Minimum Cost Arborescence algorithm
authordeba
Mon, 27 Mar 2006 08:12:01 +0000
changeset 20176064fd33807c
parent 2016 ecb067198349
child 2018 66a1f0950700
Minimum Cost Arborescence algorithm
lemon/Makefile.am
lemon/min_cost_arborescence.h
     1.1 --- a/lemon/Makefile.am	Mon Mar 27 08:01:10 2006 +0000
     1.2 +++ b/lemon/Makefile.am	Mon Mar 27 08:12:01 2006 +0000
     1.3 @@ -59,6 +59,7 @@
     1.4  	matrix_maps.h \
     1.5  	map_iterator.h \
     1.6  	max_matching.h \
     1.7 +	min_cost_arborescence.h \
     1.8  	min_cost_flow.h \
     1.9  	min_cut.h \
    1.10  	suurballe.h \
     2.1 --- /dev/null	Thu Jan 01 00:00:00 1970 +0000
     2.2 +++ b/lemon/min_cost_arborescence.h	Mon Mar 27 08:12:01 2006 +0000
     2.3 @@ -0,0 +1,561 @@
     2.4 +/* -*- C++ -*-
     2.5 + *
     2.6 + * This file is a part of LEMON, a generic C++ optimization library
     2.7 + *
     2.8 + * Copyright (C) 2003-2006
     2.9 + * Egervary Jeno Kombinatorikus Optimalizalasi Kutatocsoport
    2.10 + * (Egervary Research Group on Combinatorial Optimization, EGRES).
    2.11 + *
    2.12 + * Permission to use, modify and distribute this software is granted
    2.13 + * provided that this copyright notice appears in all copies. For
    2.14 + * precise terms see the accompanying LICENSE file.
    2.15 + *
    2.16 + * This software is provided "AS IS" with no warranty of any kind,
    2.17 + * express or implied, and with no claim as to its suitability for any
    2.18 + * purpose.
    2.19 + *
    2.20 + */
    2.21 +
    2.22 +#ifndef LEMON_MIN_COST_ARBORESCENCE_H
    2.23 +#define LEMON_MIN_COST_ARBORESCENCE_H
    2.24 +
    2.25 +///\ingroup spantree
    2.26 +///\file
    2.27 +///\brief Minimum Cost Arborescence algorithm.
    2.28 +
    2.29 +#include <vector>
    2.30 +
    2.31 +#include <lemon/list_graph.h>
    2.32 +
    2.33 +namespace lemon {
    2.34 +
    2.35 +
    2.36 +  /// \brief Default traits class of MinCostArborescence class.
    2.37 +  /// 
    2.38 +  /// Default traits class of MinCostArborescence class.
    2.39 +  /// \param _Graph Graph type.
    2.40 +  /// \param _CostMap Type of cost map.
    2.41 +  template <class _Graph, class _CostMap>
    2.42 +  struct MinCostArborescenceDefaultTraits{
    2.43 +
    2.44 +    /// \brief The graph type the algorithm runs on. 
    2.45 +    typedef _Graph Graph;
    2.46 +
    2.47 +    /// \brief The type of the map that stores the edge costs.
    2.48 +    ///
    2.49 +    /// The type of the map that stores the edge costs.
    2.50 +    /// It must meet the \ref concept::ReadMap "ReadMap" concept.
    2.51 +    typedef _CostMap CostMap;
    2.52 +
    2.53 +    /// \brief The value type of the costs.
    2.54 +    ///
    2.55 +    /// The value type of the costs.
    2.56 +    typedef typename CostMap::Value Value;
    2.57 +
    2.58 +    /// \brief The type of the map that stores which edges are 
    2.59 +    /// in the arborescence.
    2.60 +    ///
    2.61 +    /// The type of the map that stores which edges are in the arborescence.
    2.62 +    /// It must meet the \ref concept::ReadWriteMap "ReadWriteMap" concept.
    2.63 +    /// Initially it will be setted to false on each edge. The algorithm
    2.64 +    /// may set each value one time to true and maybe after it to false again.
