1608 lines
52 KiB
C++
Executable File
1608 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_COST_SCALING_H
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#define LEMON_COST_SCALING_H
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/// \ingroup min_cost_flow_algs
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/// \file
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/// \brief Cost scaling algorithm for finding a minimum cost flow.
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#include <vector>
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#include <deque>
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#include <limits>
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#include <lemon/core.h>
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#include <lemon/maps.h>
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#include <lemon/math.h>
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#include <lemon/static_graph.h>
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#include <lemon/circulation.h>
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#include <lemon/bellman_ford.h>
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namespace lemon {
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/// \brief Default traits class of CostScaling algorithm.
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///
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/// Default traits class of CostScaling algorithm.
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/// \tparam GR Digraph type.
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/// \tparam V The number type used for flow amounts, capacity bounds
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/// and supply values. By default it is \c int.
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/// \tparam C The number type used for costs and potentials.
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/// By default it is the same as \c V.
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#ifdef DOXYGEN
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template <typename GR, typename V = int, typename C = V>
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#else
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template < typename GR, typename V = int, typename C = V,
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bool integer = std::numeric_limits<C>::is_integer >
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#endif
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struct CostScalingDefaultTraits
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{
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/// The type of the digraph
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typedef GR Digraph;
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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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/// \brief The large cost type used for internal computations
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///
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/// The large cost type used for internal computations.
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/// It is \c long \c long if the \c Cost type is integer,
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/// otherwise it is \c double.
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/// \c Cost must be convertible to \c LargeCost.
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typedef double LargeCost;
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};
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// Default traits class for integer cost types
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template <typename GR, typename V, typename C>
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struct CostScalingDefaultTraits<GR, V, C, true>
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{
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typedef GR Digraph;
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typedef V Value;
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typedef C Cost;
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#ifdef LEMON_HAVE_LONG_LONG
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typedef long long LargeCost;
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#else
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typedef long LargeCost;
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#endif
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};
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/// \addtogroup min_cost_flow_algs
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/// @{
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/// \brief Implementation of the Cost Scaling algorithm for
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/// finding a \ref min_cost_flow "minimum cost flow".
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///
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/// \ref CostScaling implements a cost scaling algorithm that performs
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/// push/augment and relabel operations for finding a \ref min_cost_flow
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/// "minimum cost flow" \cite amo93networkflows,
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/// \cite goldberg90approximation,
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/// \cite goldberg97efficient, \cite bunnagel98efficient.
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/// It is a highly efficient primal-dual solution method, which
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/// can be viewed as the generalization of the \ref Preflow
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/// "preflow push-relabel" algorithm for the maximum flow problem.
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/// It is a polynomial algorithm, its running time complexity is
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/// \f$O(n^2m\log(nK))\f$, where <i>K</i> denotes the maximum arc cost.
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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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///
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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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/// \tparam TR The traits class that defines various types used by the
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/// algorithm. By default, it is \ref CostScalingDefaultTraits
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/// "CostScalingDefaultTraits<GR, V, C>".
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/// In most cases, this parameter should not be set directly,
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/// consider to use the named template parameters instead.
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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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/// \warning This algorithm does not support negative costs for
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/// arcs having infinite upper bound.
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///
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/// \note %CostScaling provides three different internal methods,
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/// from which the most efficient one is used by default.
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/// For more information, see \ref Method.
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#ifdef DOXYGEN
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template <typename GR, typename V, typename C, typename TR>
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#else
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template < typename GR, typename V = int, typename C = V,
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typename TR = CostScalingDefaultTraits<GR, V, C> >
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#endif
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class CostScaling
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{
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public:
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/// The type of the digraph
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typedef typename TR::Digraph Digraph;
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/// The type of the flow amounts, capacity bounds and supply values
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typedef typename TR::Value Value;
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/// The type of the arc costs
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typedef typename TR::Cost Cost;
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/// \brief The large cost type
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///
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/// The large cost type used for internal computations.
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/// By default, it is \c long \c long if the \c Cost type is integer,
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/// otherwise it is \c double.
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typedef typename TR::LargeCost LargeCost;
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/// \brief The \ref lemon::CostScalingDefaultTraits "traits class"
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/// of the algorithm
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typedef TR Traits;
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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 digraph contains an arc of negative cost and infinite
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/// upper bound. It means that the objective function is unbounded
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/// on that arc, however, note that it could actually be bounded
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/// over the feasible flows, but this algroithm cannot handle
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/// these cases.
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UNBOUNDED
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};
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/// \brief Constants for selecting the internal method.
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///
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/// Enum type containing constants for selecting the internal method
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/// for the \ref run() function.
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///
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/// \ref CostScaling provides three internal methods that differ mainly
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/// in their base operations, which are used in conjunction with the
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/// relabel operation.
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/// By default, the so called \ref PARTIAL_AUGMENT
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/// "Partial Augment-Relabel" method is used, which turned out to be
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/// the most efficient and the most robust on various test inputs.
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/// However, the other methods can be selected using the \ref run()
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/// function with the proper parameter.
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enum Method {
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/// Local push operations are used, i.e. flow is moved only on one
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/// admissible arc at once.
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PUSH,
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/// Augment operations are used, i.e. flow is moved on admissible
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/// paths from a node with excess to a node with deficit.
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AUGMENT,
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/// Partial augment operations are used, i.e. flow is moved on
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/// admissible paths started from a node with excess, but the
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/// lengths of these paths are limited. This method can be viewed
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/// as a combined version of the previous two operations.
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PARTIAL_AUGMENT
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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<LargeCost> LargeCostVector;
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typedef std::vector<char> BoolVector;
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// Note: vector<char> is used instead of vector<bool>
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// for efficiency reasons
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private:
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template <typename KT, typename VT>
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class StaticVectorMap {
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public:
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typedef KT Key;
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typedef VT Value;
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StaticVectorMap(std::vector<Value>& v) : _v(v) {}
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const Value& operator[](const Key& key) const {
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return _v[StaticDigraph::id(key)];
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}
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Value& operator[](const Key& key) {
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return _v[StaticDigraph::id(key)];
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}
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void set(const Key& key, const Value& val) {
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_v[StaticDigraph::id(key)] = val;
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}
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private:
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std::vector<Value>& _v;
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};
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typedef StaticVectorMap<StaticDigraph::Arc, LargeCost> LargeCostArcMap;
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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 _res_node_num;
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int _res_arc_num;
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int _root;
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// Parameters of the problem
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bool _has_lower;
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Value _sum_supply;
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int _sup_node_num;
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// Data structures for storing the digraph
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IntNodeMap _node_id;
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IntArcMap _arc_idf;
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IntArcMap _arc_idb;
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IntVector _first_out;
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BoolVector _forward;
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IntVector _source;
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IntVector _target;
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IntVector _reverse;
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// Node and arc data
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ValueVector _lower;
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ValueVector _upper;
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CostVector _scost;
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ValueVector _supply;
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ValueVector _res_cap;
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LargeCostVector _cost;
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LargeCostVector _pi;
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ValueVector _excess;
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IntVector _next_out;
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std::deque<int> _active_nodes;
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// Data for scaling
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LargeCost _epsilon;
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int _alpha;
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IntVector _buckets;
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IntVector _bucket_next;
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IntVector _bucket_prev;
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IntVector _rank;
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int _max_rank;
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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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public:
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/// \name Named Template Parameters
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/// @{
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template <typename T>
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struct SetLargeCostTraits : public Traits {
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typedef T LargeCost;
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};
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/// \brief \ref named-templ-param "Named parameter" for setting
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/// \c LargeCost type.
