
|
/// calling \ref run(), the supply of each node will be set to zero.
|
|
///
|
|
/// Using this function has the same effect as using \ref supplyMap()
|
|
/// with a map in which \c k is assigned to \c s, \c -k is
|
|
/// assigned to \c t and all other nodes have zero supply value.
|
|
///
|
|
/// \param s The source node.
|
|
/// \param t The target node.
|
|
/// \param k The required amount of flow from node \c s to node \c t
|
|
/// (i.e. the supply of \c s and the demand of \c t).
|
|
///
|
|
/// \return <tt>(*this)</tt>
|
|
NetworkSimplex& stSupply(const Node& s, const Node& t, Value k) {
|
|
for (int i = 0; i != _node_num; ++i) {
|
|
_supply[i] = 0;
|
|
}
|
|
_supply[_node_id[s]] = k;
|
|
_supply[_node_id[t]] = -k;
|
|
return *this;
|
|
}
|
|
|
|
/// \brief Set the type of the supply constraints.
|
|
///
|
|
/// This function sets the type of the supply/demand constraints.
|
|
/// If it is not used before calling \ref run(), the \ref GEQ supply
|
|
/// type will be used.
|
|
///
|
|
/// For more information, see \ref SupplyType.
|
|
///
|
|
/// \return <tt>(*this)</tt>
|
|
NetworkSimplex& supplyType(SupplyType supply_type) {
|
|
_stype = supply_type;
|
|
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(),
|
|
/// \ref supplyType().
|
|
/// For example,
|
|
/// \code
|
|
/// NetworkSimplex<ListDigraph> ns(graph);
|
|
/// ns.lowerMap(lower).upperMap(upper).costMap(cost)
|
|
/// .supplyMap(sup).run();
|
|
/// \endcode
|
|
///
|
|
/// This function can be called more than once. All the given parameters
|
|
/// are kept for the next call, unless \ref resetParams() or \ref reset()
|
|
/// is used, thus only the modified parameters have to be set again.
|
|
/// If the underlying digraph was also modified after the construction
|
|
/// of the class (or the last \ref reset() call), then the \ref reset()
|
|
/// function must be called.
|
|
///
|
|
/// \param pivot_rule The pivot rule that will be used during the
|
|
/// algorithm. For more information, see \ref PivotRule.
|
|
///
|
|
/// \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 objective function of the problem is
|
|
/// unbounded, i.e. there is a directed cycle having negative total
|
|
/// cost and infinite upper bound.
|
|
///
|
|
/// \see ProblemType, PivotRule
|
|
/// \see resetParams(), reset()
|
|
ProblemType run(PivotRule pivot_rule = BLOCK_SEARCH) {
|
|
if (!init()) return INFEASIBLE;
|
|
return start(pivot_rule);
|
|
}
|
|
|
|
/// \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(), \ref supplyType().
|
|
///
|
|
/// It is useful for multiple \ref run() calls. Basically, all the given
|
|
/// parameters are kept for the next \ref run() call, unless
|
|
/// \ref resetParams() or \ref reset() is used.
|
|
/// If the underlying digraph was also modified after the construction
|
|
/// of the class or the last \ref reset() call, then the \ref reset()
|
|
/// function must be used, otherwise \ref resetParams() is sufficient.
