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boost/graph/kolmogorov_max_flow.hpp

//  Copyright (c) 2006, Stephan Diederich
//
//  This code may be used under either of the following two licences:
//
//    Permission is hereby granted, free of charge, to any person
//    obtaining a copy of this software and associated documentation
//    files (the "Software"), to deal in the Software without
//    restriction, including without limitation the rights to use,
//    copy, modify, merge, publish, distribute, sublicense, and/or
//    sell copies of the Software, and to permit persons to whom the
//    Software is furnished to do so, subject to the following
//    conditions:
//
//    The above copyright notice and this permission notice shall be
//    included in all copies or substantial portions of the Software.
//
//    THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND,
//    EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES
//    OF MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND
//    NONINFRINGEMENT. IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT
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//    FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR
//    OTHER DEALINGS IN THE SOFTWARE. OF SUCH DAMAGE.
//
//  Or:
//
//    Distributed under the Boost Software License, Version 1.0.
//    (See accompanying file LICENSE_1_0.txt or copy at
//    http://www.boost.org/LICENSE_1_0.txt)

#ifndef BOOST_KOLMOGOROV_MAX_FLOW_HPP
#define BOOST_KOLMOGOROV_MAX_FLOW_HPP

#include <boost/config.hpp>
#include <cassert>
#include <vector>
#include <list>
#include <utility>
#include <iosfwd>
#include <algorithm> // for std::min and std::max

#include <boost/pending/queue.hpp>
#include <boost/limits.hpp>
#include <boost/property_map/property_map.hpp>
#include <boost/none_t.hpp>
#include <boost/graph/graph_concepts.hpp>
#include <boost/graph/named_function_params.hpp>

namespace boost {
  namespace detail {

    template <class Graph,
              class EdgeCapacityMap,
              class ResidualCapacityEdgeMap,
              class ReverseEdgeMap,
              class PredecessorMap,
              class ColorMap,
              class DistanceMap,
              class IndexMap>
    class kolmogorov{
      typedef typename property_traits<EdgeCapacityMap>::value_type tEdgeVal;
      typedef graph_traits<Graph> tGraphTraits;
      typedef typename tGraphTraits::vertex_iterator vertex_iterator;
      typedef typename tGraphTraits::vertex_descriptor vertex_descriptor;
      typedef typename tGraphTraits::edge_descriptor edge_descriptor;
      typedef typename tGraphTraits::edge_iterator edge_iterator;
      typedef typename tGraphTraits::out_edge_iterator out_edge_iterator;
      typedef boost::queue<vertex_descriptor> tQueue;                               //queue of vertices, used in adoption-stage
      typedef typename property_traits<ColorMap>::value_type tColorValue;
      typedef color_traits<tColorValue> tColorTraits;
      typedef typename property_traits<DistanceMap>::value_type tDistanceVal;

        public:
          kolmogorov(Graph& g,
                     EdgeCapacityMap cap,
                     ResidualCapacityEdgeMap res,
                     ReverseEdgeMap rev,
                     PredecessorMap pre,
                     ColorMap color,
                     DistanceMap dist,
                     IndexMap idx,
                     vertex_descriptor src,
                     vertex_descriptor sink):
          m_g(g),
          m_index_map(idx),
          m_cap_map(cap),
          m_res_cap_map(res),
          m_rev_edge_map(rev),
          m_pre_map(pre),
          m_tree_map(color),
          m_dist_map(dist),
          m_source(src),
          m_sink(sink),
          m_active_nodes(),
          m_in_active_list_vec(num_vertices(g), false),
          m_in_active_list_map(make_iterator_property_map(m_in_active_list_vec.begin(), m_index_map)),
          m_has_parent_vec(num_vertices(g), false),
          m_has_parent_map(make_iterator_property_map(m_has_parent_vec.begin(), m_index_map)),
          m_time_vec(num_vertices(g), 0),
          m_time_map(make_iterator_property_map(m_time_vec.begin(), m_index_map)),
          m_flow(0),
          m_time(1),
          m_last_grow_vertex(graph_traits<Graph>::null_vertex()){
            // initialize the color-map with gray-values
            vertex_iterator vi, v_end;
            for(tie(vi, v_end) = vertices(m_g); vi != v_end; ++vi){
              set_tree(*vi, tColorTraits::gray());
            }
            // Initialize flow to zero which means initializing
            // the residual capacity equal to the capacity
            edge_iterator ei, e_end;
            for(tie(ei, e_end) = edges(m_g); ei != e_end; ++ei) {
              m_res_cap_map[*ei] = m_cap_map[*ei];
              assert(m_rev_edge_map[m_rev_edge_map[*ei]] == *ei); //check if the reverse edge map is build up properly
            }
            //init the search trees with the two terminals
            set_tree(m_source, tColorTraits::black());
            set_tree(m_sink, tColorTraits::white());
            m_time_map[m_source] = 1;
            m_time_map[m_sink] = 1;
          }
          
