LEMON/LEMON-main Changeset - r812:4b1b378823dc

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Changeset - r812:4b1b378823dc

« 811:fe80a8

813:25804e »

r812:4b1b378823dc

Thu, 12 Nov 2009 23:49:05

[Not Reviewed]

0 comments (0 inline)

kpeter (Peter Kovacs)
kpeter@inf.elte.hu

Small doc improvements + unifications in MCF classes (#180)

0 3 0

default

3 files changed with 32 insertions and 32 deletions:

lemon/capacity_scaling.h

lemon/cost_scaling.h

lemon/network_simplex.h

↑ Collapse diff ↑

lemon/capacity_scaling.h

Show inline comments

 		/* -*- C++ -*-
+		 *
 		 * This file is a part of LEMON, a generic C++ optimization library
+		 *
 		 * Copyright (C) 2003-2008
 		 * Egervary Jeno Kombinatorikus Optimalizalasi Kutatocsoport
 		 * (Egervary Research Group on Combinatorial Optimization, EGRES).
+		 *
 		 * Permission to use, modify and distribute this software is granted
 		 * provided that this copyright notice appears in all copies. For
 		 * precise terms see the accompanying LICENSE file.
+		 *
 		 * This software is provided "AS IS" with no warranty of any kind,
 		 * express or implied, and with no claim as to its suitability for any
 		 * purpose.
+		 *
 		 */
 		#ifndef LEMON_CAPACITY_SCALING_H
 		#define LEMON_CAPACITY_SCALING_H
 		/// \ingroup min_cost_flow_algs
 		///
 		/// \file
 		/// \brief Capacity Scaling algorithm for finding a minimum cost flow.
 		#include <vector>
 		#include <limits>
 		#include <lemon/core.h>
 		#include <lemon/bin_heap.h>
 		namespace lemon {
 		  /// \brief Default traits class of CapacityScaling algorithm.
 		  ///
 		  /// Default traits class of CapacityScaling algorithm.
 		  /// \tparam GR Digraph type.
-		  /// \tparam V The value type used for flow amounts, capacity bounds
+		  /// \tparam V The number type used for flow amounts, capacity bounds
 		  /// and supply values. By default it is \c int.
-		  /// \tparam C The value type used for costs and potentials.
+		  /// \tparam C The number type used for costs and potentials.
 		  /// By default it is the same as \c V.
 		  template <typename GR, typename V = int, typename C = V>
 		  struct CapacityScalingDefaultTraits
+		  {
 		    /// The type of the digraph
 		    typedef GR Digraph;
 		    /// The type of the flow amounts, capacity bounds and supply values
 		    typedef V Value;
 		    /// The type of the arc costs
 		    typedef C Cost;
 		    /// \brief The type of the heap used for internal Dijkstra computations.
 		    ///
 		    /// The type of the heap used for internal Dijkstra computations.
 		    /// It must conform to the \ref lemon::concepts::Heap "Heap" concept,
 		    /// its priority type must be \c Cost and its cross reference type
 		    /// must be \ref RangeMap "RangeMap<int>".
 		    typedef BinHeap<Cost, RangeMap<int> > Heap;
 		  };
 		  /// \addtogroup min_cost_flow_algs
 		  /// @{
 		  /// \brief Implementation of the Capacity Scaling algorithm for
 		  /// finding a \ref min_cost_flow "minimum cost flow".
 		  ///
 		  /// \ref CapacityScaling implements the capacity scaling version
 		  /// of the successive shortest path algorithm for finding a
 		  /// \ref min_cost_flow "minimum cost flow". It is an efficient dual
 		  /// solution method.
 		  ///
 		  /// Most of the parameters of the problem (except for the digraph)
 		  /// can be given using separate functions, and the algorithm can be
 		  /// executed using the \ref run() function. If some parameters are not
 		  /// specified, then default values will be used.
 		  ///
 		  /// \tparam GR The digraph type the algorithm runs on.
-		  /// \tparam V The value type used for flow amounts, capacity bounds
+		  /// \tparam V The number type used for flow amounts, capacity bounds
 		  /// and supply values in the algorithm. By default it is \c int.
-		  /// \tparam C The value type used for costs and potentials in the
+		  /// \tparam C The number type used for costs and potentials in the
 		  /// algorithm. By default it is the same as \c V.
 		  ///
-		  /// \warning Both value types must be signed and all input data must
+		  /// \warning Both number types must be signed and all input data must
 		  /// be integer.
 		  /// \warning This algorithm does not support negative costs for such
 		  /// arcs that have infinite upper bound.
 		#ifdef DOXYGEN
 		  template <typename GR, typename V, typename C, typename TR>
 		#else
 		  template < typename GR, typename V = int, typename C = V,
 		             typename TR = CapacityScalingDefaultTraits<GR, V, C> >
 		#endif
 		  class CapacityScaling
+		  {
 		  public:
 		    /// The type of the digraph
 		    typedef typename TR::Digraph Digraph;
 		    /// The type of the flow amounts, capacity bounds and supply values
 		    typedef typename TR::Value Value;
 		    /// The type of the arc costs
 		    typedef typename TR::Cost Cost;
