lemon/nagamochi_ibaraki.h
author Alpar Juttner <alpar@cs.elte.hu>
Tue, 16 Nov 2010 07:46:01 +0100
changeset 917 4980b05606bd
child 978 eb252f805431
permissions -rw-r--r--
Merge
     1 /* -*- mode: C++; indent-tabs-mode: nil; -*-
     2  *
     3  * This file is a part of LEMON, a generic C++ optimization library.
     4  *
     5  * Copyright (C) 2003-2010
     6  * Egervary Jeno Kombinatorikus Optimalizalasi Kutatocsoport
     7  * (Egervary Research Group on Combinatorial Optimization, EGRES).
     8  *
     9  * Permission to use, modify and distribute this software is granted
    10  * provided that this copyright notice appears in all copies. For
    11  * precise terms see the accompanying LICENSE file.
    12  *
    13  * This software is provided "AS IS" with no warranty of any kind,
    14  * express or implied, and with no claim as to its suitability for any
    15  * purpose.
    16  *
    17  */
    18 
    19 #ifndef LEMON_NAGAMOCHI_IBARAKI_H
    20 #define LEMON_NAGAMOCHI_IBARAKI_H
    21 
    22 
    23 /// \ingroup min_cut
    24 /// \file
    25 /// \brief Implementation of the Nagamochi-Ibaraki algorithm.
    26 
    27 #include <lemon/core.h>
    28 #include <lemon/bin_heap.h>
    29 #include <lemon/bucket_heap.h>
    30 #include <lemon/maps.h>
    31 #include <lemon/radix_sort.h>
    32 #include <lemon/unionfind.h>
    33 
    34 #include <cassert>
    35 
    36 namespace lemon {
    37 
    38   /// \brief Default traits class for NagamochiIbaraki class.
    39   ///
    40   /// Default traits class for NagamochiIbaraki class.
    41   /// \param GR The undirected graph type.
    42   /// \param CM Type of capacity map.
    43   template <typename GR, typename CM>
    44   struct NagamochiIbarakiDefaultTraits {
    45     /// The type of the capacity map.
    46     typedef typename CM::Value Value;
    47 
    48     /// The undirected graph type the algorithm runs on.
    49     typedef GR Graph;
    50 
    51     /// \brief The type of the map that stores the edge capacities.
    52     ///
    53     /// The type of the map that stores the edge capacities.
    54     /// It must meet the \ref concepts::ReadMap "ReadMap" concept.
    55     typedef CM CapacityMap;
    56 
    57     /// \brief Instantiates a CapacityMap.
    58     ///
    59     /// This function instantiates a \ref CapacityMap.
    60 #ifdef DOXYGEN
    61     static CapacityMap *createCapacityMap(const Graph& graph)
    62 #else
    63     static CapacityMap *createCapacityMap(const Graph&)
    64 #endif
    65     {
    66         LEMON_ASSERT(false, "CapacityMap is not initialized");
    67         return 0; // ignore warnings
    68     }
    69 
    70     /// \brief The cross reference type used by heap.
    71     ///
    72     /// The cross reference type used by heap.
    73     /// Usually \c Graph::NodeMap<int>.
    74     typedef typename Graph::template NodeMap<int> HeapCrossRef;
    75 
    76     /// \brief Instantiates a HeapCrossRef.
    77     ///
    78     /// This function instantiates a \ref HeapCrossRef.
    79     /// \param g is the graph, to which we would like to define the
    80     /// \ref HeapCrossRef.
    81     static HeapCrossRef *createHeapCrossRef(const Graph& g) {
    82       return new HeapCrossRef(g);
    83     }
    84 
    85     /// \brief The heap type used by NagamochiIbaraki algorithm.
    86     ///
    87     /// The heap type used by NagamochiIbaraki algorithm. It has to
    88     /// maximize the priorities.
    89     ///
    90     /// \sa BinHeap
    91     /// \sa NagamochiIbaraki
    92     typedef BinHeap<Value, HeapCrossRef, std::greater<Value> > Heap;
    93 
    94     /// \brief Instantiates a Heap.