          ~kolmogorov(){}

          tEdgeVal max_flow(){
            //augment direct paths from SOURCE->SINK and SOURCE->VERTEX->SINK
            augment_direct_paths();
            //start the main-loop
            while(true){
              bool path_found;
              edge_descriptor connecting_edge;
              tie(connecting_edge, path_found) = grow(); //find a path from source to sink
              if(!path_found){
                //we're finished, no more paths were found
                break; 
              }
              ++m_time;
              augment(connecting_edge); //augment that path
              adopt(); //rebuild search tree structure
            }
            return m_flow;
          }

          //the complete class is protected, as we want access to members in derived test-class (see $(BOOST_ROOT)/libs/graph/test/kolmogorov_max_flow_test.cpp)
        protected:
          void augment_direct_paths(){
            //in a first step, we augment all direct paths from source->NODE->sink
            //and additionally paths from source->sink
            //this improves especially graphcuts for segmentation, as most of the nodes have source/sink connects
            //but shouldn't have an impact on other maxflow problems (this is done in grow() anyway)
            out_edge_iterator ei, e_end;
            for(tie(ei, e_end) = out_edges(m_source, m_g); ei != e_end; ++ei){
              edge_descriptor from_source = *ei;
              vertex_descriptor current_node = target(from_source, m_g);
              if(current_node == m_sink){
                tEdgeVal cap = m_res_cap_map[from_source];
                m_res_cap_map[from_source] = 0;
                m_flow += cap;
                continue;
              }
              edge_descriptor to_sink;
              bool is_there;
              tie(to_sink, is_there) = edge(current_node, m_sink, m_g);
              if(is_there){
                tEdgeVal cap_from_source = m_res_cap_map[from_source];
                tEdgeVal cap_to_sink = m_res_cap_map[to_sink];
                if(cap_from_source > cap_to_sink){
                  set_tree(current_node, tColorTraits::black());
                  add_active_node(current_node);
                  set_edge_to_parent(current_node, from_source);
                  m_dist_map[current_node] = 1;
                  m_time_map[current_node] = 1;
                  //add stuff to flow and update residuals
                  //we dont need to update reverse_edges, as incoming/outgoing edges to/from source/sink don't count for max-flow
                  m_res_cap_map[from_source] -= cap_to_sink;
                  m_res_cap_map[to_sink] = 0;
                  m_flow += cap_to_sink;
                } else if(cap_to_sink > 0){
                  set_tree(current_node, tColorTraits::white());
                  add_active_node(current_node);
                  set_edge_to_parent(current_node, to_sink);
                  m_dist_map[current_node] = 1;
                  m_time_map[current_node] = 1;
                  //add stuff to flow and update residuals
                  //we dont need to update reverse_edges, as incoming/outgoing edges to/from source/sink don't count for max-flow
                  m_res_cap_map[to_sink] -= cap_from_source;
                  m_res_cap_map[from_source] = 0;
                  m_flow += cap_from_source;
                }
              } else if(m_res_cap_map[from_source]){
                //there is no sink connect, so we can't augment this path
                //but to avoid adding m_source to the active nodes, we just activate this node and set the approciate things
                set_tree(current_node, tColorTraits::black());
                set_edge_to_parent(current_node, from_source);
                m_dist_map[current_node] = 1;
                m_time_map[current_node] = 1;
                add_active_node(current_node);
              }
            }
            for(tie(ei, e_end) = out_edges(m_sink, m_g); ei != e_end; ++ei){
              edge_descriptor to_sink = m_rev_edge_map[*ei];
              vertex_descriptor current_node = source(to_sink, m_g);
              if(m_res_cap_map[to_sink]){
                set_tree(current_node, tColorTraits::white());
                set_edge_to_parent(current_node, to_sink);
                m_dist_map[current_node] = 1;
                m_time_map[current_node] = 1;
                add_active_node(current_node);
              }
            }
          }