 		    /// The type of the heap used for internal Dijkstra computations
 		    typedef typename TR::Heap Heap;
 		    /// The \ref CapacityScalingDefaultTraits "traits class" of the algorithm
 		    typedef TR Traits;
 		  public:
 		    /// \brief Problem type constants for the \c run() function.
 		    ///
 		    /// Enum type containing the problem type constants that can be
 		    /// returned by the \ref run() function of the algorithm.
 		    enum ProblemType {
 		      /// The problem has no feasible solution (flow).
 		      INFEASIBLE,
 		      /// 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).
 		      OPTIMAL,
 		      /// The digraph contains an arc of negative cost and infinite
 		      /// upper bound. It means that the objective function is unbounded
 		      /// on that arc, however note that it could actually be bounded
+		      /// on that arc, however, note that it could actually be bounded
 		      /// over the feasible flows, but this algroithm cannot handle
 		      /// these cases.
 		      UNBOUNDED
 		    };
 		  private:
 		    TEMPLATE_DIGRAPH_TYPEDEFS(GR);
 		    typedef std::vector<int> IntVector;
 		    typedef std::vector<char> BoolVector;
 		    typedef std::vector<Value> ValueVector;
 		    typedef std::vector<Cost> CostVector;
 		  private:
 		    // Data related to the underlying digraph
 		    const GR &_graph;
 		    int _node_num;
 		    int _arc_num;
 		    int _res_arc_num;
 		    int _root;
 		    // Parameters of the problem
 		    bool _have_lower;
 		    Value _sum_supply;
 		    // Data structures for storing the digraph
 		    IntNodeMap _node_id;
 		    IntArcMap _arc_idf;
 		    IntArcMap _arc_idb;
 		    IntVector _first_out;
 		    BoolVector _forward;
 		    IntVector _source;
 		    IntVector _target;
 		    IntVector _reverse;
 		    // Node and arc data
 		    ValueVector _lower;
 		    ValueVector _upper;
 		    CostVector _cost;
 		    ValueVector _supply;
 		    ValueVector _res_cap;
 		    CostVector _pi;
 		    ValueVector _excess;
 		    IntVector _excess_nodes;
 		    IntVector _deficit_nodes;
@@ -262,97 +262,97 @@
 		        for (int i = 0; i < int(_proc_nodes.size()); ++i) {
 		          _pi[_proc_nodes[i]] += _dist[_proc_nodes[i]] - dt;
+		        }
 		        return t;
+		      }
 		    }; //class ResidualDijkstra
 		  public:
 		    /// \name Named Template Parameters
 		    /// @{
 		    template <typename T>
 		    struct SetHeapTraits : public Traits {
 		      typedef T Heap;
 		    };
 		    /// \brief \ref named-templ-param "Named parameter" for setting
 		    /// \c Heap type.
 		    ///
 		    /// \ref named-templ-param "Named parameter" for setting \c Heap
 		    /// type, which is used for internal Dijkstra computations.
 		    /// It must conform to the \ref lemon::concepts::Heap "Heap" concept,
 		    /// its priority type must be \c Cost and its cross reference type
 		    /// must be \ref RangeMap "RangeMap<int>".
 		    template <typename T>
 		    struct SetHeap
 		      : public CapacityScaling<GR, V, C, SetHeapTraits<T> > {
 		      typedef  CapacityScaling<GR, V, C, SetHeapTraits<T> > Create;
 		    };
 		    /// @}
 		  public:
 		    /// \brief Constructor.
 		    ///
 		    /// The constructor of the class.
 		    ///
 		    /// \param graph The digraph the algorithm runs on.
 		    CapacityScaling(const GR& graph) :
 		      _graph(graph), _node_id(graph), _arc_idf(graph), _arc_idb(graph),
 		      INF(std::numeric_limits<Value>::has_infinity ?
 		          std::numeric_limits<Value>::infinity() :
 		          std::numeric_limits<Value>::max())
+		    {
-		      // Check the value types
+		      // Check the number types
 		      LEMON_ASSERT(std::numeric_limits<Value>::is_signed,
 		        "The flow type of CapacityScaling must be signed");
 		      LEMON_ASSERT(std::numeric_limits<Cost>::is_signed,
 		        "The cost type of CapacityScaling must be signed");
 		      // Resize vectors
 		      _node_num = countNodes(_graph);
 		      _arc_num = countArcs(_graph);
 		      _res_arc_num = 2 * (_arc_num + _node_num);
 		      _root = _node_num;
 		      ++_node_num;
 		      _first_out.resize(_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);
 		      _cost.resize(_res_arc_num);
 		      _supply.resize(_node_num);
 		      _res_cap.resize(_res_arc_num);
 		      _pi.resize(_node_num);
 		      _excess.resize(_node_num);
 		      _pred.resize(_node_num);
 		      // Copy the graph
 		      int i = 0, j = 0, k = 2 * _arc_num + _node_num - 1;
 		      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)];
+		        }
@@ -366,97 +366,97 @@
 		        _reverse[k] = j;
 		        ++j; ++k;
+		      }
 		      _first_out[i] = j;
 		      _first_out[_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
 		      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>