|
|
///
|
|
/// For example,
|
|
/// \code
|
|
/// NetworkSimplex<ListDigraph> ns(graph);
|
|
///
|
|
/// // First run
|
|
/// ns.lowerMap(lower).upperMap(upper).costMap(cost)
|
|
/// .supplyMap(sup).run();
|
|
///
|
|
/// // Run again with modified cost map (resetParams() is not called,
|
|
/// // so only the cost map have to be set again)
|
|
/// cost[e] += 100;
|
|
/// ns.costMap(cost).run();
|
|
///
|
|
/// // Run again from scratch using resetParams()
|
|
/// // (the lower bounds will be set to zero on all arcs)
|
|
/// ns.resetParams();
|
|
/// ns.upperMap(capacity).costMap(cost)
|
|
/// .supplyMap(sup).run();
|
|
/// \endcode
|
|
///
|
|
/// \return <tt>(*this)</tt>
|
|
///
|
|
/// \see reset(), run()
|
|
NetworkSimplex& resetParams() {
|
|
for (int i = 0; i != _node_num; ++i) {
|
|
_supply[i] = 0;
|
|
}
|
|
for (int i = 0; i != _arc_num; ++i) {
|
|
_lower[i] = 0;
|
|
_upper[i] = INF;
|
|
_cost[i] = 1;
|
|
}
|
|
_has_lower = false;
|
|
_stype = GEQ;
|
|
return *this;
|
|
}
|
|
|
|
/// \brief Reset the internal data structures and all the parameters
|
|
/// that have been given before.
|
|
///
|
|
/// This function resets the internal data structures and all the
|
|
/// paramaters that have been given before using functions \ref lowerMap(),
|
|
/// \ref upperMap(), \ref costMap(), \ref supplyMap(), \ref stSupply(),
|
|
/// \ref supplyType().
|
|
///
|
|
/// It is useful for multiple \ref run() calls. Basically, all the given
|
|
/// parameters are kept for the next \ref run() call, unless
|
|
/// \ref resetParams() or \ref reset() is used.
|
|
/// If the underlying digraph was also modified after the construction
|
|
/// of the class or the last \ref reset() call, then the \ref reset()
|
|
/// function must be used, otherwise \ref resetParams() is sufficient.
|
|
///
|
|
/// See \ref resetParams() for examples.
|
|
///
|
|
/// \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);
|
|
_pred_dir.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 && _node_num > 1) {
|
|
// Store the arcs in a mixed order
|
|
const int skip = std::max(_arc_num / _node_num, 3);
|
|
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 += skip) >= _arc_num) i = ++j;
|
|
}
|
|
} else {
|
|
// Store the arcs in the original order
|
|
int i = 0;
|
|
for (ArcIt a(_graph); a != INVALID; ++a, ++i) {
|
|
_arc_id[a] = i;
|
|
_source[i] = _node_id[_graph.source(a)];
|
|
_target[i] = _node_id[_graph.target(a)];
|
|
}
|
|
}
|
|
|
|
// Reset parameters
|
|
resetParams();
|
|
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(m).
|
|
///
|
|
/// \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 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_id[a];
|
|
c += Number(_flow[i]) * 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 _flow[_arc_id[a]];
|
|
}
|
|
|
|
/// \brief Copy the flow values (the primal solution) into the
|
|
/// given map.
|
|
///
|
|
/// 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, _flow[_arc_id[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 Copy the potential values (the dual solution) into the
|
|
/// given map.
|
|
///
|
|
/// 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.
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///
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/// \pre \ref run() must be called before using this function.