          /**
          * returns a pair of an edge and a boolean. if the bool is true, the edge is a connection of a found path from s->t , read "the link" and 
          *   source(returnVal, m_g) is the end of the path found in the source-tree
          *   target(returnVal, m_g) is the beginning of the path found in the sink-tree
          */
          std::pair<edge_descriptor, bool> grow(){
            assert(m_orphans.empty());
            vertex_descriptor current_node;
            while((current_node = get_next_active_node()) != graph_traits<Graph>::null_vertex()){ //if there is one
              assert(get_tree(current_node) != tColorTraits::gray()  && (has_parent(current_node) || current_node==m_source || current_node==m_sink)); 
              if(get_tree(current_node) == tColorTraits::black()){ 
                //source tree growing
                out_edge_iterator ei, e_end;
                if(current_node != m_last_grow_vertex){
                  m_last_grow_vertex = current_node;
                  tie(m_last_grow_edge_it, m_last_grow_edge_end) = out_edges(current_node, m_g);
                } 
                for(; m_last_grow_edge_it != m_last_grow_edge_end; ++m_last_grow_edge_it){
                  edge_descriptor out_edge = *m_last_grow_edge_it;
                  if(m_res_cap_map[out_edge] > 0){ //check if we have capacity left on this edge
                    vertex_descriptor other_node = target(out_edge, m_g);
                    if(get_tree(other_node) == tColorTraits::gray()){ //it's a free node
                      set_tree(other_node, tColorTraits::black()); //aquire other node to our search tree
                      set_edge_to_parent(other_node, out_edge);   //set us as parent
                      m_dist_map[other_node] = m_dist_map[current_node] + 1;  //and update the distance-heuristic
                      m_time_map[other_node] = m_time_map[current_node];
                      add_active_node(other_node);
                    } else if(get_tree(other_node) == tColorTraits::black()){
                      if(is_closer_to_terminal(current_node, other_node)){ //we do this to get shorter paths. check if we are nearer to the source as its parent is
                        set_edge_to_parent(other_node, out_edge);
                        m_dist_map[other_node] = m_dist_map[current_node] + 1;
                        m_time_map[other_node] = m_time_map[current_node];
                      }
                    } else{ 
                      assert(get_tree(other_node)==tColorTraits::white());
                      //kewl, found a path from one to the other search tree, return the connecting edge in src->sink dir
                      return std::make_pair(out_edge, true);
                    }
                  }
                } //for all out-edges
              } //source-tree-growing
              else{
                assert(get_tree(current_node) == tColorTraits::white());
                out_edge_iterator ei, e_end;
                if(current_node != m_last_grow_vertex){
                  m_last_grow_vertex = current_node;
                  tie(m_last_grow_edge_it, m_last_grow_edge_end) = out_edges(current_node, m_g);
                }
                for(; m_last_grow_edge_it != m_last_grow_edge_end; ++m_last_grow_edge_it){
                  edge_descriptor in_edge = m_rev_edge_map[*m_last_grow_edge_it];
                  if(m_res_cap_map[in_edge] > 0){ //check if there is capacity left
                    vertex_descriptor other_node = source(in_edge, m_g);
                    if(get_tree(other_node) == tColorTraits::gray()){ //it's a free node
                      set_tree(other_node, tColorTraits::white());      //aquire that node to our search tree
                      set_edge_to_parent(other_node, in_edge);          //set us as parent
                      add_active_node(other_node);                      //activate that node
                      m_dist_map[other_node] = m_dist_map[current_node] + 1; //set its distance
                      m_time_map[other_node] = m_time_map[current_node];     //and time
                    } else if(get_tree(other_node) == tColorTraits::white()){
                      if(is_closer_to_terminal(current_node, other_node)){
                        //we are closer to the sink than its parent is, so we "adopt" him
                        set_edge_to_parent(other_node, in_edge);
                        m_dist_map[other_node] = m_dist_map[current_node] + 1;
                        m_time_map[other_node] = m_time_map[current_node];
                      }
                    } else{
                      assert(get_tree(other_node)==tColorTraits::black());
                      //kewl, found a path from one to the other search tree, return the connecting edge in src->sink dir
                      return std::make_pair(in_edge, true);
                    }
                  }
                } //for all out-edges
              } //sink-tree growing
              //all edges of that node are processed, and no more paths were found. so remove if from the front of the active queue
              finish_node(current_node);
            } //while active_nodes not empty
            return std::make_pair(edge_descriptor(), false); //no active nodes anymore and no path found, we're done
          }