    95     ///
    96     /// This function instantiates a \ref Heap.
    97     /// \param r is the cross reference of the heap.
    98     static Heap *createHeap(HeapCrossRef& r) {
    99       return new Heap(r);
   100     }
   101   };
   102 
   103   /// \ingroup min_cut
   104   ///
   105   /// \brief Calculates the minimum cut in an undirected graph.
   106   ///
   107   /// Calculates the minimum cut in an undirected graph with the
   108   /// Nagamochi-Ibaraki algorithm. The algorithm separates the graph's
   109   /// nodes into two partitions with the minimum sum of edge capacities
   110   /// between the two partitions. The algorithm can be used to test
   111   /// the network reliability, especially to test how many links have
   112   /// to be destroyed in the network to split it to at least two
   113   /// distinict subnetworks.
   114   ///
   115   /// The complexity of the algorithm is \f$ O(nm\log(n)) \f$ but with
   116   /// \ref FibHeap "Fibonacci heap" it can be decreased to
   117   /// \f$ O(nm+n^2\log(n)) \f$.  When the edges have unit capacities,
   118   /// \c BucketHeap can be used which yields \f$ O(nm) \f$ time
   119   /// complexity.
   120   ///
   121   /// \warning The value type of the capacity map should be able to
   122   /// hold any cut value of the graph, otherwise the result can
   123   /// overflow.
   124   /// \note This capacity is supposed to be integer type.
   125 #ifdef DOXYGEN
   126   template <typename GR, typename CM, typename TR>
   127 #else
   128   template <typename GR,
   129             typename CM = typename GR::template EdgeMap<int>,
   130             typename TR = NagamochiIbarakiDefaultTraits<GR, CM> >
   131 #endif
   132   class NagamochiIbaraki {
   133   public:
   134 
   135     typedef TR Traits;
   136     /// The type of the underlying graph.
   137     typedef typename Traits::Graph Graph;
   138 
   139     /// The type of the capacity map.
   140     typedef typename Traits::CapacityMap CapacityMap;
   141     /// The value type of the capacity map.
   142     typedef typename Traits::CapacityMap::Value Value;
   143 
   144     /// The heap type used by the algorithm.
   145     typedef typename Traits::Heap Heap;
   146     /// The cross reference type used for the heap.
   147     typedef typename Traits::HeapCrossRef HeapCrossRef;
   148 
   149     ///\name Named template parameters
   150 
   151     ///@{
   152 
   153     struct SetUnitCapacityTraits : public Traits {
   154       typedef ConstMap<typename Graph::Edge, Const<int, 1> > CapacityMap;
   155       static CapacityMap *createCapacityMap(const Graph&) {
   156         return new CapacityMap();
   157       }
   158     };
   159 
   160     /// \brief \ref named-templ-param "Named parameter" for setting
   161     /// the capacity map to a constMap<Edge, int, 1>() instance
   162     ///
   163     /// \ref named-templ-param "Named parameter" for setting
   164     /// the capacity map to a constMap<Edge, int, 1>() instance
   165     struct SetUnitCapacity
   166       : public NagamochiIbaraki<Graph, CapacityMap,
   167                                 SetUnitCapacityTraits> {
   168       typedef NagamochiIbaraki<Graph, CapacityMap,
   169                                SetUnitCapacityTraits> Create;
   170     };
   171 
   172 
   173     template <class H, class CR>
   174     struct SetHeapTraits : public Traits {
   175       typedef CR HeapCrossRef;
   176       typedef H Heap;
   177       static HeapCrossRef *createHeapCrossRef(int num) {
   178         LEMON_ASSERT(false, "HeapCrossRef is not initialized");
   179         return 0; // ignore warnings
   180       }
   181       static Heap *createHeap(HeapCrossRef &) {
   182         LEMON_ASSERT(false, "Heap is not initialized");
   183         return 0; // ignore warnings
   184       }
   185     };
   186 
   187     /// \brief \ref named-templ-param "Named parameter" for setting
   188     /// heap and cross reference type
   189     ///
   190     /// \ref named-templ-param "Named parameter" for setting heap and
   191     /// cross reference type. The heap has to maximize the priorities.