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template <typename PotentialMap>
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void potentialMap(PotentialMap &map) const {
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for (NodeIt n(_graph); n != INVALID; ++n) {
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map.set(n, _pi[_node_id[n]]);
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}
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}
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/// @}
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private:
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// Initialize internal data structures
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bool init() {
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if (_node_num == 0) return false;
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// Check the sum of supply values
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_sum_supply = 0;
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for (int i = 0; i != _node_num; ++i) {
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_sum_supply += _supply[i];
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}
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if ( !((_stype == GEQ && _sum_supply <= 0) ||
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(_stype == LEQ && _sum_supply >= 0)) ) return false;
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// Check lower and upper bounds
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LEMON_DEBUG(checkBoundMaps(),
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"Upper bounds must be greater or equal to the lower bounds");
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// Remove non-zero lower bounds
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if (_has_lower) {
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for (int i = 0; i != _arc_num; ++i) {
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Value c = _lower[i];
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if (c >= 0) {
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_cap[i] = _upper[i] < MAX ? _upper[i] - c : INF;
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} else {
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_cap[i] = _upper[i] < MAX + c ? _upper[i] - c : INF;
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}
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_supply[_source[i]] -= c;
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_supply[_target[i]] += c;
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}
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} else {
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for (int i = 0; i != _arc_num; ++i) {
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_cap[i] = _upper[i];
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}
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}
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// Initialize artifical cost
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Cost ART_COST;
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if (std::numeric_limits<Cost>::is_exact) {
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ART_COST = std::numeric_limits<Cost>::max() / 2 + 1;
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} else {
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ART_COST = 0;
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for (int i = 0; i != _arc_num; ++i) {
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if (_cost[i] > ART_COST) ART_COST = _cost[i];
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}
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ART_COST = (ART_COST + 1) * _node_num;
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}
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// Initialize arc maps
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for (int i = 0; i != _arc_num; ++i) {
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_flow[i] = 0;
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_state[i] = STATE_LOWER;
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}
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// Set data for the artificial root node
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_root = _node_num;
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_parent[_root] = -1;
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_pred[_root] = -1;
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_thread[_root] = 0;
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_rev_thread[0] = _root;
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_succ_num[_root] = _node_num + 1;
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_last_succ[_root] = _root - 1;
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_supply[_root] = -_sum_supply;
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_pi[_root] = 0;
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// Add artificial arcs and initialize the spanning tree data structure
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if (_sum_supply == 0) {
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// EQ supply constraints
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_search_arc_num = _arc_num;
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_all_arc_num = _arc_num + _node_num;
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for (int u = 0, e = _arc_num; u != _node_num; ++u, ++e) {
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_parent[u] = _root;
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_pred[u] = e;
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_thread[u] = u + 1;
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_rev_thread[u + 1] = u;
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_succ_num[u] = 1;
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_last_succ[u] = u;
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_cap[e] = INF;
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_state[e] = STATE_TREE;
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if (_supply[u] >= 0) {
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_pred_dir[u] = DIR_UP;
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_pi[u] = 0;
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_source[e] = u;
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_target[e] = _root;
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_flow[e] = _supply[u];
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_cost[e] = 0;
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} else {
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_pred_dir[u] = DIR_DOWN;
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_pi[u] = ART_COST;
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_source[e] = _root;
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_target[e] = u;
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_flow[e] = -_supply[u];
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_cost[e] = ART_COST;
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}
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}
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}
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else if (_sum_supply > 0) {
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// LEQ supply constraints
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_search_arc_num = _arc_num + _node_num;
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int f = _arc_num + _node_num;
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for (int u = 0, e = _arc_num; u != _node_num; ++u, ++e) {
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_parent[u] = _root;
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_thread[u] = u + 1;
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_rev_thread[u + 1] = u;
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_succ_num[u] = 1;
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_last_succ[u] = u;
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if (_supply[u] >= 0) {
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_pred_dir[u] = DIR_UP;
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_pi[u] = 0;
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_pred[u] = e;
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_source[e] = u;
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_target[e] = _root;
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_cap[e] = INF;
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_flow[e] = _supply[u];
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_cost[e] = 0;
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_state[e] = STATE_TREE;
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} else {
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_pred_dir[u] = DIR_DOWN;
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_pi[u] = ART_COST;
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_pred[u] = f;
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_source[f] = _root;
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_target[f] = u;
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_cap[f] = INF;
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_flow[f] = -_supply[u];
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_cost[f] = ART_COST;
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_state[f] = STATE_TREE;
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_source[e] = u;
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_target[e] = _root;
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_cap[e] = INF;
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_flow[e] = 0;
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_cost[e] = 0;
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_state[e] = STATE_LOWER;
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++f;
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}
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}
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_all_arc_num = f;
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}
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else {
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// GEQ supply constraints
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_search_arc_num = _arc_num + _node_num;
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int f = _arc_num + _node_num;
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for (int u = 0, e = _arc_num; u != _node_num; ++u, ++e) {
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_parent[u] = _root;
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_thread[u] = u + 1;
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_rev_thread[u + 1] = u;
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_succ_num[u] = 1;
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_last_succ[u] = u;
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if (_supply[u] <= 0) {
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_pred_dir[u] = DIR_DOWN;
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_pi[u] = 0;
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_pred[u] = e;
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_source[e] = _root;