    2.65 +    /// Therefore you cannot use maps like BackInserteBoolMap with this
    2.66 +    /// algorithm.   
    2.67 +    typedef typename Graph::template EdgeMap<bool> ArborescenceMap; 
    2.68 +
    2.69 +    /// \brief Instantiates a ArborescenceMap.
    2.70 +    ///
    2.71 +    /// This function instantiates a \ref ArborescenceMap. 
    2.72 +    /// \param _graph is the graph, to which we would like to define the 
    2.73 +    /// ArborescenceMap.
    2.74 +    static ArborescenceMap *createArborescenceMap(const Graph &_graph){
    2.75 +      return new ArborescenceMap(_graph);
    2.76 +    }
    2.77 +
    2.78 +  };
    2.79 +
    2.80 +  /// \ingroup spantree
    2.81 +  ///
    2.82 +  /// \brief %MinCostArborescence algorithm class.
    2.83 +  ///
    2.84 +  /// This class provides an efficient implementation of 
    2.85 +  /// %MinCostArborescence algorithm. The arborescence is a tree 
    2.86 +  /// which is directed from a given source node of the graph. One or
    2.87 +  /// more sources should be given for the algorithm and it will calculate
    2.88 +  /// the minimum cost subgraph which are union of arborescences with the
    2.89 +  /// given sources and spans all the nodes which are reachable from the
    2.90 +  /// sources. The time complexity of the algorithm is O(n^2 + e).
    2.91 +  ///
    2.92 +  /// \param _Graph The graph type the algorithm runs on. The default value
    2.93 +  /// is \ref ListGraph. The value of _Graph is not used directly by
    2.94 +  /// MinCostArborescence, it is only passed to 
    2.95 +  /// \ref MinCostArborescenceDefaultTraits.
    2.96 +  /// \param _CostMap This read-only EdgeMap determines the costs of the
    2.97 +  /// edges. It is read once for each edge, so the map may involve in
    2.98 +  /// relatively time consuming process to compute the edge cost if
    2.99 +  /// it is necessary. The default map type is \ref
   2.100 +  /// concept::StaticGraph::EdgeMap "Graph::EdgeMap<int>".  The value
   2.101 +  /// of _CostMap is not used directly by MinCostArborescence, 
   2.102 +  /// it is only passed to \ref MinCostArborescenceDefaultTraits.  
   2.103 +  /// \param _Traits Traits class to set various data types used 
   2.104 +  /// by the algorithm.  The default traits class is 
   2.105 +  /// \ref MinCostArborescenceDefaultTraits
   2.106 +  /// "MinCostArborescenceDefaultTraits<_Graph,_CostMap>".  See \ref
   2.107 +  /// MinCostArborescenceDefaultTraits for the documentation of a 
   2.108 +  /// MinCostArborescence traits class.
   2.109 +  ///
   2.110 +  /// \author Balazs Dezso
   2.111 +#ifndef DOXYGEN
   2.112 +  template <typename _Graph = ListGraph, 
   2.113 +            typename _CostMap = typename _Graph::template EdgeMap<int>,
   2.114 +            typename _Traits = 
   2.115 +            MinCostArborescenceDefaultTraits<_Graph, _CostMap> >
   2.116 +#else 
   2.117 +  template <typename _Graph, typename _CostMap, typedef _Traits>
   2.118 +#endif
   2.119 +  class MinCostArborescence {
   2.120 +  public:
   2.121 +
   2.122 +    /// \brief \ref Exception for uninitialized parameters.
   2.123 +    ///
   2.124 +    /// This error represents problems in the initialization
   2.125 +    /// of the parameters of the algorithms.    
   2.126 +    class UninitializedParameter : public lemon::UninitializedParameter {
   2.127 +    public:
   2.128 +      virtual const char* exceptionName() const {
   2.129 +	return "lemon::MinCostArborescence::UninitializedParameter";
   2.130 +      }
   2.131 +    };
   2.132 +
   2.133 +    /// The traits.