   192     template <class H, class CR = RangeMap<int> >
   193     struct SetHeap
   194       : public NagamochiIbaraki<Graph, CapacityMap, SetHeapTraits<H, CR> > {
   195       typedef NagamochiIbaraki< Graph, CapacityMap, SetHeapTraits<H, CR> >
   196       Create;
   197     };
   198 
   199     template <class H, class CR>
   200     struct SetStandardHeapTraits : public Traits {
   201       typedef CR HeapCrossRef;
   202       typedef H Heap;
   203       static HeapCrossRef *createHeapCrossRef(int size) {
   204         return new HeapCrossRef(size);
   205       }
   206       static Heap *createHeap(HeapCrossRef &crossref) {
   207         return new Heap(crossref);
   208       }
   209     };
   210 
   211     /// \brief \ref named-templ-param "Named parameter" for setting
   212     /// heap and cross reference type with automatic allocation
   213     ///
   214     /// \ref named-templ-param "Named parameter" for setting heap and
   215     /// cross reference type with automatic allocation. They should
   216     /// have standard constructor interfaces to be able to
   217     /// automatically created by the algorithm (i.e. the graph should
   218     /// be passed to the constructor of the cross reference and the
   219     /// cross reference should be passed to the constructor of the
   220     /// heap). However, external heap and cross reference objects
   221     /// could also be passed to the algorithm using the \ref heap()
   222     /// function before calling \ref run() or \ref init(). The heap
   223     /// has to maximize the priorities.
   224     /// \sa SetHeap
   225     template <class H, class CR = RangeMap<int> >
   226     struct SetStandardHeap
   227       : public NagamochiIbaraki<Graph, CapacityMap,
   228                                 SetStandardHeapTraits<H, CR> > {
   229       typedef NagamochiIbaraki<Graph, CapacityMap,
   230                                SetStandardHeapTraits<H, CR> > Create;
   231     };
   232 
   233     ///@}
   234 
   235 
   236   private:
   237 
   238     const Graph &_graph;
   239     const CapacityMap *_capacity;
   240     bool _local_capacity; // unit capacity
   241 
   242     struct ArcData {
   243       typename Graph::Node target;
   244       int prev, next;
   245     };
   246     struct EdgeData {
   247       Value capacity;
   248       Value cut;
   249     };
   250 
   251     struct NodeData {
   252       int first_arc;
   253       typename Graph::Node prev, next;
   254       int curr_arc;
   255       typename Graph::Node last_rep;
   256       Value sum;
   257     };
   258 
   259     typename Graph::template NodeMap<NodeData> *_nodes;
   260     std::vector<ArcData> _arcs;
   261     std::vector<EdgeData> _edges;
   262 
   263     typename Graph::Node _first_node;
   264     int _node_num;
   265 
   266     Value _min_cut;
   267 
   268     HeapCrossRef *_heap_cross_ref;
   269     bool _local_heap_cross_ref;
   270     Heap *_heap;
   271     bool _local_heap;
   272 
   273     typedef typename Graph::template NodeMap<typename Graph::Node> NodeList;
   274     NodeList *_next_rep;
   275 
   276     typedef typename Graph::template NodeMap<bool> MinCutMap;
   277     MinCutMap *_cut_map;
   278 
   279     void createStructures() {
   280       if (!_nodes) {
   281         _nodes = new (typename Graph::template NodeMap<NodeData>)(_graph);
   282       }
   283       if (!_capacity) {
   284         _local_capacity = true;
   285         _capacity = Traits::createCapacityMap(_graph);
   286       }
   287       if (!_heap_cross_ref) {
   288         _local_heap_cross_ref = true;
   289         _heap_cross_ref = Traits::createHeapCrossRef(_graph);
   290       }
   291       if (!_heap) {
   292         _local_heap = true;
   293         _heap = Traits::createHeap(*_heap_cross_ref);
   294       }
   295       if (!_next_rep) {
   296         _next_rep = new NodeList(_graph);
   297       }
   298       if (!_cut_map) {
   299         _cut_map = new MinCutMap(_graph);
   300       }
   301     }
   302 
   303   public :
   304 
   305     typedef NagamochiIbaraki Create;
   306 
   307 
   308     /// \brief Constructor.