 		    CapacityScaling& lowerMap(const LowerMap& map) {
 		      _have_lower = true;
 		      for (ArcIt a(_graph); a != INVALID; ++a) {
 		        _lower[_arc_idf[a]] = map[a];
 		        _lower[_arc_idb[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 on each arc).
 		    /// 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>
 		    CapacityScaling& upperMap(const UpperMap& map) {
 		      for (ArcIt a(_graph); a != INVALID; ++a) {
 		        _upper[_arc_idf[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>
 		    CapacityScaling& costMap(const CostMap& map) {
 		      for (ArcIt a(_graph); a != INVALID; ++a) {
 		        _cost[_arc_idf[a]] =  map[a];
 		        _cost[_arc_idb[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>
 		    template<typename SupplyMap>
 		    CapacityScaling& supplyMap(const SupplyMap& map) {
 		      for (NodeIt n(_graph); n != INVALID; ++n) {
@@ -469,110 +469,110 @@
 		    ///
 		    /// 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 such 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>
 		    CapacityScaling& 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;
+		    }
 		    /// @}
 		    /// \name Execution control
 		    /// The algorithm can be executed using \ref run().
 		    /// @{
 		    /// \brief Run the algorithm.
 		    ///
 		    /// This function runs the algorithm.
 		    /// The paramters can be specified using functions \ref lowerMap(),
 		    /// \ref upperMap(), \ref costMap(), \ref supplyMap(), \ref stSupply().
 		    /// For example,
 		    /// \code
 		    ///   CapacityScaling<ListDigraph> cs(graph);
 		    ///   cs.lowerMap(lower).upperMap(upper).costMap(cost)
 		    ///     .supplyMap(sup).run();
 		    /// \endcode
 		    ///
 		    /// This function can be called more than once. All the parameters
 		    /// that have been given are kept for the next call, unless
 		    /// \ref reset() is called, thus only the modified parameters
 		    /// have to be set again. See \ref reset() for examples.
 		    /// However the underlying digraph must not be modified after this
+		    /// However, the underlying digraph must not be modified after this
 		    /// class have been constructed, since it copies and extends the graph.
 		    ///
 		    /// \param factor The capacity scaling factor. It must be larger than
 		    /// one to use scaling. If it is less or equal to one, then scaling
 		    /// will be disabled.
 		    ///
 		    /// \return \c INFEASIBLE if no feasible flow exists,
 		    /// \n \c OPTIMAL if the problem has optimal solution
 		    /// (i.e. it is feasible and bounded), and the algorithm has found
 		    /// optimal flow and node potentials (primal and dual solutions),
 		    /// \n \c UNBOUNDED if the digraph contains an arc of negative cost
 		    /// and infinite upper bound. It means that the objective function
 		    /// is unbounded on that arc, however note that it could actually be
+		    /// is unbounded on that arc, however, note that it could actually be
 		    /// bounded over the feasible flows, but this algroithm cannot handle
 		    /// these cases.
 		    ///
 		    /// \see ProblemType
 		    ProblemType run(int factor = 4) {
 		      _factor = factor;
 		      ProblemType pt = init();
 		      if (pt != OPTIMAL) return pt;
 		      return start();
+		    }
 		    /// \brief Reset all the parameters that have been given before.
 		    ///
 		    /// This function resets all the paramaters that have been given
 		    /// before using functions \ref lowerMap(), \ref upperMap(),
 		    /// \ref costMap(), \ref supplyMap(), \ref stSupply().
 		    ///
 		    /// It is useful for multiple run() calls. If this function is not
 		    /// used, all the parameters given before are kept for the next
 		    /// \ref run() call.
 		    /// However, the underlying digraph must not be modified after this
 		    /// class have been constructed, since it copies and extends the graph.
 		    ///
 		    /// For example,
 		    /// \code
 		    ///   CapacityScaling<ListDigraph> cs(graph);
 		    ///
 		    ///   // First run
 		    ///   cs.lowerMap(lower).upperMap(upper).costMap(cost)
 		    ///     .supplyMap(sup).run();
 		    ///
 		    ///   // Run again with modified cost map (reset() is not called,
 		    ///   // so only the cost map have to be set again)
 		    ///   cost[e] += 100;
 		    ///   cs.costMap(cost).run();
 		    ///
 		    ///   // Run again from scratch using reset()
 		    ///   // (the lower bounds will be set to zero on all arcs)
 		    ///   cs.reset();
 		    ///   cs.upperMap(capacity).costMap(cost)
 		    ///     .supplyMap(sup).run();
 		    /// \endcode
 		    ///
 		    /// \return <tt>(*this)</tt>
 		    CapacityScaling& reset() {
 		      for (int i = 0; i != _node_num; ++i) {
 		        _supply[i] = 0;
+		      }