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///
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/// \ref named-templ-param "Named parameter" for setting \c LargeCost
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/// type, which is used for internal computations in the algorithm.
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/// \c Cost must be convertible to \c LargeCost.
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template <typename T>
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struct SetLargeCost
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: public CostScaling<GR, V, C, SetLargeCostTraits<T> > {
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typedef CostScaling<GR, V, C, SetLargeCostTraits<T> > Create;
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};
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/// @}
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protected:
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CostScaling() {}
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public:
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/// \brief Constructor.
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///
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/// The constructor of the class.
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///
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/// \param graph The digraph the algorithm runs on.
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CostScaling(const GR& graph) :
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_graph(graph), _node_id(graph), _arc_idf(graph), _arc_idb(graph),
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INF(std::numeric_limits<Value>::has_infinity ?
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std::numeric_limits<Value>::infinity() :
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std::numeric_limits<Value>::max())
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{
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// Check the number types
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LEMON_ASSERT(std::numeric_limits<Value>::is_signed,
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"The flow type of CostScaling must be signed");
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LEMON_ASSERT(std::numeric_limits<Cost>::is_signed,
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"The cost type of CostScaling must be signed");
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// Reset data structures
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reset();
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}
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/// \name Parameters
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/// The parameters of the algorithm can be specified using these
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/// functions.
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/// @{
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/// \brief Set the lower bounds on the arcs.
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///
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/// This function sets the lower bounds on the arcs.
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/// If it is not used before calling \ref run(), the lower bounds
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/// will be set to zero on all arcs.
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///
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/// \param map An arc map storing the lower bounds.
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/// Its \c Value type must be convertible to the \c Value type
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/// of the algorithm.
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///
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/// \return <tt>(*this)</tt>
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template <typename LowerMap>
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CostScaling& lowerMap(const LowerMap& map) {
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_has_lower = true;
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for (ArcIt a(_graph); a != INVALID; ++a) {
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_lower[_arc_idf[a]] = map[a];
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}
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return *this;
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}
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/// \brief Set the upper bounds (capacities) on the arcs.
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///
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/// This function sets the upper bounds (capacities) on the arcs.
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/// If it is not used before calling \ref run(), the upper bounds
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/// will be set to \ref INF on all arcs (i.e. the flow value will be
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/// unbounded from above).
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///
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/// \param map An arc map storing the upper bounds.
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/// Its \c Value type must be convertible to the \c Value type
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/// of the algorithm.
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///
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/// \return <tt>(*this)</tt>
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template<typename UpperMap>
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CostScaling& upperMap(const UpperMap& map) {
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for (ArcIt a(_graph); a != INVALID; ++a) {
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_upper[_arc_idf[a]] = map[a];
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}
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return *this;
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}
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/// \brief Set the costs of the arcs.
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///
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/// This function sets the costs of the arcs.
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/// If it is not used before calling \ref run(), the costs
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/// will be set to \c 1 on all arcs.
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///
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/// \param map An arc map storing the costs.
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/// Its \c Value type must be convertible to the \c Cost type
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/// of the algorithm.
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///
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/// \return <tt>(*this)</tt>
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template<typename CostMap>
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CostScaling& costMap(const CostMap& map) {
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for (ArcIt a(_graph); a != INVALID; ++a) {
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_scost[_arc_idf[a]] = map[a];
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_scost[_arc_idb[a]] = -map[a];
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}
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return *this;
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}
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/// \brief Set the supply values of the nodes.
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///
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/// This function sets the supply values of the nodes.
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/// If neither this function nor \ref stSupply() is used before
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/// calling \ref run(), the supply of each node will be set to zero.
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///
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/// \param map A node map storing the supply values.
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/// Its \c Value type must be convertible to the \c Value type
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/// of the algorithm.
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///
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/// \return <tt>(*this)</tt>
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template<typename SupplyMap>
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CostScaling& supplyMap(const SupplyMap& map) {
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for (NodeIt n(_graph); n != INVALID; ++n) {
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_supply[_node_id[n]] = map[n];
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}
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return *this;
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}
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/// \brief Set single source and target nodes and a supply value.
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///
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/// This function sets a single source node and a single target node
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/// and the required flow value.
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/// If neither this function nor \ref supplyMap() is used before
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/// calling \ref run(), the supply of each node will be set to zero.
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///
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/// Using this function has the same effect as using \ref supplyMap()
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/// with a map in which \c k is assigned to \c s, \c -k is
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/// assigned to \c t and all other nodes have zero supply value.
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///
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/// \param s The source node.
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/// \param t The target node.
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/// \param k The required amount of flow from node \c s to node \c t
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/// (i.e. the supply of \c s and the demand of \c t).
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///
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/// \return <tt>(*this)</tt>
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CostScaling& stSupply(const Node& s, const Node& t, Value k) {
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for (int i = 0; i != _res_node_num; ++i) {
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_supply[i] = 0;
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}
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_supply[_node_id[s]] = k;
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_supply[_node_id[t]] = -k;
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return *this;
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}
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/// @}
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/// \name Execution control
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/// The algorithm can be executed using \ref run().
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/// @{
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/// \brief Run the algorithm.
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///
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/// This function runs the algorithm.
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/// The paramters can be specified using functions \ref lowerMap(),
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/// \ref upperMap(), \ref costMap(), \ref supplyMap(), \ref stSupply().
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/// For example,
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/// \code
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/// CostScaling<ListDigraph> cs(graph);
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/// cs.lowerMap(lower).upperMap(upper).costMap(cost)
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/// .supplyMap(sup).run();
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/// \endcode
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///
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/// This function can be called more than once. All the given parameters
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/// are kept for the next call, unless \ref resetParams() or \ref reset()
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/// is used, thus only the modified parameters have to be set again.
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/// If the underlying digraph was also modified after the construction
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/// of the class (or the last \ref reset() call), then the \ref reset()
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/// function must be called.
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///
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/// \param method The internal method that will be used in the
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/// algorithm. For more information, see \ref Method.
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/// \param factor The cost scaling factor. It must be at least two.