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_target[e] = u;
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_cap[e] = INF;
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_flow[e] = -_supply[u];
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_cost[e] = 0;
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_state[e] = STATE_TREE;
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} else {
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_pred_dir[u] = DIR_UP;
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_pi[u] = -ART_COST;
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_pred[u] = f;
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_source[f] = u;
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_target[f] = _root;
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_cap[f] = INF;
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_flow[f] = _supply[u];
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_state[f] = STATE_TREE;
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_cost[f] = ART_COST;
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_source[e] = _root;
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_target[e] = u;
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_cap[e] = INF;
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_flow[e] = 0;
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_cost[e] = 0;
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_state[e] = STATE_LOWER;
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++f;
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}
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}
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_all_arc_num = f;
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}
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return true;
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}
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// Check if the upper bound is greater than or equal to the lower bound
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// on each arc.
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bool checkBoundMaps() {
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for (int j = 0; j != _arc_num; ++j) {
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if (_upper[j] < _lower[j]) return false;
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}
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return true;
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}
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// Find the join node
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void findJoinNode() {
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int u = _source[in_arc];
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int v = _target[in_arc];
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while (u != v) {
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if (_succ_num[u] < _succ_num[v]) {
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u = _parent[u];
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} else {
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v = _parent[v];
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}
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}
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join = u;
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}
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// Find the leaving arc of the cycle and returns true if the
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// leaving arc is not the same as the entering arc
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bool findLeavingArc() {
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// Initialize first and second nodes according to the direction
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// of the cycle
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int first, second;
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if (_state[in_arc] == STATE_LOWER) {
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first = _source[in_arc];
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second = _target[in_arc];
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} else {
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first = _target[in_arc];
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second = _source[in_arc];
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}
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delta = _cap[in_arc];
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int result = 0;
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Value c, d;
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int e;
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// Search the cycle form the first node to the join node
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for (int u = first; u != join; u = _parent[u]) {
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e = _pred[u];
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d = _flow[e];
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if (_pred_dir[u] == DIR_DOWN) {
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c = _cap[e];
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d = c >= MAX ? INF : c - d;
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}
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if (d < delta) {
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delta = d;
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u_out = u;
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result = 1;
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}
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}
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// Search the cycle form the second node to the join node
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for (int u = second; u != join; u = _parent[u]) {
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e = _pred[u];
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d = _flow[e];
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if (_pred_dir[u] == DIR_UP) {
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c = _cap[e];
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d = c >= MAX ? INF : c - d;
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}
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if (d <= delta) {
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delta = d;
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u_out = u;
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result = 2;
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}
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}
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if (result == 1) {
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u_in = first;
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v_in = second;
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} else {
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u_in = second;
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v_in = first;
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}
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return result != 0;
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}
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// Change _flow and _state vectors
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void changeFlow(bool change) {
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// Augment along the cycle
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if (delta > 0) {
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Value val = _state[in_arc] * delta;
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_flow[in_arc] += val;
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for (int u = _source[in_arc]; u != join; u = _parent[u]) {
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_flow[_pred[u]] -= _pred_dir[u] * val;
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}
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for (int u = _target[in_arc]; u != join; u = _parent[u]) {
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_flow[_pred[u]] += _pred_dir[u] * val;
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}
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}
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// Update the state of the entering and leaving arcs
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if (change) {
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_state[in_arc] = STATE_TREE;
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_state[_pred[u_out]] =
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(_flow[_pred[u_out]] == 0) ? STATE_LOWER : STATE_UPPER;
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} else {
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_state[in_arc] = -_state[in_arc];
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}
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}
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// Update the tree structure
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void updateTreeStructure() {
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int old_rev_thread = _rev_thread[u_out];
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int old_succ_num = _succ_num[u_out];
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int old_last_succ = _last_succ[u_out];
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v_out = _parent[u_out];
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// Check if u_in and u_out coincide
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if (u_in == u_out) {
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// Update _parent, _pred, _pred_dir
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_parent[u_in] = v_in;
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_pred[u_in] = in_arc;
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_pred_dir[u_in] = u_in == _source[in_arc] ? DIR_UP : DIR_DOWN;
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// Update _thread and _rev_thread
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if (_thread[v_in] != u_out) {
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int after = _thread[old_last_succ];
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_thread[old_rev_thread] = after;
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_rev_thread[after] = old_rev_thread;
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after = _thread[v_in];
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_thread[v_in] = u_out;
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_rev_thread[u_out] = v_in;
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_thread[old_last_succ] = after;
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_rev_thread[after] = old_last_succ;
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}
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} else {
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// Handle the case when old_rev_thread equals to v_in
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// (it also means that join and v_out coincide)
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int thread_continue = old_rev_thread == v_in ?