lemon/cost_scaling.h

Show inline comments

 		/* -*- C++ -*-
+		 *
 		 * This file is a part of LEMON, a generic C++ optimization library
+		 *
 		 * Copyright (C) 2003-2008
 		 * Egervary Jeno Kombinatorikus Optimalizalasi Kutatocsoport
 		 * (Egervary Research Group on Combinatorial Optimization, EGRES).
+		 *
 		 * Permission to use, modify and distribute this software is granted
 		 * provided that this copyright notice appears in all copies. For
 		 * precise terms see the accompanying LICENSE file.
+		 *
 		 * This software is provided "AS IS" with no warranty of any kind,
 		 * express or implied, and with no claim as to its suitability for any
 		 * purpose.
+		 *
 		 */
 		#ifndef LEMON_COST_SCALING_H
 		#define LEMON_COST_SCALING_H
 		/// \ingroup min_cost_flow_algs
 		/// \file
 		/// \brief Cost scaling algorithm for finding a minimum cost flow.
 		#include <vector>
 		#include <deque>
 		#include <limits>
 		#include <lemon/core.h>
 		#include <lemon/maps.h>
 		#include <lemon/math.h>
 		#include <lemon/static_graph.h>
 		#include <lemon/circulation.h>
 		#include <lemon/bellman_ford.h>
 		namespace lemon {
 		  /// \brief Default traits class of CostScaling algorithm.
 		  ///
 		  /// Default traits class of CostScaling algorithm.
 		  /// \tparam GR Digraph type.
-		  /// \tparam V The value type used for flow amounts, capacity bounds
+		  /// \tparam V The number type used for flow amounts, capacity bounds
 		  /// and supply values. By default it is \c int.
-		  /// \tparam C The value type used for costs and potentials.
+		  /// \tparam C The number type used for costs and potentials.
 		  /// By default it is the same as \c V.
 		#ifdef DOXYGEN
 		  template <typename GR, typename V = int, typename C = V>
 		#else
 		  template < typename GR, typename V = int, typename C = V,
 		             bool integer = std::numeric_limits<C>::is_integer >
 		#endif
 		  struct CostScalingDefaultTraits
+		  {
 		    /// The type of the digraph
 		    typedef GR Digraph;
 		    /// The type of the flow amounts, capacity bounds and supply values
 		    typedef V Value;
 		    /// The type of the arc costs
 		    typedef C Cost;
 		    /// \brief The large cost type used for internal computations
 		    ///
 		    /// The large cost type used for internal computations.
 		    /// It is \c long \c long if the \c Cost type is integer,
 		    /// otherwise it is \c double.
 		    /// \c Cost must be convertible to \c LargeCost.
 		    typedef double LargeCost;
 		  };
 		  // Default traits class for integer cost types
 		  template <typename GR, typename V, typename C>
 		  struct CostScalingDefaultTraits<GR, V, C, true>
+		  {
 		    typedef GR Digraph;
 		    typedef V Value;
 		    typedef C Cost;
 		#ifdef LEMON_HAVE_LONG_LONG
 		    typedef long long LargeCost;
 		#else
 		    typedef long LargeCost;
 		#endif
 		  };
 		  /// \addtogroup min_cost_flow_algs
 		  /// @{
 		  /// \brief Implementation of the Cost Scaling algorithm for
 		  /// finding a \ref min_cost_flow "minimum cost flow".
 		  ///
 		  /// \ref CostScaling implements a cost scaling algorithm that performs
 		  /// push/augment and relabel operations for finding a minimum cost
 		  /// flow. It is an efficient primal-dual solution method, which
 		  /// can be viewed as the generalization of the \ref Preflow
 		  /// "preflow push-relabel" algorithm for the maximum flow problem.
 		  ///
 		  /// Most of the parameters of the problem (except for the digraph)
 		  /// can be given using separate functions, and the algorithm can be
 		  /// executed using the \ref run() function. If some parameters are not
 		  /// specified, then default values will be used.
 		  ///
 		  /// \tparam GR The digraph type the algorithm runs on.
-		  /// \tparam V The value type used for flow amounts, capacity bounds
+		  /// \tparam V The number type used for flow amounts, capacity bounds
 		  /// and supply values in the algorithm. By default it is \c int.
-		  /// \tparam C The value type used for costs and potentials in the
+		  /// \tparam C The number type used for costs and potentials in the
 		  /// algorithm. By default it is the same as \c V.
 		  ///
-		  /// \warning Both value types must be signed and all input data must
+		  /// \warning Both number types must be signed and all input data must
 		  /// be integer.
 		  /// \warning This algorithm does not support negative costs for such
 		  /// arcs that have infinite upper bound.
 		  ///
 		  /// \note %CostScaling provides three different internal methods,
 		  /// from which the most efficient one is used by default.
 		  /// For more information, see \ref Method.
 		#ifdef DOXYGEN
 		  template <typename GR, typename V, typename C, typename TR>
 		#else
 		  template < typename GR, typename V = int, typename C = V,
 		             typename TR = CostScalingDefaultTraits<GR, V, C> >
 		#endif
 		  class CostScaling
+		  {
 		  public:
 		    /// The type of the digraph
 		    typedef typename TR::Digraph Digraph;
 		    /// The type of the flow amounts, capacity bounds and supply values
 		    typedef typename TR::Value Value;
 		    /// The type of the arc costs
 		    typedef typename TR::Cost Cost;
 		    /// \brief The large cost type
 		    ///
 		    /// The large cost type used for internal computations.