   2.134 +    typedef _Traits Traits;
   2.135 +    /// The type of the underlying graph.
   2.136 +    typedef typename Traits::Graph Graph;
   2.137 +    /// The type of the map that stores the edge costs.
   2.138 +    typedef typename Traits::CostMap CostMap;
   2.139 +    ///The type of the costs of the edges.
   2.140 +    typedef typename Traits::Value Value;
   2.141 +    ///The type of the map that stores which edges are in the arborescence.
   2.142 +    typedef typename Traits::ArborescenceMap ArborescenceMap;
   2.143 +
   2.144 +  protected:
   2.145 +
   2.146 +    typedef typename Graph::Node Node;
   2.147 +    typedef typename Graph::Edge Edge;
   2.148 +    typedef typename Graph::NodeIt NodeIt;
   2.149 +    typedef typename Graph::EdgeIt EdgeIt;
   2.150 +    typedef typename Graph::InEdgeIt InEdgeIt;
   2.151 +    typedef typename Graph::OutEdgeIt OutEdgeIt;
   2.152 +
   2.153 +    struct CostEdge {
   2.154 +
   2.155 +      Edge edge;
   2.156 +      Value value;
   2.157 +
   2.158 +      CostEdge() {}
   2.159 +      CostEdge(Edge _edge, Value _value) : edge(_edge), value(_value) {}
   2.160 +
   2.161 +    };
   2.162 +
   2.163 +    const Graph* graph;
   2.164 +    const CostMap* cost;
   2.165 +
   2.166 +    ArborescenceMap* _arborescence_map;
   2.167 +    bool local_arborescence_map;
   2.168 +
   2.169 +    typedef typename Graph::template NodeMap<int> LevelMap;
   2.170 +    LevelMap *_level;
   2.171 +
   2.172 +    typedef typename Graph::template NodeMap<CostEdge> CostEdgeMap;
   2.173 +    CostEdgeMap *_cost_edges; 
   2.174 +
   2.175 +    struct StackLevel {
   2.176 +
   2.177 +      std::vector<CostEdge> edges;
   2.178 +      int node_level;
   2.179 +
   2.180 +    };
   2.181 +
   2.182 +    std::vector<StackLevel> level_stack;    
   2.183 +    std::vector<Node> queue;
   2.184 +
   2.185 +    int node_counter;
   2.186 +
   2.187 +  public:
   2.188 +
   2.189 +    /// \name Named template parameters
   2.190 +
   2.191 +    /// @{
   2.192 +
   2.193 +    template <class T>
   2.194 +    struct DefArborescenceMapTraits : public Traits {
   2.195 +      typedef T ArborescenceMap;
   2.196 +      static ArborescenceMap *createArborescenceMap(const Graph &)
   2.197 +      {
   2.198 +	throw UninitializedParameter();
   2.199 +      }
   2.200 +    };
   2.201 +
   2.202 +    /// \brief \ref named-templ-param "Named parameter" for 
   2.203 +    /// setting ArborescenceMap type
   2.204 +    ///
   2.205 +    /// \ref named-templ-param "Named parameter" for setting 
   2.206 +    /// ArborescenceMap type
   2.207 +    template <class T>
   2.208 +    struct DefArborescenceMap 
   2.209 +      : public MinCostArborescence<Graph, CostMap,
   2.210 +                                   DefArborescenceMapTraits<T> > {
   2.211 +      typedef MinCostArborescence<Graph, CostMap, 
   2.212 +                                   DefArborescenceMapTraits<T> > Create;
   2.213 +    };
   2.214 +    
   2.215 +    /// @}
   2.216 +
   2.217 +    /// \brief Constructor.
   2.218 +    ///
   2.219 +    /// \param _graph The graph the algorithm will run on.
   2.220 +    /// \param _cost The cost map used by the algorithm.