          /**
          * augments path from s->t and updates residual graph
          * source(e, m_g) is the end of the path found in the source-tree
          * target(e, m_g) is the beginning of the path found in the sink-tree
          * this phase generates orphans on satured edges, if the attached verts are from different search-trees
          * orphans are ordered in distance to sink/source. first the farest from the source are front_inserted into the orphans list,
          * and after that the sink-tree-orphans are front_inserted. when going to adoption stage the orphans are popped_front, and so we process the nearest 
          * verts to the terminals first
          */
          void augment(edge_descriptor e){
            assert(get_tree(target(e, m_g)) == tColorTraits::white());
            assert(get_tree(source(e, m_g)) == tColorTraits::black());
            assert(m_orphans.empty());

            const tEdgeVal bottleneck = find_bottleneck(e);
            //now we push the found flow through the path
            //for each edge we saturate we have to look for the verts that belong to that edge, one of them becomes an orphans
            //now process the connecting edge
            m_res_cap_map[e] -= bottleneck;
            assert(m_res_cap_map[e] >= 0);
            m_res_cap_map[m_rev_edge_map[e]] += bottleneck;

            //now we follow the path back to the source
            vertex_descriptor current_node = source(e, m_g);
            while(current_node != m_source){
              edge_descriptor pred = get_edge_to_parent(current_node);
              m_res_cap_map[pred] -= bottleneck;
              assert(m_res_cap_map[pred] >= 0);
              m_res_cap_map[m_rev_edge_map[pred]] += bottleneck;
              if(m_res_cap_map[pred] == 0){
                set_no_parent(current_node);
                m_orphans.push_front(current_node);
              }
              current_node = source(pred, m_g);
            }
            //then go forward in the sink-tree
            current_node = target(e, m_g);
            while(current_node != m_sink){
              edge_descriptor pred = get_edge_to_parent(current_node);
              m_res_cap_map[pred] -= bottleneck;
              assert(m_res_cap_map[pred] >= 0);
              m_res_cap_map[m_rev_edge_map[pred]] += bottleneck;
              if(m_res_cap_map[pred] == 0){
                set_no_parent(current_node);
                m_orphans.push_front(current_node);
              }
              current_node = target(pred, m_g);
            }
            //and add it to the max-flow
            m_flow += bottleneck;
          }

          /**
           * returns the bottleneck of a s->t path (end_of_path is last vertex in source-tree, begin_of_path is first vertex in sink-tree)
           */
          inline tEdgeVal find_bottleneck(edge_descriptor e){
            BOOST_USING_STD_MIN();
            tEdgeVal minimum_cap = m_res_cap_map[e];
            vertex_descriptor current_node = source(e, m_g);
            //first go back in the source tree
            while(current_node != m_source){
              edge_descriptor pred = get_edge_to_parent(current_node);
              minimum_cap = min BOOST_PREVENT_MACRO_SUBSTITUTION(minimum_cap, m_res_cap_map[pred]);
              current_node = source(pred, m_g);
            }
            //then go forward in the sink-tree
            current_node = target(e, m_g);
            while(current_node != m_sink){
              edge_descriptor pred = get_edge_to_parent(current_node);
              minimum_cap = min BOOST_PREVENT_MACRO_SUBSTITUTION(minimum_cap, m_res_cap_map[pred]);
              current_node = target(pred, m_g);
            }
            return minimum_cap;
          }