 		    /// Using the \ref CostScalingDefaultTraits "default traits class",
 		    /// it is \c long \c long if the \c Cost type is integer,
 		    /// otherwise it is \c double.
 		    typedef typename TR::LargeCost LargeCost;
 		    /// The \ref CostScalingDefaultTraits "traits class" of the algorithm
 		    typedef TR Traits;
 		  public:
 		    /// \brief Problem type constants for the \c run() function.
 		    ///
 		    /// Enum type containing the problem type constants that can be
 		    /// returned by the \ref run() function of the algorithm.
 		    enum ProblemType {
 		      /// The problem has no feasible solution (flow).
 		      INFEASIBLE,
 		      /// 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).
 		      OPTIMAL,
 		      /// The digraph contains an arc of negative cost and infinite
 		      /// upper bound. It means that the objective function is unbounded
 		      /// on that arc, however note that it could actually be bounded
+		      /// on that arc, however, note that it could actually be bounded
 		      /// over the feasible flows, but this algroithm cannot handle
 		      /// these cases.
 		      UNBOUNDED
 		    };
 		    /// \brief Constants for selecting the internal method.
 		    ///
 		    /// Enum type containing constants for selecting the internal method
 		    /// for the \ref run() function.
 		    ///
 		    /// \ref CostScaling provides three internal methods that differ mainly
 		    /// in their base operations, which are used in conjunction with the
 		    /// relabel operation.
 		    /// By default, the so called \ref PARTIAL_AUGMENT
 		    /// "Partial Augment-Relabel" method is used, which proved to be
 		    /// the most efficient and the most robust on various test inputs.
 		    /// However, the other methods can be selected using the \ref run()
 		    /// function with the proper parameter.
 		    enum Method {
 		      /// Local push operations are used, i.e. flow is moved only on one
 		      /// admissible arc at once.
 		      PUSH,
 		      /// Augment operations are used, i.e. flow is moved on admissible
 		      /// paths from a node with excess to a node with deficit.
 		      AUGMENT,
 		      /// Partial augment operations are used, i.e. flow is moved on
 		      /// admissible paths started from a node with excess, but the
 		      /// lengths of these paths are limited. This method can be viewed
 		      /// as a combined version of the previous two operations.
 		      PARTIAL_AUGMENT
 		    };
 		  private:
 		    TEMPLATE_DIGRAPH_TYPEDEFS(GR);
 		    typedef std::vector<int> IntVector;
 		    typedef std::vector<char> BoolVector;
 		    typedef std::vector<Value> ValueVector;
 		    typedef std::vector<Cost> CostVector;
 		    typedef std::vector<LargeCost> LargeCostVector;
 		  private:
 		    template <typename KT, typename VT>
 		    class VectorMap {
 		    public:
 		      typedef KT Key;
@@ -280,97 +280,97 @@
 		  public:
 		    /// \brief Constant for infinite upper bounds (capacities).
 		    ///
 		    /// Constant for infinite upper bounds (capacities).
 		    /// It is \c std::numeric_limits<Value>::infinity() if available,
 		    /// \c std::numeric_limits<Value>::max() otherwise.
 		    const Value INF;
 		  public:
 		    /// \name Named Template Parameters
 		    /// @{
 		    template <typename T>
 		    struct SetLargeCostTraits : public Traits {
 		      typedef T LargeCost;
 		    };
 		    /// \brief \ref named-templ-param "Named parameter" for setting
 		    /// \c LargeCost type.
 		    ///
 		    /// \ref named-templ-param "Named parameter" for setting \c LargeCost
 		    /// type, which is used for internal computations in the algorithm.
 		    /// \c Cost must be convertible to \c LargeCost.
 		    template <typename T>
 		    struct SetLargeCost
 		      : public CostScaling<GR, V, C, SetLargeCostTraits<T> > {
 		      typedef  CostScaling<GR, V, C, SetLargeCostTraits<T> > Create;
 		    };
 		    /// @}
 		  public:
 		    /// \brief Constructor.
 		    ///
 		    /// The constructor of the class.
 		    ///
 		    /// \param graph The digraph the algorithm runs on.
 		    CostScaling(const GR& graph) :
 		      _graph(graph), _node_id(graph), _arc_idf(graph), _arc_idb(graph),
 		      _cost_map(_cost_vec), _pi_map(_pi),
 		      INF(std::numeric_limits<Value>::has_infinity ?
 		          std::numeric_limits<Value>::infinity() :
 		          std::numeric_limits<Value>::max())
+		    {
-		      // Check the value types
+		      // Check the number types
 		      LEMON_ASSERT(std::numeric_limits<Value>::is_signed,
 		        "The flow type of CostScaling must be signed");
 		      LEMON_ASSERT(std::numeric_limits<Cost>::is_signed,
 		        "The cost type of CostScaling must be signed");
 		      // 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);
 		      _arc_vec.reserve(_res_arc_num);
 		      _cost_vec.reserve(_res_arc_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;
@@ -388,97 +388,97 @@
 		        _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
 		      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>
 		    CostScaling& lowerMap(const LowerMap& map) {
 		      _have_lower = true;
 		      for (ArcIt a(_graph); a != INVALID; ++a) {
 		        _lower[_arc_idf[a]] = map[a];
 		        _lower[_arc_idb[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 on each arc).