   2.221 +    MinCostArborescence(const Graph& _graph, const CostMap& _cost) 
   2.222 +      : graph(&_graph), cost(&_cost),
   2.223 +        _arborescence_map(0), local_arborescence_map(false), 
   2.224 +        _level(0), _cost_edges(0) {}
   2.225 +
   2.226 +    /// \brief Destructor.
   2.227 +    ~MinCostArborescence() {
   2.228 +      destroyStructures();
   2.229 +    }
   2.230 +
   2.231 +    /// \brief Sets the arborescence map.
   2.232 +    /// 
   2.233 +    /// Sets the arborescence map.
   2.234 +    /// \return \c (*this)
   2.235 +    MinCostArborescence& arborescenceMap(ArborescenceMap& m) {
   2.236 +      _arborescence_map = &m;
   2.237 +      return *this;
   2.238 +    }
   2.239 +
   2.240 +    /// \name Query Functions
   2.241 +    /// The result of the %MinCostArborescence algorithm can be obtained 
   2.242 +    /// using these functions.\n
   2.243 +    /// Before the use of these functions,
   2.244 +    /// either run() or start() must be called.
   2.245 +    
   2.246 +    /// @{
   2.247 +
   2.248 +    /// \brief Returns a reference to the arborescence map.
   2.249 +    ///
   2.250 +    /// Returns a reference to the arborescence map.
   2.251 +    const ArborescenceMap& arborescenceMap() const {
   2.252 +      return *_arborescence_map;
   2.253 +    }
   2.254 +
   2.255 +    /// \brief Returns true if the edge is in the arborescence.
   2.256 +    ///
   2.257 +    /// Returns true if the edge is in the arborescence.
   2.258 +    /// \param edge The edge of the graph.
   2.259 +    /// \pre \ref run() must be called before using this function.
   2.260 +    bool arborescenceEdge(Edge edge) const {
   2.261 +      return (*_arborescence_map)[edge];
   2.262 +    }
   2.263 + 
   2.264 +    /// \brief Returns the cost of the arborescence.
   2.265 +    ///
   2.266 +    /// Returns the cost of the arborescence.
   2.267 +   Value arborescenceCost() const {
   2.268 +      Value sum = 0;
   2.269 +      for (EdgeIt it(*graph); it != INVALID; ++it) {
   2.270 +        if (arborescenceEdge(it)) {
   2.271 +          sum += (*cost)[it];
   2.272 +        }
   2.273 +      }
   2.274 +      return sum;
   2.275 +    }
   2.276 +
   2.277 +    /// @}
   2.278 +    
   2.279 +    /// \name Execution control
   2.280 +    /// The simplest way to execute the algorithm is to use
   2.281 +    /// one of the member functions called \c run(...). \n
   2.282 +    /// If you need more control on the execution,
   2.283 +    /// first you must call \ref init(), then you can add several 
   2.284 +    /// source nodes with \ref addSource().
   2.285 +    /// Finally \ref start() will perform the actual path
   2.286 +    /// computation.
   2.287 +
   2.288 +    ///@{
   2.289 +
   2.290 +    /// \brief Initializes the internal data structures.
   2.291 +    ///
   2.292 +    /// Initializes the internal data structures.
   2.293 +    ///
   2.294 +    void init() {
   2.295 +      initStructures();
   2.296 +      for (NodeIt it(*graph); it != INVALID; ++it) {
   2.297 +        (*_cost_edges)[it].edge = INVALID;
   2.298 +        (*_level)[it] = -3; 
   2.299 +      }
   2.300 +      for (EdgeIt it(*graph); it != INVALID; ++it) {
   2.301 +        _arborescence_map->set(it, false);
   2.302 +      }
   2.303 +    }
   2.304 +
   2.305 +    /// \brief Adds a new source node.
   2.306 +    ///
   2.307 +    /// Adds a new source node to the algorithm.