          /**
          * rebuild search trees
          * empty the queue of orphans, and find new parents for them or just drop them from the search trees
          */
          void adopt(){
            while(!m_orphans.empty() || !m_child_orphans.empty()){
              vertex_descriptor current_node;
              if(m_child_orphans.empty()){
                //get the next orphan from the main-queue  and remove it
                current_node = m_orphans.front();
                m_orphans.pop_front();
              } else{
                current_node = m_child_orphans.front();
                m_child_orphans.pop();
              }
              if(get_tree(current_node) == tColorTraits::black()){ 
                //we're in the source-tree
                tDistanceVal min_distance = (std::numeric_limits<tDistanceVal>::max)();
                edge_descriptor new_parent_edge;
                out_edge_iterator ei, e_end;
                for(tie(ei, e_end) = out_edges(current_node, m_g); ei != e_end; ++ei){
                  const edge_descriptor in_edge = m_rev_edge_map[*ei];
                  assert(target(in_edge, m_g) == current_node); //we should be the target of this edge
                  if(m_res_cap_map[in_edge] > 0){
                    vertex_descriptor other_node = source(in_edge, m_g);
                    if(get_tree(other_node) == tColorTraits::black() && has_source_connect(other_node)){
                      if(m_dist_map[other_node] < min_distance){
                        min_distance = m_dist_map[other_node];
                        new_parent_edge = in_edge;
                      }
                    }
                  }
                }
                if(min_distance != (std::numeric_limits<tDistanceVal>::max)()){
                  set_edge_to_parent(current_node, new_parent_edge);
                  m_dist_map[current_node] = min_distance + 1;
                  m_time_map[current_node] = m_time;
                } else{
                  m_time_map[current_node] = 0;
                  for(tie(ei, e_end) = out_edges(current_node, m_g); ei != e_end; ++ei){
                    edge_descriptor in_edge = m_rev_edge_map[*ei];
                    vertex_descriptor other_node = source(in_edge, m_g);
                    if(get_tree(other_node) == tColorTraits::black() && has_parent(other_node)){
                      if(m_res_cap_map[in_edge] > 0){
                        add_active_node(other_node);
                      }
                      if(source(get_edge_to_parent(other_node), m_g) == current_node){
                        //we are the parent of that node
                        //it has to find a new parent, too
                        set_no_parent(other_node);
                        m_child_orphans.push(other_node);
                      }
                    }
                  }
                  set_tree(current_node, tColorTraits::gray());
                } //no parent found
              } //source-tree-adoption
              else{
                //now we should be in the sink-tree, check that...
                assert(get_tree(current_node) == tColorTraits::white());
                out_edge_iterator ei, e_end;
                edge_descriptor new_parent_edge;
                tDistanceVal min_distance = (std::numeric_limits<tDistanceVal>::max)();
                for(tie(ei, e_end) = out_edges(current_node, m_g); ei != e_end; ++ei){
                  const edge_descriptor out_edge = *ei;
                  if(m_res_cap_map[out_edge] > 0){
                    const vertex_descriptor other_node = target(out_edge, m_g);
                    if(get_tree(other_node) == tColorTraits::white() && has_sink_connect(other_node))
                      if(m_dist_map[other_node] < min_distance){
                        min_distance = m_dist_map[other_node];
                        new_parent_edge = out_edge;
                      }
                  }
                }
                if(min_distance != (std::numeric_limits<tDistanceVal>::max)()){
                  set_edge_to_parent(current_node, new_parent_edge);
                  m_dist_map[current_node] = min_distance + 1;
                  m_time_map[current_node] = m_time;
                } else{
                  m_time_map[current_node] = 0;
                  for(tie(ei, e_end) = out_edges(current_node, m_g); ei != e_end; ++ei){
                    const edge_descriptor out_edge = *ei;
                    const vertex_descriptor other_node = target(out_edge, m_g);
                    if(get_tree(other_node) == tColorTraits::white() && has_parent(other_node)){ 
                      if(m_res_cap_map[out_edge] > 0){
                        add_active_node(other_node);
                      }
                      if(target(get_edge_to_parent(other_node), m_g) == current_node){
                        //we were it's parent, so it has to find a new one, too
                        set_no_parent(other_node);
                        m_child_orphans.push(other_node);
                      }
                    }
                  }
                  set_tree(current_node, tColorTraits::gray());
                } //no parent found
              } //sink-tree adoption
            } //while !orphans.empty()
          } //adopt