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_thread[old_last_succ] : _thread[v_in];
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// Update _thread and _parent along the stem nodes (i.e. the nodes
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// between u_in and u_out, whose parent have to be changed)
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int stem = u_in; // the current stem node
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int par_stem = v_in; // the new parent of stem
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int next_stem; // the next stem node
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int last = _last_succ[u_in]; // the last successor of stem
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int before, after = _thread[last];
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_thread[v_in] = u_in;
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_dirty_revs.clear();
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_dirty_revs.push_back(v_in);
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while (stem != u_out) {
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// Insert the next stem node into the thread list
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next_stem = _parent[stem];
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_thread[last] = next_stem;
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_dirty_revs.push_back(last);
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// Remove the subtree of stem from the thread list
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before = _rev_thread[stem];
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_thread[before] = after;
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_rev_thread[after] = before;
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// Change the parent node and shift stem nodes
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_parent[stem] = par_stem;
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par_stem = stem;
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stem = next_stem;
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// Update last and after
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last = _last_succ[stem] == _last_succ[par_stem] ?
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_rev_thread[par_stem] : _last_succ[stem];
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after = _thread[last];
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}
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_parent[u_out] = par_stem;
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_thread[last] = thread_continue;
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_rev_thread[thread_continue] = last;
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_last_succ[u_out] = last;
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// Remove the subtree of u_out from the thread list except for
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// the case when old_rev_thread equals to v_in
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if (old_rev_thread != v_in) {
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_thread[old_rev_thread] = after;
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_rev_thread[after] = old_rev_thread;
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}
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// Update _rev_thread using the new _thread values
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for (int i = 0; i != int(_dirty_revs.size()); ++i) {
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int u = _dirty_revs[i];
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_rev_thread[_thread[u]] = u;
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}
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// Update _pred, _pred_dir, _last_succ and _succ_num for the
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// stem nodes from u_out to u_in
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int tmp_sc = 0, tmp_ls = _last_succ[u_out];
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for (int u = u_out, p = _parent[u]; u != u_in; u = p, p = _parent[u]) {
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_pred[u] = _pred[p];
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_pred_dir[u] = -_pred_dir[p];
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tmp_sc += _succ_num[u] - _succ_num[p];