   2.308 +    void addSource(Node source) {
   2.309 +      std::vector<Node> nodes;
   2.310 +      nodes.push_back(source);
   2.311 +      while (!nodes.empty()) {
   2.312 +        Node node = nodes.back();
   2.313 +        nodes.pop_back();
   2.314 +        for (OutEdgeIt it(*graph, node); it != INVALID; ++it) {
   2.315 +          if ((*_level)[graph->target(it)] == -3) {
   2.316 +            (*_level)[graph->target(it)] = -2;
   2.317 +            nodes.push_back(graph->target(it));
   2.318 +            queue.push_back(graph->target(it));
   2.319 +          }
   2.320 +        }
   2.321 +      }
   2.322 +      (*_level)[source] = -1;
   2.323 +    }
   2.324 +
   2.325 +    /// \brief Processes the next node in the priority queue.
   2.326 +    ///
   2.327 +    /// Processes the next node in the priority queue.
   2.328 +    ///
   2.329 +    /// \return The processed node.
   2.330 +    ///
   2.331 +    /// \warning The queue must not be empty!
   2.332 +    Node processNextNode() {
   2.333 +      node_counter = 0;
   2.334 +      Node node = queue.back();
   2.335 +      queue.pop_back();
   2.336 +      if ((*_level)[node] == -2) {
   2.337 +        Edge edge = prepare(node);
   2.338 +        while ((*_level)[graph->source(edge)] != -1) {
   2.339 +          if ((*_level)[graph->source(edge)] >= 0) {
   2.340 +            edge = contract(bottom((*_level)[graph->source(edge)]));
   2.341 +          } else {
   2.342 +            edge = prepare(graph->source(edge));
   2.343 +          }
   2.344 +        }
   2.345 +        finalize(graph->target(edge));
   2.346 +        level_stack.clear();        
   2.347 +      }
   2.348 +      return node;
   2.349 +    }
   2.350 +
   2.351 +    /// \brief Returns the number of the nodes to be processed.
   2.352 +    ///
   2.353 +    /// Returns the number of the nodes to be processed.
   2.354 +    int queueSize() const {
   2.355 +      return queue.size();
   2.356 +    }
   2.357 +
   2.358 +    /// \brief Returns \c false if there are nodes to be processed.
   2.359 +    ///
   2.360 +    /// Returns \c false if there are nodes to be processed.
   2.361 +    bool emptyQueue() const {
   2.362 +      return queue.empty();
   2.363 +    }
   2.364 +
   2.365 +    /// \brief Executes the algorithm.
   2.366 +    ///
   2.367 +    /// Executes the algorithm.
   2.368 +    ///
   2.369 +    /// \pre init() must be called and at least one node should be added
   2.370 +    /// with addSource() before using this function.
   2.371 +    ///
   2.372 +    ///\note mca.start() is just a shortcut of the following code.
   2.373 +    ///\code
   2.374 +    ///while (!mca.emptyQueue()) {
   2.375 +    ///  mca.processNextNode();
   2.376 +    ///}
   2.377 +    ///\endcode
   2.378 +    void start() {
   2.379 +      while (!emptyQueue()) {
   2.380 +        processNextNode();
   2.381 +      }
   2.382 +    }
   2.383 +
   2.384 +    /// \brief Runs %MinCostArborescence algorithm from node \c s.
   2.385 +    /// 
   2.386 +    /// This method runs the %MinCostArborescence algorithm from 
   2.387 +    /// a root node \c s.
   2.388 +    ///
   2.389 +    ///\note mca.run(s) is just a shortcut of the following code.