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///
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/// \return \c INFEASIBLE if no feasible flow exists,
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/// \n \c OPTIMAL if the problem has optimal solution
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/// (i.e. it is feasible and bounded), and the algorithm has found
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/// optimal flow and node potentials (primal and dual solutions),
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/// \n \c UNBOUNDED if the digraph contains an arc of negative cost
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/// and infinite upper bound. It means that the objective function
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/// is unbounded on that arc, however, note that it could actually be
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/// bounded over the feasible flows, but this algroithm cannot handle
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/// these cases.
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///
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/// \see ProblemType, Method
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/// \see resetParams(), reset()
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ProblemType run(Method method = PARTIAL_AUGMENT, int factor = 16) {
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LEMON_ASSERT(factor >= 2, "The scaling factor must be at least 2");
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_alpha = factor;
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ProblemType pt = init();
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if (pt != OPTIMAL) return pt;
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start(method);
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return OPTIMAL;
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}
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/// \brief Reset all the parameters that have been given before.
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|
///
|
|
/// This function resets all the paramaters that have been given
|
|
/// before using functions \ref lowerMap(), \ref upperMap(),
|
|
/// \ref costMap(), \ref supplyMap(), \ref stSupply().
|
|
///
|
|
/// It is useful for multiple \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
|
|
/// CostScaling<ListDigraph> cs(graph);
|
|
///
|
|
/// // First run
|
|
/// cs.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;
|
|
/// cs.costMap(cost).run();
|
|
///
|
|
/// // Run again from scratch using resetParams()
|
|
/// // (the lower bounds will be set to zero on all arcs)
|
|
/// cs.resetParams();
|
|
/// cs.upperMap(capacity).costMap(cost)
|
|
/// .supplyMap(sup).run();
|
|
/// \endcode
|
|
///
|
|
/// \return <tt>(*this)</tt>
|
|
///
|
|
/// \see reset(), run()
|
|
CostScaling& resetParams() {
|
|
for (int i = 0; i != _res_node_num; ++i) {
|
|
_supply[i] = 0;
|
|
}
|
|
int limit = _first_out[_root];
|
|
for (int j = 0; j != limit; ++j) {
|
|
_lower[j] = 0;
|
|
_upper[j] = INF;
|
|
_scost[j] = _forward[j] ? 1 : -1;
|
|
}
|
|
for (int j = limit; j != _res_arc_num; ++j) {
|
|
_lower[j] = 0;
|
|
_upper[j] = INF;
|
|
_scost[j] = 0;
|
|
_scost[_reverse[j]] = 0;
|
|
}
|
|
_has_lower = false;
|
|
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().
|
|
///
|
|
/// It is useful for multiple \ref run() calls. By default, 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()
|
|
CostScaling& reset() {
|
|
// Resize vectors
|
|
_node_num = countNodes(_graph);
|
|
_arc_num = countArcs(_graph);
|
|
_res_node_num = _node_num + 1;
|
|
_res_arc_num = 2 * (_arc_num + _node_num);
|
|
_root = _node_num;
|
|
|
|
_first_out.resize(_res_node_num + 1);
|
|
_forward.resize(_res_arc_num);
|
|
_source.resize(_res_arc_num);
|
|
_target.resize(_res_arc_num);
|
|
_reverse.resize(_res_arc_num);
|
|
|
|
_lower.resize(_res_arc_num);
|
|
_upper.resize(_res_arc_num);
|
|
_scost.resize(_res_arc_num);
|
|
_supply.resize(_res_node_num);
|
|
|
|
_res_cap.resize(_res_arc_num);
|
|
_cost.resize(_res_arc_num);
|
|
_pi.resize(_res_node_num);
|
|
_excess.resize(_res_node_num);
|
|
_next_out.resize(_res_node_num);
|
|
|
|
// Copy the graph
|
|
int i = 0, j = 0, k = 2 * _arc_num + _node_num;
|
|
for (NodeIt n(_graph); n != INVALID; ++n, ++i) {
|
|
_node_id[n] = i;
|
|
}
|
|
i = 0;
|
|
for (NodeIt n(_graph); n != INVALID; ++n, ++i) {
|
|
_first_out[i] = j;
|
|
for (OutArcIt a(_graph, n); a != INVALID; ++a, ++j) {
|
|
_arc_idf[a] = j;
|
|
_forward[j] = true;
|
|
_source[j] = i;
|
|
_target[j] = _node_id[_graph.runningNode(a)];
|
|
}
|
|
for (InArcIt a(_graph, n); a != INVALID; ++a, ++j) {
|
|
_arc_idb[a] = j;
|
|
_forward[j] = false;
|
|
_source[j] = i;
|
|
_target[j] = _node_id[_graph.runningNode(a)];
|
|
}
|
|
_forward[j] = false;
|
|
_source[j] = i;
|
|
_target[j] = _root;
|
|
_reverse[j] = k;
|
|
_forward[k] = true;
|
|
_source[k] = _root;
|
|
_target[k] = i;
|
|
_reverse[k] = j;
|
|
++j; ++k;
|
|
}
|
|
_first_out[i] = j;
|
|
_first_out[_res_node_num] = k;
|
|
for (ArcIt a(_graph); a != INVALID; ++a) {
|
|
int fi = _arc_idf[a];
|
|
int bi = _arc_idb[a];
|
|
_reverse[fi] = bi;
|
|
_reverse[bi] = fi;
|
|
}
|
|
|
|
// 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
|
|
/// cs.totalCost<double>();
|
|
/// \endcode
|
|
/// It is useful if the total cost cannot be stored in the \c Cost
|
|
/// type of the algorithm, which is the default return type of the
|
|
/// function.
|
|
///
|
|
/// \pre \ref run() must be called before using this function.
|
|
template <typename Number>
|
|
Number totalCost() const {
|
|
Number c = 0;
|
|
for (ArcIt a(_graph); a != INVALID; ++a) {
|
|
int i = _arc_idb[a];
|
|
c += static_cast<Number>(_res_cap[i]) *
|
|
(-static_cast<Number>(_scost[i]));
|
|
}
|
|
return c;
|
|
}
|
|
|
|
#ifndef DOXYGEN
|
|
Cost totalCost() const {
|
|
return totalCost<Cost>();
|
|
}
|
|
#endif
|
|
|
|
/// \brief Return the flow on the given arc.
|
|
///
|
|
/// This function returns the flow on the given arc.
|
|
///
|
|
/// \pre \ref run() must be called before using this function.
|
|
Value flow(const Arc& a) const {
|
|
return _res_cap[_arc_idb[a]];
|
|
}
|
|
|
|
/// \brief 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, _res_cap[_arc_idb[a]]);
|
|
}
|
|
}
|
|
|
|
/// \brief Return the potential (dual value) of the given node.
|
|
///
|
|
/// This function returns the potential (dual value) of the
|
|
/// given node.