 		    /// 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>
 		    CostScaling& upperMap(const UpperMap& map) {
 		      for (ArcIt a(_graph); a != INVALID; ++a) {
 		        _upper[_arc_idf[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>
 		    CostScaling& costMap(const CostMap& map) {
 		      for (ArcIt a(_graph); a != INVALID; ++a) {
 		        _scost[_arc_idf[a]] =  map[a];
 		        _scost[_arc_idb[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>
 		    template<typename SupplyMap>
 		    CostScaling& supplyMap(const SupplyMap& map) {
 		      for (NodeIt n(_graph); n != INVALID; ++n) {
@@ -504,119 +504,119 @@
 		    /// (i.e. the supply of \c s and the demand of \c t).
 		    ///
 		    /// \return <tt>(*this)</tt>
 		    CostScaling& stSupply(const Node& s, const Node& t, Value k) {
 		      for (int i = 0; i != _res_node_num; ++i) {
 		        _supply[i] = 0;
+		      }
 		      _supply[_node_id[s]] =  k;
 		      _supply[_node_id[t]] = -k;
 		      return *this;
+		    }
 		    /// @}
 		    /// \name Execution control
 		    /// The algorithm can be executed using \ref run().
 		    /// @{
 		    /// \brief Run the algorithm.
 		    ///
 		    /// This function runs the algorithm.
 		    /// The paramters can be specified using functions \ref lowerMap(),
 		    /// \ref upperMap(), \ref costMap(), \ref supplyMap(), \ref stSupply().
 		    /// For example,
 		    /// \code
 		    ///   CostScaling<ListDigraph> cs(graph);
 		    ///   cs.lowerMap(lower).upperMap(upper).costMap(cost)
 		    ///     .supplyMap(sup).run();
 		    /// \endcode
 		    ///
 		    /// This function can be called more than once. All the parameters
 		    /// that have been given are kept for the next call, unless
 		    /// \ref reset() is called, thus only the modified parameters
 		    /// have to be set again. See \ref reset() for examples.
 		    /// However, the underlying digraph must not be modified after this
 		    /// class have been constructed, since it copies and extends the graph.
 		    ///
 		    /// \param method The internal method that will be used in the
 		    /// algorithm. For more information, see \ref Method.
 		    /// \param factor The cost scaling factor. It must be larger than one.
 		    ///
 		    /// \return \c INFEASIBLE if no feasible flow exists,
 		    /// \n \c OPTIMAL if the problem has optimal solution
 		    /// (i.e. it is feasible and bounded), and the algorithm has found
 		    /// optimal flow and node potentials (primal and dual solutions),
 		    /// \n \c UNBOUNDED if the digraph contains an arc of negative cost
 		    /// and infinite upper bound. It means that the objective function
 		    /// is unbounded on that arc, however note that it could actually be
+		    /// is unbounded on that arc, however, note that it could actually be
 		    /// bounded over the feasible flows, but this algroithm cannot handle
 		    /// these cases.
 		    ///
 		    /// \see ProblemType, Method
 		    ProblemType run(Method method = PARTIAL_AUGMENT, int factor = 8) {
 		      _alpha = factor;
 		      ProblemType pt = init();
 		      if (pt != OPTIMAL) return pt;
 		      start(method);
 		      return OPTIMAL;
+		    }
 		    /// \brief Reset all the parameters that have been given before.
 		    ///
 		    /// This function resets all the paramaters that have been given
 		    /// before using functions \ref lowerMap(), \ref upperMap(),
 		    /// \ref costMap(), \ref supplyMap(), \ref stSupply().
 		    ///
 		    /// It is useful for multiple run() calls. If this function is not
 		    /// used, all the parameters given before are kept for the next
 		    /// \ref run() call.
 		    /// However the underlying digraph must not be modified after this
+		    /// However, the underlying digraph must not be modified after this
 		    /// class have been constructed, since it copies and extends the graph.
 		    ///
 		    /// For example,
 		    /// \code
 		    ///   CostScaling<ListDigraph> cs(graph);
 		    ///
 		    ///   // First run
 		    ///   cs.lowerMap(lower).upperMap(upper).costMap(cost)
 		    ///     .supplyMap(sup).run();
 		    ///
 		    ///   // Run again with modified cost map (reset() is not called,
 		    ///   // so only the cost map have to be set again)
 		    ///   cost[e] += 100;
 		    ///   cs.costMap(cost).run();
 		    ///
 		    ///   // Run again from scratch using reset()
 		    ///   // (the lower bounds will be set to zero on all arcs)
 		    ///   cs.reset();
 		    ///   cs.upperMap(capacity).costMap(cost)
 		    ///     .supplyMap(sup).run();
 		    /// \endcode
 		    ///
 		    /// \return <tt>(*this)</tt>
 		    CostScaling& reset() {
 		      for (int i = 0; i != _res_node_num; ++i) {
 		        _supply[i] = 0;
+		      }
 		      int limit = _first_out[_root];
 		      for (int j = 0; j != limit; ++j) {
 		        _lower[j] = 0;
 		        _upper[j] = INF;
 		        _scost[j] = _forward[j] ? 1 : -1;
+		      }
 		      for (int j = limit; j != _res_arc_num; ++j) {
 		        _lower[j] = 0;
 		        _upper[j] = INF;
 		        _scost[j] = 0;
 		        _scost[_reverse[j]] = 0;
+		      }
 		      _have_lower = false;
 		      return *this;
+		    }
 		    /// @}
 		    /// \name Query Functions
 		    /// The results of the algorithm can be obtained using these
 		    /// functions.\n