   2.390 +    ///\code
   2.391 +    ///mca.init();
   2.392 +    ///mca.addSource(s);
   2.393 +    ///mca.start();
   2.394 +    ///\endcode
   2.395 +    void run(Node node) {
   2.396 +      init();
   2.397 +      addSource(node);
   2.398 +      start();
   2.399 +    }
   2.400 +
   2.401 +    ///@}
   2.402 +
   2.403 +  protected:
   2.404 +
   2.405 +    void initStructures() {
   2.406 +      if (!_arborescence_map) {
   2.407 +        local_arborescence_map = true;
   2.408 +        _arborescence_map = Traits::createArborescenceMap(*graph);
   2.409 +      }
   2.410 +      if (!_level) {
   2.411 +        _level = new LevelMap(*graph);
   2.412 +      }
   2.413 +      if (!_cost_edges) {
   2.414 +        _cost_edges = new CostEdgeMap(*graph);
   2.415 +      }
   2.416 +    }
   2.417 +
   2.418 +    void destroyStructures() {
   2.419 +      if (_level) {
   2.420 +        delete _level;
   2.421 +      }
   2.422 +      if (!_cost_edges) {
   2.423 +        delete _cost_edges;
   2.424 +      }
   2.425 +      if (local_arborescence_map) {
   2.426 +        delete _arborescence_map;
   2.427 +      }
   2.428 +    }
   2.429 +
   2.430 +    Edge prepare(Node node) {
   2.431 +      std::vector<Node> nodes;
   2.432 +      (*_level)[node] = node_counter;
   2.433 +      for (InEdgeIt it(*graph, node); it != INVALID; ++it) {
   2.434 +        Edge edge = it;
   2.435 +        Value value = (*cost)[it];
   2.436 +        if (graph->source(edge) == node || 
   2.437 +            (*_level)[graph->source(edge)] == -3) continue;
   2.438 +        if ((*_cost_edges)[graph->source(edge)].edge == INVALID) {
   2.439 +          (*_cost_edges)[graph->source(edge)].edge = edge;
   2.440 +          (*_cost_edges)[graph->source(edge)].value = value;
   2.441 +          nodes.push_back(graph->source(edge));
   2.442 +        } else {
   2.443 +          if ((*_cost_edges)[graph->source(edge)].value > value) {
   2.444 +            (*_cost_edges)[graph->source(edge)].edge = edge;
   2.445 +            (*_cost_edges)[graph->source(edge)].value = value;
   2.446 +          }
   2.447 +        }      
   2.448 +      }
   2.449 +      CostEdge minimum = (*_cost_edges)[nodes[0]]; 
   2.450 +      for (int i = 1; i < (int)nodes.size(); ++i) {
   2.451 +        if ((*_cost_edges)[nodes[i]].value < minimum.value) {
   2.452 +          minimum = (*_cost_edges)[nodes[i]];
   2.453 +        }
   2.454 +      }
   2.455 +      StackLevel level;
   2.456 +      level.node_level = node_counter;
   2.457 +      for (int i = 0; i < (int)nodes.size(); ++i) {
   2.458 +        (*_cost_edges)[nodes[i]].value -= minimum.value;
   2.459 +        level.edges.push_back((*_cost_edges)[nodes[i]]);
   2.460 +        (*_cost_edges)[nodes[i]].edge = INVALID;
   2.461 +      }
   2.462 +      level_stack.push_back(level);
   2.463 +      ++node_counter;
   2.464 +      _arborescence_map->set(minimum.edge, true);
   2.465 +      return minimum.edge;
   2.466 +    }
   2.467 +  
   2.468 +    Edge contract(int node_bottom) {
   2.469 +      std::vector<Node> nodes;
   2.470 +      while (!level_stack.empty() && 
   2.471 +             level_stack.back().node_level >= node_bottom) {
   2.472 +        for (int i = 0; i < (int)level_stack.back().edges.size(); ++i) {
   2.473 +          Edge edge = level_stack.back().edges[i].edge;
   2.474 +          Value value = level_stack.back().edges[i].value;
   2.475 +          if ((*_level)[graph->source(edge)] >= node_bottom) continue;
   2.476 +          if ((*_cost_edges)[graph->source(edge)].edge == INVALID) {
   2.477 +            (*_cost_edges)[graph->source(edge)].edge = edge;
   2.478 +            (*_cost_edges)[graph->source(edge)].value = value;