   309     ///
   310     /// \param graph The graph the algorithm runs on.
   311     /// \param capacity The capacity map used by the algorithm.
   312     NagamochiIbaraki(const Graph& graph, const CapacityMap& capacity)
   313       : _graph(graph), _capacity(&capacity), _local_capacity(false),
   314         _nodes(0), _arcs(), _edges(), _min_cut(),
   315         _heap_cross_ref(0), _local_heap_cross_ref(false),
   316         _heap(0), _local_heap(false),
   317         _next_rep(0), _cut_map(0) {}
   318 
   319     /// \brief Constructor.
   320     ///
   321     /// This constructor can be used only when the Traits class
   322     /// defines how can the local capacity map be instantiated.
   323     /// If the SetUnitCapacity used the algorithm automatically
   324     /// constructs the capacity map.
   325     ///
   326     ///\param graph The graph the algorithm runs on.
   327     NagamochiIbaraki(const Graph& graph)
   328       : _graph(graph), _capacity(0), _local_capacity(false),
   329         _nodes(0), _arcs(), _edges(), _min_cut(),
   330         _heap_cross_ref(0), _local_heap_cross_ref(false),
   331         _heap(0), _local_heap(false),
   332         _next_rep(0), _cut_map(0) {}
   333 
   334     /// \brief Destructor.
   335     ///
   336     /// Destructor.
   337     ~NagamochiIbaraki() {
   338       if (_local_capacity) delete _capacity;
   339       if (_nodes) delete _nodes;
   340       if (_local_heap) delete _heap;
   341       if (_local_heap_cross_ref) delete _heap_cross_ref;
   342       if (_next_rep) delete _next_rep;
   343       if (_cut_map) delete _cut_map;
   344     }
   345 
   346     /// \brief Sets the heap and the cross reference used by algorithm.
   347     ///
   348     /// Sets the heap and the cross reference used by algorithm.
   349     /// If you don't use this function before calling \ref run(),
   350     /// it will allocate one. The destuctor deallocates this
   351     /// automatically allocated heap and cross reference, of course.
   352     /// \return <tt> (*this) </tt>
   353     NagamochiIbaraki &heap(Heap& hp, HeapCrossRef &cr)
   354     {
   355       if (_local_heap_cross_ref) {
   356         delete _heap_cross_ref;
   357         _local_heap_cross_ref = false;
   358       }
   359       _heap_cross_ref = &cr;
   360       if (_local_heap) {
   361         delete _heap;
   362         _local_heap = false;
   363       }
   364       _heap = &hp;
   365       return *this;
   366     }
   367 
   368     /// \name Execution control
   369     /// The simplest way to execute the algorithm is to use
   370     /// one of the member functions called \c run().
   371     /// \n
   372     /// If you need more control on the execution,
   373     /// first you must call \ref init() and then call the start()
   374     /// or proper times the processNextPhase() member functions.
   375 
   376     ///@{
   377 
   378     /// \brief Initializes the internal data structures.
   379     ///
   380     /// Initializes the internal data structures.