|
|
///
|
|
/// \pre \ref run() must be called before using this function.
|
|
Cost potential(const Node& n) const {
|
|
return static_cast<Cost>(_pi[_node_id[n]]);
|
|
}
|
|
|
|
/// \brief 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.
|
|
///
|
|
/// \pre \ref run() must be called before using this function.
|
|
template <typename PotentialMap>
|
|
void potentialMap(PotentialMap &map) const {
|
|
for (NodeIt n(_graph); n != INVALID; ++n) {
|
|
map.set(n, static_cast<Cost>(_pi[_node_id[n]]));
|
|
}
|
|
}
|
|
|
|
/// @}
|
|
|
|
private:
|
|
|
|
// Initialize the algorithm
|
|
ProblemType init() {
|
|
if (_res_node_num <= 1) return INFEASIBLE;
|
|
|
|
// Check the sum of supply values
|
|
_sum_supply = 0;
|
|
for (int i = 0; i != _root; ++i) {
|
|
_sum_supply += _supply[i];
|
|
}
|
|
if (_sum_supply > 0) return INFEASIBLE;
|
|
|
|
// Check lower and upper bounds
|
|
LEMON_DEBUG(checkBoundMaps(),
|
|
"Upper bounds must be greater or equal to the lower bounds");
|
|
|
|
|
|
// Initialize vectors
|
|
for (int i = 0; i != _res_node_num; ++i) {
|
|
_pi[i] = 0;
|
|
_excess[i] = _supply[i];
|
|
}
|
|
|
|
// Remove infinite upper bounds and check negative arcs
|
|
const Value MAX = std::numeric_limits<Value>::max();
|
|
int last_out;
|
|
if (_has_lower) {
|
|
for (int i = 0; i != _root; ++i) {
|
|
last_out = _first_out[i+1];
|
|
for (int j = _first_out[i]; j != last_out; ++j) {
|
|
if (_forward[j]) {
|
|
Value c = _scost[j] < 0 ? _upper[j] : _lower[j];
|
|
if (c >= MAX) return UNBOUNDED;
|
|
_excess[i] -= c;
|
|
_excess[_target[j]] += c;
|
|
}
|
|
}
|
|
}
|
|
} else {
|
|
for (int i = 0; i != _root; ++i) {
|
|
last_out = _first_out[i+1];
|
|
for (int j = _first_out[i]; j != last_out; ++j) {
|
|
if (_forward[j] && _scost[j] < 0) {
|
|
Value c = _upper[j];
|
|
if (c >= MAX) return UNBOUNDED;
|
|
_excess[i] -= c;
|
|
_excess[_target[j]] += c;
|
|
}
|
|
}
|
|
}
|
|
}
|
|
Value ex, max_cap = 0;
|
|
for (int i = 0; i != _res_node_num; ++i) {
|
|
ex = _excess[i];
|
|
_excess[i] = 0;
|
|
if (ex < 0) max_cap -= ex;
|
|
}
|
|
for (int j = 0; j != _res_arc_num; ++j) {
|
|
if (_upper[j] >= MAX) _upper[j] = max_cap;
|
|
}
|
|
|
|
// Initialize the large cost vector and the epsilon parameter
|
|
_epsilon = 0;
|
|
LargeCost lc;
|
|
for (int i = 0; i != _root; ++i) {
|
|
last_out = _first_out[i+1];
|
|
for (int j = _first_out[i]; j != last_out; ++j) {
|
|
lc = static_cast<LargeCost>(_scost[j]) * _res_node_num * _alpha;
|
|
_cost[j] = lc;
|
|
if (lc > _epsilon) _epsilon = lc;
|
|
}
|
|
}
|
|
_epsilon /= _alpha;
|
|
|
|
// Initialize maps for Circulation and remove non-zero lower bounds
|
|
ConstMap<Arc, Value> low(0);
|
|
typedef typename Digraph::template ArcMap<Value> ValueArcMap;
|
|
typedef typename Digraph::template NodeMap<Value> ValueNodeMap;
|
|
ValueArcMap cap(_graph), flow(_graph);
|
|
ValueNodeMap sup(_graph);
|
|
for (NodeIt n(_graph); n != INVALID; ++n) {
|
|
sup[n] = _supply[_node_id[n]];
|
|
}
|
|
if (_has_lower) {
|
|
for (ArcIt a(_graph); a != INVALID; ++a) {
|
|
int j = _arc_idf[a];
|
|
Value c = _lower[j];
|
|
cap[a] = _upper[j] - c;
|
|
sup[_graph.source(a)] -= c;
|
|
sup[_graph.target(a)] += c;
|
|
}
|
|
} else {
|
|
for (ArcIt a(_graph); a != INVALID; ++a) {
|
|
cap[a] = _upper[_arc_idf[a]];
|
|
}
|
|
}
|
|
|
|
_sup_node_num = 0;
|
|
for (NodeIt n(_graph); n != INVALID; ++n) {
|
|
if (sup[n] > 0) ++_sup_node_num;
|
|
}
|
|
|
|
// Find a feasible flow using Circulation
|
|
Circulation<Digraph, ConstMap<Arc, Value>, ValueArcMap, ValueNodeMap>
|
|
circ(_graph, low, cap, sup);
|
|
if (!circ.flowMap(flow).run()) return INFEASIBLE;
|
|
|
|
// Set residual capacities and handle GEQ supply type
|
|
if (_sum_supply < 0) {
|
|
for (ArcIt a(_graph); a != INVALID; ++a) {
|
|
Value fa = flow[a];
|
|
_res_cap[_arc_idf[a]] = cap[a] - fa;
|
|
_res_cap[_arc_idb[a]] = fa;
|
|
sup[_graph.source(a)] -= fa;
|
|
sup[_graph.target(a)] += fa;
|
|
}
|
|
for (NodeIt n(_graph); n != INVALID; ++n) {
|
|
_excess[_node_id[n]] = sup[n];
|
|
}
|
|
for (int a = _first_out[_root]; a != _res_arc_num; ++a) {
|
|
int u = _target[a];
|
|
int ra = _reverse[a];
|
|
_res_cap[a] = -_sum_supply + 1;
|
|
_res_cap[ra] = -_excess[u];
|
|
_cost[a] = 0;
|
|
_cost[ra] = 0;
|
|
_excess[u] = 0;
|
|
}
|
|
} else {
|
|
for (ArcIt a(_graph); a != INVALID; ++a) {
|
|
Value fa = flow[a];
|
|
_res_cap[_arc_idf[a]] = cap[a] - fa;
|
|
_res_cap[_arc_idb[a]] = fa;
|
|
}
|
|
for (int a = _first_out[_root]; a != _res_arc_num; ++a) {
|
|
int ra = _reverse[a];
|
|
_res_cap[a] = 0;
|
|
_res_cap[ra] = 0;
|
|
_cost[a] = 0;
|
|
_cost[ra] = 0;
|
|
}
|
|
}
|
|
|
|
// Initialize data structures for buckets
|
|
_max_rank = _alpha * _res_node_num;
|
|
_buckets.resize(_max_rank);
|
|
_bucket_next.resize(_res_node_num + 1);
|
|
_bucket_prev.resize(_res_node_num + 1);
|
|
_rank.resize(_res_node_num + 1);
|
|
|
|
return OPTIMAL;
|
|
}
|
|
|
|
// Check if the upper bound is greater than or equal to the lower bound
|
|
// on each forward arc.