   2.479 +            nodes.push_back(graph->source(edge));
   2.480 +          } else {
   2.481 +            if ((*_cost_edges)[graph->source(edge)].value > value) {
   2.482 +              (*_cost_edges)[graph->source(edge)].edge = edge;
   2.483 +              (*_cost_edges)[graph->source(edge)].value = value;
   2.484 +            }
   2.485 +          }
   2.486 +        }
   2.487 +        level_stack.pop_back();
   2.488 +      }
   2.489 +      CostEdge minimum = (*_cost_edges)[nodes[0]]; 
   2.490 +      for (int i = 1; i < (int)nodes.size(); ++i) {
   2.491 +        if ((*_cost_edges)[nodes[i]].value < minimum.value) {
   2.492 +          minimum = (*_cost_edges)[nodes[i]];
   2.493 +        }
   2.494 +      }
   2.495 +      StackLevel level;
   2.496 +      level.node_level = node_bottom;
   2.497 +      for (int i = 0; i < (int)nodes.size(); ++i) {
   2.498 +        (*_cost_edges)[nodes[i]].value -= minimum.value;
   2.499 +        level.edges.push_back((*_cost_edges)[nodes[i]]);
   2.500 +        (*_cost_edges)[nodes[i]].edge = INVALID;
   2.501 +      }
   2.502 +      level_stack.push_back(level);
   2.503 +      _arborescence_map->set(minimum.edge, true);
   2.504 +      return minimum.edge;
   2.505 +    }
   2.506 +
   2.507 +    int bottom(int level) {
   2.508 +      int k = level_stack.size() - 1;
   2.509 +      while (level_stack[k].node_level > level) {
   2.510 +        --k;
   2.511 +      }
   2.512 +      return level_stack[k].node_level;
   2.513 +    }
   2.514 +
   2.515 +    void finalize(Node source) {
   2.516 +      std::vector<Node> nodes;
   2.517 +      nodes.push_back(source);
   2.518 +      while (!nodes.empty()) {
   2.519 +        Node node = nodes.back();
   2.520 +        nodes.pop_back();
   2.521 +        for (OutEdgeIt it(*graph, node); it != INVALID; ++it) {
   2.522 +          if ((*_level)[graph->target(it)] >= 0 && (*_arborescence_map)[it]) {
   2.523 +            (*_level)[graph->target(it)] = -1;
   2.524 +            nodes.push_back(graph->target(it));
   2.525 +          } else {
   2.526 +            _arborescence_map->set(it, false);
   2.527 +          }
   2.528 +        }
   2.529 +      }
   2.530 +      (*_level)[source] = -1;      
   2.531 +    }
   2.532 +
   2.533 +  };
   2.534 +
   2.535 +  /// \ingroup spantree
   2.536 +  ///
   2.537 +  /// \brief Function type interface for MinCostArborescence algorithm.
   2.538 +  ///
   2.539 +  /// Function type interface for MinCostArborescence algorithm.
   2.540 +  /// \param graph The Graph that the algorithm runs on.
   2.541 +  /// \param cost The CostMap of the edges.
   2.542 +  /// \param source The source of the arborescence.
   2.543 +  /// \retval arborescence The bool EdgeMap which stores the arborescence.
   2.544 +  /// \return The cost of the arborescence. 
   2.545 +  ///
   2.546 +  /// \sa MinCostArborescence
   2.547 +  template <typename Graph, typename CostMap, typename ArborescenceMap>
   2.548 +  typename CostMap::Value minCostArborescence(const Graph& graph, 
   2.549 +                                              const CostMap& cost,
   2.550 +                                              typename Graph::Node source,
   2.551 +                                              ArborescenceMap& arborescence) {
   2.552 +    typename MinCostArborescence<Graph, CostMap>
   2.553 +      ::template DefArborescenceMap<ArborescenceMap>
   2.554 +      ::Create mca(graph, cost);
   2.555 +    mca.arborescenceMap(arborescence);
   2.556 +    mca.run(source);
   2.557 +    return mca.arborescenceCost();
   2.558 +  }
   2.559 +
   2.560 +}
   2.561 +
   2.562 +#endif
   2.563 +
   2.564 +// Hilbert - Huang