lemon/network_simplex.h

Show inline comments

 		/* -*- mode: C++; indent-tabs-mode: nil; -*-
+		 *
 		 * This file is a part of LEMON, a generic C++ optimization library.
+		 *
 		 * Copyright (C) 2003-2009
 		 * Egervary Jeno Kombinatorikus Optimalizalasi Kutatocsoport
 		 * (Egervary Research Group on Combinatorial Optimization, EGRES).
+		 *
 		 * Permission to use, modify and distribute this software is granted
 		 * provided that this copyright notice appears in all copies. For
 		 * precise terms see the accompanying LICENSE file.
+		 *
 		 * This software is provided "AS IS" with no warranty of any kind,
 		 * express or implied, and with no claim as to its suitability for any
 		 * purpose.
+		 *
 		 */
 		#ifndef LEMON_NETWORK_SIMPLEX_H
 		#define LEMON_NETWORK_SIMPLEX_H
 		/// \ingroup min_cost_flow_algs
 		///
 		/// \file
 		/// \brief Network Simplex algorithm for finding a minimum cost flow.
 		#include <vector>
 		#include <limits>
 		#include <algorithm>
 		#include <lemon/core.h>
 		#include <lemon/math.h>
 		namespace lemon {
 		  /// \addtogroup min_cost_flow_algs
 		  /// @{
 		  /// \brief Implementation of the primal Network Simplex algorithm
 		  /// for finding a \ref min_cost_flow "minimum cost flow".
 		  ///
 		  /// \ref NetworkSimplex implements the primal Network Simplex algorithm
 		  /// for finding a \ref min_cost_flow "minimum cost flow"
 		  /// \ref amo93networkflows, \ref dantzig63linearprog,
 		  /// \ref kellyoneill91netsimplex.
 		  /// This algorithm is a specialized version of the linear programming
 		  /// simplex method directly for the minimum cost flow problem.
-		  /// It is one of the most efficient solution methods.
+		  /// This algorithm is a highly efficient specialized version of the
 		  /// linear programming simplex method directly for the minimum cost
 		  /// flow problem.
 		  ///
 		  /// In general this class is the fastest implementation available
 		  /// in LEMON for the minimum cost flow problem.
-		  /// Moreover it supports both directions of the supply/demand inequality
+		  /// In general, %NetworkSimplex is the fastest implementation available
 		  /// in LEMON for this problem.
 		  /// Moreover, it supports both directions of the supply/demand inequality
 		  /// constraints. For more information, see \ref SupplyType.
 		  ///
 		  /// Most of the parameters of the problem (except for the digraph)
 		  /// can be given using separate functions, and the algorithm can be
 		  /// executed using the \ref run() function. If some parameters are not
 		  /// specified, then default values will be used.
 		  ///
 		  /// \tparam GR The digraph type the algorithm runs on.
-		  /// \tparam V The value type used for flow amounts, capacity bounds
+		  /// \tparam V The number type used for flow amounts, capacity bounds
 		  /// and supply values in the algorithm. By default, it is \c int.
-		  /// \tparam C The value type used for costs and potentials in the
+		  /// \tparam C The number type used for costs and potentials in the
 		  /// algorithm. By default, it is the same as \c V.
 		  ///
-		  /// \warning Both value types must be signed and all input data must
+		  /// \warning Both number types must be signed and all input data must
 		  /// be integer.
 		  ///
 		  /// \note %NetworkSimplex provides five different pivot rule
 		  /// implementations, from which the most efficient one is used
 		  /// by default. For more information, see \ref PivotRule.
 		  template <typename GR, typename V = int, typename C = V>
 		  class NetworkSimplex
+		  {
 		  public:
 		    /// The type of the flow amounts, capacity bounds and supply values
 		    typedef V Value;
 		    /// The type of the arc costs
 		    typedef C Cost;
 		  public:
 		    /// \brief Problem type constants for the \c run() function.
 		    ///
 		    /// Enum type containing the problem type constants that can be
 		    /// returned by the \ref run() function of the algorithm.
 		    enum ProblemType {
 		      /// The problem has no feasible solution (flow).
 		      INFEASIBLE,
 		      /// 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).
 		      OPTIMAL,
 		      /// The objective function of the problem is unbounded, i.e.
 		      /// there is a directed cycle having negative total cost and
 		      /// infinite upper bound.
 		      UNBOUNDED
 		    };
 		    /// \brief Constants for selecting the type of the supply constraints.
 		    ///
 		    /// Enum type containing constants for selecting the supply type,
 		    /// i.e. the direction of the inequalities in the supply/demand
 		    /// constraints of the \ref min_cost_flow "minimum cost flow problem".
 		    ///
 		    /// The default supply type is \c GEQ, the \c LEQ type can be
 		    /// selected using \ref supplyType().
 		    /// The equality form is a special case of both supply types.
 		    enum SupplyType {
 		      /// This option means that there are <em>"greater or equal"</em>
 		      /// supply/demand constraints in the definition of the problem.
 		      GEQ,
 		      /// This option means that there are <em>"less or equal"</em>
 		      /// supply/demand constraints in the definition of the problem.
 		      LEQ
 		    };
 		    /// \brief Constants for selecting the pivot rule.
 		    ///