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_succ_num[u] = tmp_sc;
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_last_succ[p] = tmp_ls;
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}
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_pred[u_in] = in_arc;
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_pred_dir[u_in] = u_in == _source[in_arc] ? DIR_UP : DIR_DOWN;
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_succ_num[u_in] = old_succ_num;
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}
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// Update _last_succ from v_in towards the root
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int up_limit_out = _last_succ[join] == v_in ? join : -1;
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int last_succ_out = _last_succ[u_out];
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for (int u = v_in; u != -1 && _last_succ[u] == v_in; u = _parent[u]) {
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_last_succ[u] = last_succ_out;
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}
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|
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// Update _last_succ from v_out towards the root
|
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if (join != old_rev_thread && v_in != old_rev_thread) {
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for (int u = v_out; u != up_limit_out && _last_succ[u] == old_last_succ;
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u = _parent[u]) {
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_last_succ[u] = old_rev_thread;
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}
|
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}
|
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else if (last_succ_out != old_last_succ) {
|
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for (int u = v_out; u != up_limit_out && _last_succ[u] == old_last_succ;
|
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u = _parent[u]) {
|
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_last_succ[u] = last_succ_out;
|
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}
|
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}
|
|
|
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// Update _succ_num from v_in to join
|
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for (int u = v_in; u != join; u = _parent[u]) {
|
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_succ_num[u] += old_succ_num;
|
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}
|
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// Update _succ_num from v_out to join
|
|
for (int u = v_out; u != join; u = _parent[u]) {
|
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_succ_num[u] -= old_succ_num;
|
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}
|
|
}
|
|
|
|
// Update potentials in the subtree that has been moved
|
|
void updatePotential() {
|
|
Cost sigma = _pi[v_in] - _pi[u_in] -
|
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_pred_dir[u_in] * _cost[in_arc];
|
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int end = _thread[_last_succ[u_in]];
|
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for (int u = u_in; u != end; u = _thread[u]) {
|
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_pi[u] += sigma;
|
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}
|
|
}
|
|
|
|
// 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;
|
|
if (_sum_supply >= 0) {
|
|
if (supply_nodes.size() == 1 && demand_nodes.size() == 1) {
|
|
// Perform a reverse graph search from the sink to the source
|
|
typename GR::template NodeMap<bool> reached(_graph, false);
|
|
Node s = supply_nodes[0], t = demand_nodes[0];
|
|
std::vector<Node> stack;
|
|
reached[t] = true;
|
|
stack.push_back(t);
|
|
while (!stack.empty()) {
|
|
Node u, v = stack.back();
|
|
stack.pop_back();
|
|
if (v == s) break;
|
|
for (InArcIt a(_graph, v); a != INVALID; ++a) {
|
|
if (reached[u = _graph.source(a)]) continue;
|
|
int j = _arc_id[a];
|
|
if (_cap[j] >= total) {
|
|
arc_vector.push_back(j);
|
|
reached[u] = true;
|
|
stack.push_back(u);
|
|
}
|
|
}
|
|
}
|
|
} else {
|
|
// Find the min. cost incoming arc for each demand node
|
|
for (int i = 0; i != int(demand_nodes.size()); ++i) {
|
|
Node v = demand_nodes[i];
|
|
Cost c, min_cost = std::numeric_limits<Cost>::max();
|
|
Arc min_arc = INVALID;
|
|
for (InArcIt a(_graph, v); a != INVALID; ++a) {
|
|