          /**
          * return next active vertex if there is one, otherwise a null_vertex
          */    
          inline vertex_descriptor get_next_active_node(){
            while(true){
              if(m_active_nodes.empty())
                return graph_traits<Graph>::null_vertex();
              vertex_descriptor v = m_active_nodes.front();

              if(!has_parent(v) && v != m_source && v != m_sink){ //if it has no parent, this node can't be active(if its not source or sink)
                m_active_nodes.pop();
                m_in_active_list_map[v] = false;
              } else{
                assert(get_tree(v) == tColorTraits::black() || get_tree(v) == tColorTraits::white());
                return v;
              }
            }
          }

          /**
          * adds v as an active vertex, but only if its not in the list already
          */            
          inline void add_active_node(vertex_descriptor v){
            assert(get_tree(v) != tColorTraits::gray());
            if(m_in_active_list_map[v]){
              return;
            } else{
              m_in_active_list_map[v] = true;
              m_active_nodes.push(v);
            }
          }

          /**
           * finish_node removes a node from the front of the active queue (its called in grow phase, if no more paths can be found using this node)
           */
          inline void finish_node(vertex_descriptor v){
            assert(m_active_nodes.front() == v);
            m_active_nodes.pop();
            m_in_active_list_map[v] = false;
            m_last_grow_vertex = graph_traits<Graph>::null_vertex();
          }

          /**
          * removes a vertex from the queue of active nodes (actually this does nothing, 
          * but checks if this node has no parent edge, as this is the criteria for beeing no more active) 
          */
          inline void remove_active_node(vertex_descriptor v){
            assert(!has_parent(v));
          }

          /**
          * returns the search tree of v; tColorValue::black() for source tree, white() for sink tree, gray() for no tree
          */
          inline tColorValue get_tree(vertex_descriptor v) const {
            return m_tree_map[v];
          }

          /**
          * sets search tree of v; tColorValue::black() for source tree, white() for sink tree, gray() for no tree
          */
          inline void set_tree(vertex_descriptor v, tColorValue t){
            m_tree_map[v] = t;
          }

          /**
           * returns edge to parent vertex of v;
           */
          inline edge_descriptor get_edge_to_parent(vertex_descriptor v) const{
            return m_pre_map[v];
          }

          /**
           * returns true if the edge stored in m_pre_map[v] is a valid entry
           */
          inline bool has_parent(vertex_descriptor v) const{
            return m_has_parent_map[v];  
          }

          /**
           * sets edge to parent vertex of v; 
          */            
          inline void set_edge_to_parent(vertex_descriptor v, edge_descriptor f_edge_to_parent){
            assert(m_res_cap_map[f_edge_to_parent] > 0);
            m_pre_map[v] = f_edge_to_parent;
            m_has_parent_map[v] = true;
          }

          /**
           * removes the edge to parent of v (this is done by invalidating the entry an additional map)
           */
          inline void set_no_parent(vertex_descriptor v){
            m_has_parent_map[v] = false;
          }