 		    /// Enum type containing constants for selecting the pivot rule for
 		    /// the \ref run() function.
 		    ///
 		    /// \ref NetworkSimplex provides five different pivot rule
 		    /// implementations that significantly affect the running time
 		    /// of the algorithm.
 		    /// By default, \ref BLOCK_SEARCH "Block Search" is used, which
 		    /// proved to be the most efficient and the most robust on various
-		    /// test inputs according to our benchmark tests.
 		    /// test inputs.
 		    /// However, another pivot rule can be selected using the \ref run()
 		    /// function with the proper parameter.
 		    enum PivotRule {
 		      /// The \e First \e Eligible pivot rule.
 		      /// The next eligible arc is selected in a wraparound fashion
 		      /// in every iteration.
 		      FIRST_ELIGIBLE,
 		      /// The \e Best \e Eligible pivot rule.
 		      /// The best eligible arc is selected in every iteration.
 		      BEST_ELIGIBLE,
 		      /// The \e Block \e Search pivot rule.
 		      /// A specified number of arcs are examined in every iteration
 		      /// in a wraparound fashion and the best eligible arc is selected
 		      /// from this block.
 		      BLOCK_SEARCH,
 		      /// The \e Candidate \e List pivot rule.
 		      /// In a major iteration a candidate list is built from eligible arcs
 		      /// in a wraparound fashion and in the following minor iterations
 		      /// the best eligible arc is selected from this list.
 		      CANDIDATE_LIST,
 		      /// The \e Altering \e Candidate \e List pivot rule.
 		      /// It is a modified version of the Candidate List method.
 		      /// It keeps only the several best eligible arcs from the former
 		      /// candidate list and extends this list in every iteration.
 		      ALTERING_LIST
 		    };
 		  private:
 		    TEMPLATE_DIGRAPH_TYPEDEFS(GR);
 		    typedef std::vector<int> IntVector;
 		    typedef std::vector<char> CharVector;
 		    typedef std::vector<Value> ValueVector;
 		    typedef std::vector<Cost> CostVector;
 		    // State constants for arcs
 		    enum ArcStateEnum {
 		      STATE_UPPER = -1,
 		      STATE_TREE  =  0,
 		      STATE_LOWER =  1
 		    };
@@ -592,189 +592,189 @@
 		        for (e = 0; e < _next_arc; ++e) {
 		          _cand_cost[e] = _state[e] *
 		            (_cost[e] + _pi[_source[e]] - _pi[_target[e]]);
 		          if (_cand_cost[e] < 0) {
 		            _candidates[_curr_length++] = e;
+		          }
 		          if (--cnt == 0) {
 		            if (_curr_length > limit) goto search_end;
 		            limit = 0;
 		            cnt = _block_size;
+		          }
+		        }
 		        if (_curr_length == 0) return false;
 		      search_end:
 		        // Make heap of the candidate list (approximating a partial sort)
 		        make_heap( _candidates.begin(), _candidates.begin() + _curr_length,
 		                   _sort_func );
 		        // Pop the first element of the heap
 		        _in_arc = _candidates[0];
 		        _next_arc = e;
 		        pop_heap( _candidates.begin(), _candidates.begin() + _curr_length,
 		                  _sort_func );
 		        _curr_length = std::min(_head_length, _curr_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 have to be stored in a
 		    /// mixed order in the internal data structure.
 		    /// In special cases, it could lead to better overall performance,
 		    /// but it is usually slower. Therefore it is disabled by default.
 		    NetworkSimplex(const GR& graph, bool arc_mixing = false) :
 		      _graph(graph), _node_id(graph), _arc_id(graph),
 		      MAX(std::numeric_limits<Value>::max()),
 		      INF(std::numeric_limits<Value>::has_infinity ?
 		          std::numeric_limits<Value>::infinity() : MAX)
+		    {
-		      // Check the value types
+		      // 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");
 		      // 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);
 		      _forward.resize(all_node_num);
 		      _thread.resize(all_node_num);
 		      _rev_thread.resize(all_node_num);
 		      _succ_num.resize(all_node_num);
 		      _last_succ.resize(all_node_num);
 		      _state.resize(max_arc_num);
 		      // Copy the graph
 		      int i = 0;
 		      for (NodeIt n(_graph); n != INVALID; ++n, ++i) {
 		        _node_id[n] = i;
+		      }
 		      if (arc_mixing) {
 		        // Store the arcs in a mixed order
 		        int k = std::max(int(std::sqrt(double(_arc_num))), 10);
 		        int i = 0, j = 0;
 		        for (ArcIt a(_graph); a != INVALID; ++a) {
 		          _arc_id[a] = i;
 		          _source[i] = _node_id[_graph.source(a)];
 		          _target[i] = _node_id[_graph.target(a)];
 		          if ((i += k) >= _arc_num) i = ++j;
+		        }
 		      } else {
 		        // Store the arcs in the original order
 		        int i = 0;
 		        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
 		      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) {
 		      _have_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 on each arc).
 		    /// 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>
 		    template<typename SupplyMap>
 		    NetworkSimplex& supplyMap(const SupplyMap& map) {
 		      for (NodeIt n(_graph); n != INVALID; ++n) {
 		        _supply[_node_id[n]] = map[n];

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