   381     void init() {
   382       createStructures();
   383 
   384       int edge_num = countEdges(_graph);
   385       _edges.resize(edge_num);
   386       _arcs.resize(2 * edge_num);
   387 
   388       typename Graph::Node prev = INVALID;
   389       _node_num = 0;
   390       for (typename Graph::NodeIt n(_graph); n != INVALID; ++n) {
   391         (*_cut_map)[n] = false;
   392         (*_next_rep)[n] = INVALID;
   393         (*_nodes)[n].last_rep = n;
   394         (*_nodes)[n].first_arc = -1;
   395         (*_nodes)[n].curr_arc = -1;
   396         (*_nodes)[n].prev = prev;
   397         if (prev != INVALID) {
   398           (*_nodes)[prev].next = n;
   399         }
   400         (*_nodes)[n].next = INVALID;
   401         (*_nodes)[n].sum = 0;
   402         prev = n;
   403         ++_node_num;
   404       }
   405 
   406       _first_node = typename Graph::NodeIt(_graph);
   407 
   408       int index = 0;
   409       for (typename Graph::NodeIt n(_graph); n != INVALID; ++n) {
   410         for (typename Graph::OutArcIt a(_graph, n); a != INVALID; ++a) {
   411           typename Graph::Node m = _graph.target(a);
   412           
   413           if (!(n < m)) continue;
   414 
   415           (*_nodes)[n].sum += (*_capacity)[a];
   416           (*_nodes)[m].sum += (*_capacity)[a];
   417           
   418           int c = (*_nodes)[m].curr_arc;
   419           if (c != -1 && _arcs[c ^ 1].target == n) {
   420             _edges[c >> 1].capacity += (*_capacity)[a];
   421           } else {
   422             _edges[index].capacity = (*_capacity)[a];
   423             
   424             _arcs[index << 1].prev = -1;
   425             if ((*_nodes)[n].first_arc != -1) {
   426               _arcs[(*_nodes)[n].first_arc].prev = (index << 1);
   427             }
   428             _arcs[index << 1].next = (*_nodes)[n].first_arc;
   429             (*_nodes)[n].first_arc = (index << 1);
   430             _arcs[index << 1].target = m;
   431 
   432             (*_nodes)[m].curr_arc = (index << 1);
   433             
   434             _arcs[(index << 1) | 1].prev = -1;
   435             if ((*_nodes)[m].first_arc != -1) {
   436               _arcs[(*_nodes)[m].first_arc].prev = ((index << 1) | 1);
   437             }
   438             _arcs[(index << 1) | 1].next = (*_nodes)[m].first_arc;
   439             (*_nodes)[m].first_arc = ((index << 1) | 1);
   440             _arcs[(index << 1) | 1].target = n;
   441             
   442             ++index;
   443           }
   444         }
   445       }
   446 
   447       typename Graph::Node cut_node = INVALID;
   448       _min_cut = std::numeric_limits<Value>::max();
   449 
   450       for (typename Graph::Node n = _first_node; 
   451            n != INVALID; n = (*_nodes)[n].next) {
   452         if ((*_nodes)[n].sum < _min_cut) {
   453           cut_node = n;
   454           _min_cut = (*_nodes)[n].sum;
   455         }
   456       }
   457       (*_cut_map)[cut_node] = true;
   458       if (_min_cut == 0) {
   459         _first_node = INVALID;
   460       }
   461     }
   462 
   463   public:
   464 
   465     /// \brief Processes the next phase
   466     ///
   467     /// Processes the next phase in the algorithm. It must be called
   468     /// at most one less the number of the nodes in the graph.
   469     ///
   470     ///\return %True when the algorithm finished.