          /**
           * checks if vertex v has a connect to the sink-vertex (@var m_sink)
           * @param v the vertex which is checked
           * @return true if a path to the sink was found, false if not
           */
          inline bool has_sink_connect(vertex_descriptor v){
            tDistanceVal current_distance = 0;
            vertex_descriptor current_vertex = v;
            while(true){
              if(m_time_map[current_vertex] == m_time){
                //we found a node which was already checked this round. use it for distance calculations
                current_distance += m_dist_map[current_vertex];
                break;
              }
              if(current_vertex == m_sink){
                m_time_map[m_sink] = m_time;
                break; 
              }
              if(has_parent(current_vertex)){
                //it has a parent, so get it
                current_vertex = target(get_edge_to_parent(current_vertex), m_g);
                ++current_distance;
              } else{
                //no path found
                return false;
              }
            }
            current_vertex=v;
            while(m_time_map[current_vertex] != m_time){
              m_dist_map[current_vertex] = current_distance--;
              m_time_map[current_vertex] = m_time;
              current_vertex = target(get_edge_to_parent(current_vertex), m_g);
            }
            return true;
          }

          /**
           * checks if vertex v has a connect to the source-vertex (@var m_source)
           * @param v the vertex which is checked
           * @return true if a path to the source was found, false if not
           */
          inline bool has_source_connect(vertex_descriptor v){
            tDistanceVal current_distance = 0;
            vertex_descriptor current_vertex = v;
            while(true){
              if(m_time_map[current_vertex] == m_time){
                //we found a node which was already checked this round. use it for distance calculations
                current_distance += m_dist_map[current_vertex];
                break;
              }
              if(current_vertex == m_source){
                m_time_map[m_source] = m_time;
                break;
              }
              if(has_parent(current_vertex)){
                //it has a parent, so get it
                current_vertex = source(get_edge_to_parent(current_vertex), m_g);
                ++current_distance;
              } else{
                //no path found
                return false;
              }
            }
            current_vertex=v;
            while(m_time_map[current_vertex] != m_time){
                m_dist_map[current_vertex] = current_distance-- ;
                m_time_map[current_vertex] = m_time;
                current_vertex = source(get_edge_to_parent(current_vertex), m_g);
            }
            return true;
          }

          /**
          * returns true, if p is closer to a terminal than q
          */
          inline bool is_closer_to_terminal(vertex_descriptor p, vertex_descriptor q){
            //checks the timestamps first, to build no cycles, and after that the real distance
            return (m_time_map[q] <= m_time_map[p] && m_dist_map[q] > m_dist_map[p]+1);
          }

          ////////
          // member vars
          ////////
          Graph& m_g;
          IndexMap m_index_map;
          EdgeCapacityMap m_cap_map;
          ResidualCapacityEdgeMap m_res_cap_map;
          ReverseEdgeMap m_rev_edge_map;
          PredecessorMap m_pre_map; //stores paths found in the growth stage
          ColorMap m_tree_map; //maps each vertex into one of the two search tree or none (gray())
          DistanceMap m_dist_map; //stores distance to source/sink nodes
          vertex_descriptor m_source;
          vertex_descriptor m_sink;

          tQueue m_active_nodes;
          std::vector<bool> m_in_active_list_vec;
          iterator_property_map<std::vector<bool>::iterator, IndexMap> m_in_active_list_map;

          std::list<vertex_descriptor> m_orphans;
          tQueue m_child_orphans; // we use a second queuqe for child orphans, as they are FIFO processed

          std::vector<bool> m_has_parent_vec;
          iterator_property_map<std::vector<bool>::iterator, IndexMap> m_has_parent_map;

          std::vector<long> m_time_vec; //timestamp of each node, used for sink/source-path calculations
          iterator_property_map<std::vector<long>::iterator, IndexMap> m_time_map;
          tEdgeVal m_flow;
          long m_time;
          vertex_descriptor m_last_grow_vertex;
          out_edge_iterator m_last_grow_edge_it;
          out_edge_iterator m_last_grow_edge_end;
    };
  } //namespace detail
  