|
|
bool checkBoundMaps() {
|
|
for (int j = 0; j != _res_arc_num; ++j) {
|
|
if (_forward[j] && _upper[j] < _lower[j]) return false;
|
|
}
|
|
return true;
|
|
}
|
|
|
|
// Execute the algorithm and transform the results
|
|
void start(Method method) {
|
|
const int MAX_PARTIAL_PATH_LENGTH = 4;
|
|
|
|
switch (method) {
|
|
case PUSH:
|
|
startPush();
|
|
break;
|
|
case AUGMENT:
|
|
startAugment(_res_node_num - 1);
|
|
break;
|
|
case PARTIAL_AUGMENT:
|
|
startAugment(MAX_PARTIAL_PATH_LENGTH);
|
|
break;
|
|
}
|
|
|
|
// Compute node potentials (dual solution)
|
|
for (int i = 0; i != _res_node_num; ++i) {
|
|
_pi[i] = static_cast<Cost>(_pi[i] / (_res_node_num * _alpha));
|
|
}
|
|
bool optimal = true;
|
|
for (int i = 0; optimal && i != _res_node_num; ++i) {
|
|
LargeCost pi_i = _pi[i];
|
|
int last_out = _first_out[i+1];
|
|
for (int j = _first_out[i]; j != last_out; ++j) {
|
|
if (_res_cap[j] > 0 && _scost[j] + pi_i - _pi[_target[j]] < 0) {
|
|
optimal = false;
|
|
break;
|
|
}
|
|
}
|
|
}
|
|
|
|
if (!optimal) {
|
|
// Compute node potentials for the original costs with BellmanFord
|
|
// (if it is necessary)
|
|
typedef std::pair<int, int> IntPair;
|
|
StaticDigraph sgr;
|
|
std::vector<IntPair> arc_vec;
|
|
std::vector<LargeCost> cost_vec;
|
|
LargeCostArcMap cost_map(cost_vec);
|
|
|
|
arc_vec.clear();
|
|
cost_vec.clear();
|
|
for (int j = 0; j != _res_arc_num; ++j) {
|
|
if (_res_cap[j] > 0) {
|
|
int u = _source[j], v = _target[j];
|
|
arc_vec.push_back(IntPair(u, v));
|
|
cost_vec.push_back(_scost[j] + _pi[u] - _pi[v]);
|
|
}
|
|
}
|
|
sgr.build(_res_node_num, arc_vec.begin(), arc_vec.end());
|
|
|
|
typename BellmanFord<StaticDigraph, LargeCostArcMap>::Create
|
|
bf(sgr, cost_map);
|
|
bf.init(0);
|
|
bf.start();
|
|
|
|
for (int i = 0; i != _res_node_num; ++i) {
|
|
_pi[i] += bf.dist(sgr.node(i));
|
|
}
|
|
}
|
|
|
|
// Shift potentials to meet the requirements of the GEQ type
|
|
// optimality conditions
|
|
LargeCost max_pot = _pi[_root];
|
|
for (int i = 0; i != _res_node_num; ++i) {
|
|
if (_pi[i] > max_pot) max_pot = _pi[i];
|
|
}
|
|
if (max_pot != 0) {
|
|
for (int i = 0; i != _res_node_num; ++i) {
|
|
_pi[i] -= max_pot;
|
|
}
|
|
}
|
|
|
|
// Handle non-zero lower bounds
|
|
if (_has_lower) {
|
|
int limit = _first_out[_root];
|
|
for (int j = 0; j != limit; ++j) {
|
|
if (_forward[j]) _res_cap[_reverse[j]] += _lower[j];
|
|
}
|
|
}
|
|
}
|
|
|
|
// Initialize a cost scaling phase
|
|
void initPhase() {
|
|
// Saturate arcs not satisfying the optimality condition
|
|
for (int u = 0; u != _res_node_num; ++u) {
|
|
int last_out = _first_out[u+1];
|
|
LargeCost pi_u = _pi[u];
|
|
for (int a = _first_out[u]; a != last_out; ++a) {
|
|
Value delta = _res_cap[a];
|
|
if (delta > 0) {
|
|
int v = _target[a];
|
|
if (_cost[a] + pi_u - _pi[v] < 0) {
|
|
_excess[u] -= delta;
|
|
_excess[v] += delta;
|
|
_res_cap[a] = 0;
|
|
_res_cap[_reverse[a]] += delta;
|
|
}
|
|
}
|
|
}
|
|
}
|
|
|
|
// Find active nodes (i.e. nodes with positive excess)
|
|
for (int u = 0; u != _res_node_num; ++u) {
|
|
if (_excess[u] > 0) _active_nodes.push_back(u);
|
|
}
|
|
|
|
// Initialize the next arcs
|
|
for (int u = 0; u != _res_node_num; ++u) {
|
|
_next_out[u] = _first_out[u];
|
|
}
|
|
}
|
|
|
|
// Price (potential) refinement heuristic
|
|
bool priceRefinement() {
|
|
|
|
// Stack for stroing the topological order
|
|
IntVector stack(_res_node_num);
|
|
int stack_top;
|
|
|
|
// Perform phases
|
|
while (topologicalSort(stack, stack_top)) {
|
|
|
|
// Compute node ranks in the acyclic admissible network and
|
|
// store the nodes in buckets
|
|
for (int i = 0; i != _res_node_num; ++i) {
|
|
_rank[i] = 0;
|
|
}
|
|
const int bucket_end = _root + 1;
|
|
for (int r = 0; r != _max_rank; ++r) {
|
|
_buckets[r] = bucket_end;
|
|
}
|
|
int top_rank = 0;
|
|
for ( ; stack_top >= 0; --stack_top) {
|
|
int u = stack[stack_top], v;
|
|
int rank_u = _rank[u];
|
|
|
|
LargeCost rc, pi_u = _pi[u];
|
|
int last_out = _first_out[u+1];
|
|
for (int a = _first_out[u]; a != last_out; ++a) {
|
|
if (_res_cap[a] > 0) {
|
|
v = _target[a];
|
|
rc = _cost[a] + pi_u - _pi[v];
|
|
if (rc < 0) {
|
|
LargeCost nrc = static_cast<LargeCost>((-rc - 0.5) / _epsilon);
|
|
if (nrc < LargeCost(_max_rank)) {
|
|
int new_rank_v = rank_u + static_cast<int>(nrc);
|
|
if (new_rank_v > _rank[v]) {
|
|
_rank[v] = new_rank_v;
|
|
}
|
|
}
|
|
}
|
|
}
|
|
}
|
|
|
|
if (rank_u > 0) {
|
|
top_rank = std::max(top_rank, rank_u);
|
|
int bfirst = _buckets[rank_u];