   471     bool processNextPhase() {
   472       if (_first_node == INVALID) return true;
   473 
   474       _heap->clear();
   475       for (typename Graph::Node n = _first_node; 
   476            n != INVALID; n = (*_nodes)[n].next) {
   477         (*_heap_cross_ref)[n] = Heap::PRE_HEAP;
   478       }
   479 
   480       std::vector<typename Graph::Node> order;
   481       order.reserve(_node_num);
   482       int sep = 0;
   483 
   484       Value alpha = 0;
   485       Value pmc = std::numeric_limits<Value>::max();
   486 
   487       _heap->push(_first_node, static_cast<Value>(0));
   488       while (!_heap->empty()) {
   489         typename Graph::Node n = _heap->top();
   490         Value v = _heap->prio();
   491 
   492         _heap->pop();
   493         for (int a = (*_nodes)[n].first_arc; a != -1; a = _arcs[a].next) {
   494           switch (_heap->state(_arcs[a].target)) {
   495           case Heap::PRE_HEAP: 
   496             {
   497               Value nv = _edges[a >> 1].capacity;
   498               _heap->push(_arcs[a].target, nv);
   499               _edges[a >> 1].cut = nv;
   500             } break;
   501           case Heap::IN_HEAP:
   502             {
   503               Value nv = _edges[a >> 1].capacity + (*_heap)[_arcs[a].target];
   504               _heap->decrease(_arcs[a].target, nv);
   505               _edges[a >> 1].cut = nv;
   506             } break;
   507           case Heap::POST_HEAP:
   508             break;
   509           }
   510         }
   511 
   512         alpha += (*_nodes)[n].sum;
   513         alpha -= 2 * v;
   514 
   515         order.push_back(n);
   516         if (!_heap->empty()) {
   517           if (alpha < pmc) {
   518             pmc = alpha;
   519             sep = order.size();
   520           }
   521         }
   522       }
   523 
   524       if (static_cast<int>(order.size()) < _node_num) {
   525         _first_node = INVALID;
   526         for (typename Graph::NodeIt n(_graph); n != INVALID; ++n) {
   527           (*_cut_map)[n] = false;
   528         }
   529         for (int i = 0; i < static_cast<int>(order.size()); ++i) {
   530           typename Graph::Node n = order[i];
   531           while (n != INVALID) {
   532             (*_cut_map)[n] = true;
   533             n = (*_next_rep)[n];
   534           }
   535         }
   536         _min_cut = 0;
   537         return true;
   538       }
   539 
   540       if (pmc < _min_cut) {
   541         for (typename Graph::NodeIt n(_graph); n != INVALID; ++n) {
   542           (*_cut_map)[n] = false;
   543         }
   544         for (int i = 0; i < sep; ++i) {
   545           typename Graph::Node n = order[i];
   546           while (n != INVALID) {
   547             (*_cut_map)[n] = true;
   548             n = (*_next_rep)[n];
   549           }
   550         }
   551         _min_cut = pmc;
   552       }
   553 
   554       for (typename Graph::Node n = _first_node;
   555            n != INVALID; n = (*_nodes)[n].next) {
   556         bool merged = false;
   557         for (int a = (*_nodes)[n].first_arc; a != -1; a = _arcs[a].next) {
   558           if (!(_edges[a >> 1].cut < pmc)) {
   559             if (!merged) {
   560               for (int b = (*_nodes)[n].first_arc; b != -1; b = _arcs[b].next) {
   561                 (*_nodes)[_arcs[b].target].curr_arc = b;          
   562               }
   563               merged = true;
   564             }
   565             typename Graph::Node m = _arcs[a].target;
   566             int nb = 0;
   567             for (int b = (*_nodes)[m].first_arc; b != -1; b = nb) {
   568               nb = _arcs[b].next;
   569               if ((b ^ a) == 1) continue;
   570               typename Graph::Node o = _arcs[b].target;
   571               int c = (*_nodes)[o].curr_arc; 
   572               if (c != -1 && _arcs[c ^ 1].target == n) {
   573                 _edges[c >> 1].capacity += _edges[b >> 1].capacity;
   574                 (*_nodes)[n].sum += _edges[b >> 1].capacity;
   575                 if (_edges[b >> 1].cut < _edges[c >> 1].cut) {
   576                   _edges[b >> 1].cut = _edges[c >> 1].cut;