c = _cost[_arc_id[a]];
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if (c < min_cost) {
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min_cost = c;
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min_arc = a;
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|
}
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|
}
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if (min_arc != INVALID) {
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arc_vector.push_back(_arc_id[min_arc]);
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}
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|
}
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|
}
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} else {
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// Find the min. cost outgoing arc for each supply node
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for (int i = 0; i != int(supply_nodes.size()); ++i) {
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Node u = supply_nodes[i];
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Cost c, min_cost = std::numeric_limits<Cost>::max();
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Arc min_arc = INVALID;
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for (OutArcIt a(_graph, u); a != INVALID; ++a) {
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c = _cost[_arc_id[a]];
|
|
if (c < min_cost) {
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|
min_cost = c;
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|
min_arc = a;
|
|
}
|
|
}
|
|
if (min_arc != INVALID) {
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|
arc_vector.push_back(_arc_id[min_arc]);
|
|
}
|
|
}
|
|
}
|
|
|
|
// Perform heuristic initial pivots
|
|
for (int i = 0; i != int(arc_vector.size()); ++i) {
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|
in_arc = arc_vector[i];
|
|
if (_state[in_arc] * (_cost[in_arc] + _pi[_source[in_arc]] -
|
|
_pi[_target[in_arc]]) >= 0) continue;
|
|
findJoinNode();
|
|
bool change = findLeavingArc();
|
|
if (delta >= MAX) return false;
|
|
changeFlow(change);
|
|
if (change) {
|
|
updateTreeStructure();
|
|
updatePotential();
|
|
}
|
|
}
|
|
return true;
|
|
}
|
|
|
|
// Execute the algorithm
|
|
ProblemType start(PivotRule pivot_rule) {
|
|
// Select the pivot rule implementation
|
|
switch (pivot_rule) {
|
|
case FIRST_ELIGIBLE:
|
|
return start<FirstEligiblePivotRule>();
|
|
case BEST_ELIGIBLE:
|
|
return start<BestEligiblePivotRule>();
|
|
case BLOCK_SEARCH:
|
|
return start<BlockSearchPivotRule>();
|
|
case CANDIDATE_LIST:
|
|
return start<CandidateListPivotRule>();
|
|
case ALTERING_LIST:
|
|
return start<AlteringListPivotRule>();
|
|
}
|
|
return INFEASIBLE; // avoid warning
|
|
}
|
|
|
|
template <typename PivotRuleImpl>
|
|
ProblemType start() {
|
|
PivotRuleImpl pivot(*this);
|
|
|
|
// Perform heuristic initial pivots
|
|
if (!initialPivots()) return UNBOUNDED;
|
|
|
|
// Execute the Network Simplex algorithm
|
|
while (pivot.findEnteringArc()) {
|
|
findJoinNode();
|
|
bool change = findLeavingArc();
|
|
if (delta >= MAX) return UNBOUNDED;
|
|
changeFlow(change);
|
|
if (change) {
|
|
updateTreeStructure();
|
|
updatePotential();
|
|
}
|
|
}
|
|
|
|
// Check feasibility
|
|
for (int e = _search_arc_num; e != _all_arc_num; ++e) {
|
|
if (_flow[e] != 0) return INFEASIBLE;
|
|
}
|
|
|
|
// Transform the solution and the supply map to the original form
|
|
if (_has_lower) {
|
|
for (int i = 0; i != _arc_num; ++i) {
|
|
Value c = _lower[i];
|
|
if (c != 0) {
|
|
_flow[i] += c;
|
|
_supply[_source[i]] += c;
|
|
_supply[_target[i]] -= c;
|
|
}
|
|
}
|
|
}
|
|
|
|
// Shift potentials to meet the requirements of the GEQ/LEQ type
|
|
// optimality conditions
|
|
if (_sum_supply == 0) {
|
|
if (_stype == GEQ) {
|
|
Cost max_pot = -std::numeric_limits<Cost>::max();
|
|
for (int i = 0; i != _node_num; ++i) {
|
|
if (_pi[i] > max_pot) max_pot = _pi[i];
|
|
}
|
|
if (max_pot > 0) {
|
|
for (int i = 0; i != _node_num; ++i)
|
|
_pi[i] -= max_pot;
|
|
}
|
|
} else {
|
|
Cost min_pot = std::numeric_limits<Cost>::max();
|
|
for (int i = 0; i != _node_num; ++i) {
|
|
if (_pi[i] < min_pot) min_pot = _pi[i];
|
|
}
|
|
if (min_pot < 0) {
|
|
for (int i = 0; i != _node_num; ++i)
|
|
_pi[i] -= min_pot;
|
|
}
|
|
}
|
|
}
|
|
|
|
return OPTIMAL;
|
|
}
|
|
|
|
}; //class NetworkSimplex
|
|
|
|
///@}
|
|
|
|
} //namespace lemon
|
|
|
|
#endif //LEMON_NETWORK_SIMPLEX_H
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