|
|
_bucket_next[u] = bfirst;
|
|
_bucket_prev[bfirst] = u;
|
|
_buckets[rank_u] = u;
|
|
}
|
|
}
|
|
|
|
// Check if the current flow is epsilon-optimal
|
|
if (top_rank == 0) {
|
|
return true;
|
|
}
|
|
|
|
// Process buckets in top-down order
|
|
for (int rank = top_rank; rank > 0; --rank) {
|
|
while (_buckets[rank] != bucket_end) {
|
|
// Remove the first node from the current bucket
|
|
int u = _buckets[rank];
|
|
_buckets[rank] = _bucket_next[u];
|
|
|
|
// Search the outgoing arcs of u
|
|
LargeCost rc, pi_u = _pi[u];
|
|
int last_out = _first_out[u+1];
|
|
int v, old_rank_v, new_rank_v;
|
|
for (int a = _first_out[u]; a != last_out; ++a) {
|
|
if (_res_cap[a] > 0) {
|
|
v = _target[a];
|
|
old_rank_v = _rank[v];
|
|
|
|
if (old_rank_v < rank) {
|
|
|
|
// Compute the new rank of node v
|
|
rc = _cost[a] + pi_u - _pi[v];
|
|
if (rc < 0) {
|
|
new_rank_v = rank;
|
|
} else {
|
|
LargeCost nrc = rc / _epsilon;
|
|
new_rank_v = 0;
|
|
if (nrc < LargeCost(_max_rank)) {
|
|
new_rank_v = rank - 1 - static_cast<int>(nrc);
|
|
}
|
|
}
|
|
|
|
// Change the rank of node v
|
|
if (new_rank_v > old_rank_v) {
|
|
_rank[v] = new_rank_v;
|
|
|
|
// Remove v from its old bucket
|
|
if (old_rank_v > 0) {
|
|
if (_buckets[old_rank_v] == v) {
|
|
_buckets[old_rank_v] = _bucket_next[v];
|
|
} else {
|
|
int pv = _bucket_prev[v], nv = _bucket_next[v];
|
|
_bucket_next[pv] = nv;
|
|
_bucket_prev[nv] = pv;
|
|
}
|
|
}
|
|
|
|
// Insert v into its new bucket
|
|
int nv = _buckets[new_rank_v];
|
|
_bucket_next[v] = nv;
|
|
_bucket_prev[nv] = v;
|
|
_buckets[new_rank_v] = v;
|
|
}
|
|
}
|
|
}
|
|
}
|
|
|
|
// Refine potential of node u
|
|
_pi[u] -= rank * _epsilon;
|
|
}
|
|
}
|
|
|
|
}
|
|
|
|
return false;
|
|
}
|
|
|
|
// Find and cancel cycles in the admissible network and
|
|
// determine topological order using DFS
|
|
bool topologicalSort(IntVector &stack, int &stack_top) {
|
|
const int MAX_CYCLE_CANCEL = 1;
|
|
|
|
BoolVector reached(_res_node_num, false);
|
|
BoolVector processed(_res_node_num, false);
|
|
IntVector pred(_res_node_num);
|
|
for (int i = 0; i != _res_node_num; ++i) {
|
|
_next_out[i] = _first_out[i];
|
|
}
|
|
stack_top = -1;
|
|
|
|
int cycle_cnt = 0;
|
|
for (int start = 0; start != _res_node_num; ++start) {
|
|
if (reached[start]) continue;
|
|
|
|
// Start DFS search from this start node
|
|
pred[start] = -1;
|
|
int tip = start, v;
|
|
while (true) {
|
|
// Check the outgoing arcs of the current tip node
|
|
reached[tip] = true;
|
|
LargeCost pi_tip = _pi[tip];
|
|
int a, last_out = _first_out[tip+1];
|
|
for (a = _next_out[tip]; a != last_out; ++a) {
|
|
if (_res_cap[a] > 0) {
|
|
v = _target[a];
|
|
if (_cost[a] + pi_tip - _pi[v] < 0) {
|
|
if (!reached[v]) {
|
|
// A new node is reached
|
|
reached[v] = true;
|
|
pred[v] = tip;
|
|
_next_out[tip] = a;
|
|
tip = v;
|
|
a = _next_out[tip];
|
|
last_out = _first_out[tip+1];
|
|
break;
|
|
}
|
|
else if (!processed[v]) {
|
|
// A cycle is found
|
|
++cycle_cnt;
|
|
_next_out[tip] = a;
|
|
|
|
// Find the minimum residual capacity along the cycle
|
|
Value d, delta = _res_cap[a];
|
|
int u, delta_node = tip;
|
|
for (u = tip; u != v; ) {
|
|
u = pred[u];
|
|
d = _res_cap[_next_out[u]];
|
|
if (d <= delta) {
|
|
delta = d;
|
|
delta_node = u;
|
|
}
|
|
}
|
|
|
|
// Augment along the cycle
|
|
_res_cap[a] -= delta;
|
|
_res_cap[_reverse[a]] += delta;
|
|
for (u = tip; u != v; ) {
|
|
u = pred[u];
|
|
int ca = _next_out[u];
|
|
_res_cap[ca] -= delta;
|
|
_res_cap[_reverse[ca]] += delta;
|
|
}
|
|
|
|
// Check the maximum number of cycle canceling
|
|
if (cycle_cnt >= MAX_CYCLE_CANCEL) {
|
|
return false;
|
|
}
|
|
|
|
// Roll back search to delta_node
|
|
if (delta_node != tip) {
|
|
for (u = tip; u != delta_node; u = pred[u]) {
|
|
reached[u] = false;
|
|
}
|
|
tip = delta_node;
|
|
a = _next_out[tip] + 1;
|
|
last_out = _first_out[tip+1];
|
|
break;
|
|
}
|
|
}
|
|
}
|
|
}
|
|
}
|
|
|
|
// Step back to the previous node
|
|
if (a == last_out) {
|
|
processed[tip] = true;
|
|
stack[++stack_top] = tip;
|
|
tip = pred[tip];
|
|
if (tip < 0) {
|
|
// Finish DFS from the current start node
|
|
break;
|
|
}
|
|
++_next_out[tip];
|
|
}
|
|
}
|
|
|
|
}
|
|
|
|
return (cycle_cnt == 0);
|
|
}
|
|
|
|
// Global potential update heuristic
|
|
void globalUpdate() {
|
|
const int bucket_end = _root + 1;
|
|
|
|
// Initialize buckets
|
|
for (int r = 0; r != _max_rank; ++r) {
|
|
_buckets[r] = bucket_end;
|
|
}
|
|
Value total_excess = 0;
|
|
int b0 = bucket_end;