   577                 }
   578                 if (_arcs[b ^ 1].prev != -1) {
   579                   _arcs[_arcs[b ^ 1].prev].next = _arcs[b ^ 1].next;
   580                 } else {
   581                   (*_nodes)[o].first_arc = _arcs[b ^ 1].next;
   582                 }
   583                 if (_arcs[b ^ 1].next != -1) {
   584                   _arcs[_arcs[b ^ 1].next].prev = _arcs[b ^ 1].prev;
   585                 }
   586               } else {
   587                 if (_arcs[a].next != -1) {
   588                   _arcs[_arcs[a].next].prev = b;
   589                 }
   590                 _arcs[b].next = _arcs[a].next;
   591                 _arcs[b].prev = a;
   592                 _arcs[a].next = b;
   593                 _arcs[b ^ 1].target = n;
   594 
   595                 (*_nodes)[n].sum += _edges[b >> 1].capacity;
   596                 (*_nodes)[o].curr_arc = b;
   597               }
   598             }
   599 
   600             if (_arcs[a].prev != -1) {
   601               _arcs[_arcs[a].prev].next = _arcs[a].next;
   602             } else {
   603               (*_nodes)[n].first_arc = _arcs[a].next;
   604             }            
   605             if (_arcs[a].next != -1) {
   606               _arcs[_arcs[a].next].prev = _arcs[a].prev;
   607             }
   608 
   609             (*_nodes)[n].sum -= _edges[a >> 1].capacity;
   610             (*_next_rep)[(*_nodes)[n].last_rep] = m;
   611             (*_nodes)[n].last_rep = (*_nodes)[m].last_rep;
   612             
   613             if ((*_nodes)[m].prev != INVALID) {
   614               (*_nodes)[(*_nodes)[m].prev].next = (*_nodes)[m].next;
   615             } else{
   616               _first_node = (*_nodes)[m].next;
   617             }
   618             if ((*_nodes)[m].next != INVALID) {
   619               (*_nodes)[(*_nodes)[m].next].prev = (*_nodes)[m].prev;
   620             }
   621             --_node_num;
   622           }
   623         }
   624       }
   625 
   626       if (_node_num == 1) {
   627         _first_node = INVALID;
   628         return true;
   629       }
   630 
   631       return false;
   632     }
   633 
   634     /// \brief Executes the algorithm.
   635     ///
   636     /// Executes the algorithm.
   637     ///
   638     /// \pre init() must be called
   639     void start() {
   640       while (!processNextPhase()) {}
   641     }
   642 
   643 
   644     /// \brief Runs %NagamochiIbaraki algorithm.
   645     ///
   646     /// This method runs the %Min cut algorithm
   647     ///
   648     /// \note mc.run(s) is just a shortcut of the following code.
   649     ///\code
   650     ///  mc.init();
   651     ///  mc.start();
   652     ///\endcode
   653     void run() {
   654       init();
   655       start();
   656     }
   657 
   658     ///@}
   659 
   660     /// \name Query Functions
   661     ///
   662     /// The result of the %NagamochiIbaraki
   663     /// algorithm can be obtained using these functions.\n
   664     /// Before the use of these functions, either run() or start()
   665     /// must be called.
   666 
   667     ///@{
   668 
   669     /// \brief Returns the min cut value.
   670     ///
   671     /// Returns the min cut value if the algorithm finished.
   672     /// After the first processNextPhase() it is a value of a
   673     /// valid cut in the graph.
   674     Value minCutValue() const {
   675       return _min_cut;
   676     }
   677 
   678     /// \brief Returns a min cut in a NodeMap.
   679     ///
   680     /// It sets the nodes of one of the two partitions to true and
   681     /// the other partition to false.
   682     /// \param cutMap A \ref concepts::WriteMap "writable" node map with
   683     /// \c bool (or convertible) value type.
   684     template <typename CutMap>
   685     Value minCutMap(CutMap& cutMap) const {
   686       for (typename Graph::NodeIt n(_graph); n != INVALID; ++n) {
   687         cutMap.set(n, (*_cut_map)[n]);
   688       }
   689       return minCutValue();
   690     }
   691 
   692     ///@}
   693 
   694   };
   695 }
   696 
   697 #endif