|
|
for (int i = 0; i != _res_node_num; ++i) {
|
|
if (_excess[i] < 0) {
|
|
_rank[i] = 0;
|
|
_bucket_next[i] = b0;
|
|
_bucket_prev[b0] = i;
|
|
b0 = i;
|
|
} else {
|
|
total_excess += _excess[i];
|
|
_rank[i] = _max_rank;
|
|
}
|
|
}
|
|
if (total_excess == 0) return;
|
|
_buckets[0] = b0;
|
|
|
|
// Search the buckets
|
|
int r = 0;
|
|
for ( ; r != _max_rank; ++r) {
|
|
while (_buckets[r] != bucket_end) {
|
|
// Remove the first node from the current bucket
|
|
int u = _buckets[r];
|
|
_buckets[r] = _bucket_next[u];
|
|
|
|
// Search the incoming arcs of u
|
|
LargeCost pi_u = _pi[u];
|
|
int last_out = _first_out[u+1];
|
|
for (int a = _first_out[u]; a != last_out; ++a) {
|
|
int ra = _reverse[a];
|
|
if (_res_cap[ra] > 0) {
|
|
int v = _source[ra];
|
|
int old_rank_v = _rank[v];
|
|
if (r < old_rank_v) {
|
|
// Compute the new rank of v
|
|
LargeCost nrc = (_cost[ra] + _pi[v] - pi_u) / _epsilon;
|
|
int new_rank_v = old_rank_v;
|
|
if (nrc < LargeCost(_max_rank)) {
|
|
new_rank_v = r + 1 + static_cast<int>(nrc);
|
|
}
|
|
|
|
// Change the rank of v
|
|
if (new_rank_v < old_rank_v) {
|
|
_rank[v] = new_rank_v;
|
|
_next_out[v] = _first_out[v];
|
|
|
|
// Remove v from its old bucket
|
|
if (old_rank_v < _max_rank) {
|
|
if (_buckets[old_rank_v] == v) {
|
|
_buckets[old_rank_v] = _bucket_next[v];
|
|
} else {
|
|
int pv = _bucket_prev[v], nv = _bucket_next[v];
|
|
_bucket_next[pv] = nv;
|
|
_bucket_prev[nv] = pv;
|
|
}
|
|
}
|
|
|
|
// Insert v into its new bucket
|
|
int nv = _buckets[new_rank_v];
|
|
_bucket_next[v] = nv;
|
|
_bucket_prev[nv] = v;
|
|
_buckets[new_rank_v] = v;
|
|
}
|
|
}
|
|
}
|
|
}
|
|
|
|
// Finish search if there are no more active nodes
|
|
if (_excess[u] > 0) {
|
|
total_excess -= _excess[u];
|
|
if (total_excess <= 0) break;
|
|
}
|
|
}
|
|
if (total_excess <= 0) break;
|
|
}
|
|
|
|
// Relabel nodes
|
|
for (int u = 0; u != _res_node_num; ++u) {
|
|
int k = std::min(_rank[u], r);
|
|
if (k > 0) {
|
|
_pi[u] -= _epsilon * k;
|
|
_next_out[u] = _first_out[u];
|
|
}
|
|
}
|
|
}
|
|
|
|
/// Execute the algorithm performing augment and relabel operations
|
|
void startAugment(int max_length) {
|
|
// Paramters for heuristics
|
|
const int PRICE_REFINEMENT_LIMIT = 2;
|
|
const double GLOBAL_UPDATE_FACTOR = 1.0;
|
|
const int global_update_skip = static_cast<int>(GLOBAL_UPDATE_FACTOR *
|
|
(_res_node_num + _sup_node_num * _sup_node_num));
|
|
int next_global_update_limit = global_update_skip;
|
|
|
|
// Perform cost scaling phases
|
|
IntVector path;
|
|
BoolVector path_arc(_res_arc_num, false);
|
|
int relabel_cnt = 0;
|
|
int eps_phase_cnt = 0;
|
|
for ( ; _epsilon >= 1; _epsilon = _epsilon < _alpha && _epsilon > 1 ?
|
|
1 : _epsilon / _alpha )
|
|
{
|
|
++eps_phase_cnt;
|
|
|
|
// Price refinement heuristic
|
|
if (eps_phase_cnt >= PRICE_REFINEMENT_LIMIT) {
|
|
if (priceRefinement()) continue;
|
|
}
|
|
|
|
// Initialize current phase
|
|
initPhase();
|
|
|
|
// Perform partial augment and relabel operations
|
|
while (true) {
|
|
// Select an active node (FIFO selection)
|
|
while (_active_nodes.size() > 0 &&
|
|
_excess[_active_nodes.front()] <= 0) {
|
|
_active_nodes.pop_front();
|
|
}
|
|
if (_active_nodes.size() == 0) break;
|
|
int start = _active_nodes.front();
|
|
|
|
// Find an augmenting path from the start node
|
|
int tip = start;
|
|
while (int(path.size()) < max_length && _excess[tip] >= 0) {
|
|
int u;
|
|
LargeCost rc, min_red_cost = std::numeric_limits<LargeCost>::max();
|
|
LargeCost pi_tip = _pi[tip];
|
|
int last_out = _first_out[tip+1];
|
|
for (int a = _next_out[tip]; a != last_out; ++a) {
|
|
if (_res_cap[a] > 0) {
|
|
u = _target[a];
|
|
rc = _cost[a] + pi_tip - _pi[u];
|
|
if (rc < 0) {
|
|
path.push_back(a);
|
|
_next_out[tip] = a;
|
|
if (path_arc[a]) {
|
|
goto augment; // a cycle is found, stop path search
|
|
}
|
|
tip = u;
|
|
path_arc[a] = true;
|
|
goto next_step;
|
|
}
|
|
else if (rc < min_red_cost) {
|
|
min_red_cost = rc;
|
|
}
|
|
}
|
|
}
|
|
|
|
// Relabel tip node
|
|
if (tip != start) {
|
|
int ra = _reverse[path.back()];
|
|
min_red_cost =
|
|
std::min(min_red_cost, _cost[ra] + pi_tip - _pi[_target[ra]]);
|
|
}
|
|
last_out = _next_out[tip];
|
|
for (int a = _first_out[tip]; a != last_out; ++a) {
|
|
if (_res_cap[a] > 0) {
|
|
rc = _cost[a] + pi_tip - _pi[_target[a]];
|
|
if (rc < min_red_cost) {
|
|
min_red_cost = rc;
|
|
}
|
|
}
|
|
}
|
|
_pi[tip] -= min_red_cost + _epsilon;
|
|
_next_out[tip] = _first_out[tip];
|
|
++relabel_cnt;
|
|
|
|
// Step back
|
|
if (tip != start) {
|
|
int pa = path.back();
|
|
path_arc[pa] = false;
|
|
tip = _source[pa];
|
|
path.pop_back();
|
|
}
|
|
|
|
next_step: ;
|
|
}
|
|
|
|
// Augment along the found path (as much flow as possible)
|
|
augment:
|
|
Value delta;
|
|
int pa, u, v = start;
|
|
for (int i = 0; i != int(path.size()); ++i) {
|
|
pa = path[i];
|
|
u = v;
|
|
v = _target[pa];
|
|
path_arc[pa] = false;
|
|
delta = std::min(_res_cap[pa], _excess[u]);
|
|
_res_cap[pa] -= delta;
|
|
_res_cap[_reverse[pa]] += delta;
|
|
_excess[u] -= delta;
|
|
_excess[v] += delta;
|
|
if (_excess[v] > 0 && _excess[v] <= delta) {
|
|
_active_nodes.push_back(v);
|
|
}
|
|
}
|
|
path.clear();
|
|
|
|
// Global update heuristic
|
|
if (relabel_cnt >= next_global_update_limit) {
|
|
globalUpdate();
|
|
next_global_update_limit += global_update_skip;
|
|
}
|
|
}
|
|
|
|
}
|
|
|
|
}
|
|
|
|
/// Execute the algorithm performing push and relabel operations
|
|
void startPush() {
|
|
// Paramters for heuristics
|
|
const int PRICE_REFINEMENT_LIMIT = 2;
|
|
const double GLOBAL_UPDATE_FACTOR = 2.0;
|
|
|
|
const int global_update_skip = static_cast<int>(GLOBAL_UPDATE_FACTOR *
|
|
(_res_node_num + _sup_node_num * _sup_node_num));
|
|
int next_global_update_limit = global_update_skip;
|
|
|
|
// Perform cost scaling phases
|
|
BoolVector hyper(_res_node_num, false);
|
|
LargeCostVector hyper_cost(_res_node_num);
|
|
int relabel_cnt = 0;
|
|
int eps_phase_cnt = 0;
|
|
for ( ; _epsilon >= 1; _epsilon = _epsilon < _alpha && _epsilon > 1 ?
|
|
1 : _epsilon / _alpha )
|
|
{
|
|
++eps_phase_cnt;
|
|
|
|
// Price refinement heuristic
|
|
if (eps_phase_cnt >= PRICE_REFINEMENT_LIMIT) {
|
|
if (priceRefinement()) continue;
|
|
}
|
|
|
|
// Initialize current phase
|
|
initPhase();
|
|
|
|
// Perform push and relabel operations
|
|
while (_active_nodes.size() > 0) {
|
|
LargeCost min_red_cost, rc, pi_n;
|
|
Value delta;
|
|
int n, t, a, last_out = _res_arc_num;
|
|
|
|
next_node:
|
|
// Select an active node (FIFO selection)
|
|
n = _active_nodes.front();
|
|
last_out = _first_out[n+1];
|
|
pi_n = _pi[n];
|
|
|
|
// Perform push operations if there are admissible arcs
|
|
if (_excess[n] > 0) {
|
|
for (a = _next_out[n]; a != last_out; ++a) {
|
|
if (_res_cap[a] > 0 &&
|
|
_cost[a] + pi_n - _pi[_target[a]] < 0) {
|
|
delta = std::min(_res_cap[a], _excess[n]);
|
|
t = _target[a];
|
|
|
|
// Push-look-ahead heuristic
|
|
Value ahead = -_excess[t];
|
|
int last_out_t = _first_out[t+1];
|
|
LargeCost pi_t = _pi[t];
|
|
for (int ta = _next_out[t]; ta != last_out_t; ++ta) {
|
|
if (_res_cap[ta] > 0 &&
|
|
_cost[ta] + pi_t - _pi[_target[ta]] < 0)
|
|
ahead += _res_cap[ta];
|
|
if (ahead >= delta) break;
|
|
}
|
|
if (ahead < 0) ahead = 0;
|
|
|
|
// Push flow along the arc
|
|
if (ahead < delta && !hyper[t]) {
|
|
_res_cap[a] -= ahead;
|
|
_res_cap[_reverse[a]] += ahead;
|
|
_excess[n] -= ahead;
|
|
_excess[t] += ahead;
|
|
_active_nodes.push_front(t);
|
|
hyper[t] = true;
|
|
hyper_cost[t] = _cost[a] + pi_n - pi_t;
|
|
_next_out[n] = a;
|
|
goto next_node;
|
|
} else {
|
|
_res_cap[a] -= delta;
|
|
_res_cap[_reverse[a]] += delta;
|
|
_excess[n] -= delta;
|
|
_excess[t] += delta;
|
|
if (_excess[t] > 0 && _excess[t] <= delta)
|
|
_active_nodes.push_back(t);
|
|
}
|
|
|
|
if (_excess[n] == 0) {
|
|
_next_out[n] = a;
|
|
goto remove_nodes;
|
|
}
|
|
}
|
|
}
|
|
_next_out[n] = a;
|
|
}
|
|
|
|
// Relabel the node if it is still active (or hyper)
|
|
if (_excess[n] > 0 || hyper[n]) {
|
|
min_red_cost = hyper[n] ? -hyper_cost[n] :
|
|
std::numeric_limits<LargeCost>::max();
|
|
for (int a = _first_out[n]; a != last_out; ++a) {
|
|
if (_res_cap[a] > 0) {
|
|
rc = _cost[a] + pi_n - _pi[_target[a]];
|
|
if (rc < min_red_cost) {
|
|
min_red_cost = rc;
|
|
}
|
|
}
|
|
}
|
|
_pi[n] -= min_red_cost + _epsilon;
|
|
_next_out[n] = _first_out[n];
|
|
hyper[n] = false;
|
|
++relabel_cnt;
|
|
}
|
|
|
|
// Remove nodes that are not active nor hyper
|
|
remove_nodes:
|
|
while ( _active_nodes.size() > 0 &&
|
|
_excess[_active_nodes.front()] <= 0 &&
|
|
!hyper[_active_nodes.front()] ) {
|
|
_active_nodes.pop_front();
|
|
}
|
|
|
|
// Global update heuristic
|
|
if (relabel_cnt >= next_global_update_limit) {
|
|
globalUpdate();
|
|
for (int u = 0; u != _res_node_num; ++u)
|
|
hyper[u] = false;
|
|
next_global_update_limit += global_update_skip;
|
|
}
|
|
}
|
|
}
|
|
}
|
|
|
|
}; //class CostScaling
|
|
|
|
///@}
|
|
|
|
} //namespace lemon
|
|
|
|
#endif //LEMON_COST_SCALING_H
|