  /**
   * non-named-parameter version, given everything
   * this is the catch all version
   */                   
  template <class Graph, class CapacityEdgeMap, class ResidualCapacityEdgeMap, class ReverseEdgeMap, 
    class PredecessorMap, class ColorMap, class DistanceMap, class IndexMap>
  typename property_traits<CapacityEdgeMap>::value_type
  kolmogorov_max_flow
      (Graph& g,
       CapacityEdgeMap cap,
       ResidualCapacityEdgeMap res_cap,
       ReverseEdgeMap rev_map,
       PredecessorMap pre_map,
       ColorMap color,
       DistanceMap dist,
       IndexMap idx,
       typename graph_traits<Graph>::vertex_descriptor src,
       typename graph_traits<Graph>::vertex_descriptor sink
       )
  {
    typedef typename graph_traits<Graph>::vertex_descriptor vertex_descriptor;
    typedef typename graph_traits<Graph>::edge_descriptor edge_descriptor;
    //as this method is the last one before we instantiate the solver, we do the concept checks here
    function_requires<VertexListGraphConcept<Graph> >(); //to have vertices(), num_vertices(),
    function_requires<EdgeListGraphConcept<Graph> >(); //to have edges()
    function_requires<IncidenceGraphConcept<Graph> >(); //to have source(), target() and out_edges()
    function_requires<LvaluePropertyMapConcept<CapacityEdgeMap, edge_descriptor> >(); //read flow-values from edges
    function_requires<Mutable_LvaluePropertyMapConcept<ResidualCapacityEdgeMap, edge_descriptor> >(); //write flow-values to residuals
    function_requires<LvaluePropertyMapConcept<ReverseEdgeMap, edge_descriptor> >(); //read out reverse edges
    function_requires<Mutable_LvaluePropertyMapConcept<PredecessorMap, vertex_descriptor> >(); //store predecessor there
    function_requires<Mutable_LvaluePropertyMapConcept<ColorMap, vertex_descriptor> >(); //write corresponding tree
    function_requires<Mutable_LvaluePropertyMapConcept<DistanceMap, vertex_descriptor> >(); //write distance to source/sink
    function_requires<ReadablePropertyMapConcept<IndexMap, vertex_descriptor> >(); //get index 0...|V|-1
    assert(num_vertices(g) >= 2 && src != sink);
    detail::kolmogorov<Graph, CapacityEdgeMap, ResidualCapacityEdgeMap, ReverseEdgeMap, PredecessorMap, ColorMap, DistanceMap, IndexMap>
        algo(g, cap, res_cap, rev_map, pre_map, color, dist, idx, src, sink);
        return algo.max_flow();
  }

  /**
   * non-named-parameter version, given: capacity, residucal_capacity, reverse_edges, and an index map.
   */
  template <class Graph, class CapacityEdgeMap, class ResidualCapacityEdgeMap, class ReverseEdgeMap, class IndexMap>
  typename property_traits<CapacityEdgeMap>::value_type
   kolmogorov_max_flow
       (Graph& g,
       CapacityEdgeMap cap,
       ResidualCapacityEdgeMap res_cap,
       ReverseEdgeMap rev,
       IndexMap idx,
       typename graph_traits<Graph>::vertex_descriptor src,
       typename graph_traits<Graph>::vertex_descriptor sink)
   {
     typename graph_traits<Graph>::vertices_size_type n_verts = num_vertices(g);
     std::vector<typename graph_traits<Graph>::edge_descriptor> predecessor_vec(n_verts);
     std::vector<default_color_type> color_vec(n_verts);
     std::vector<typename graph_traits<Graph>::vertices_size_type> distance_vec(n_verts);
     return kolmogorov_max_flow
         (g, cap, res_cap, rev,
          make_iterator_property_map(predecessor_vec.begin(), idx),
          make_iterator_property_map(color_vec.begin(), idx),
          make_iterator_property_map(distance_vec.begin(), idx),
          idx, src, sink);
   }
   
  /**
   * non-named-parameter version, some given: capacity, residual_capacity, reverse_edges, color_map and an index map.
   * Use this if you are interested in the minimum cut, as the color map provides that info
   */
   template <class Graph, class CapacityEdgeMap, class ResidualCapacityEdgeMap, class ReverseEdgeMap, class ColorMap, class IndexMap>
   typename property_traits<CapacityEdgeMap>::value_type
   kolmogorov_max_flow
       (Graph& g,
        CapacityEdgeMap cap,
        ResidualCapacityEdgeMap res_cap,
        ReverseEdgeMap rev,
        ColorMap color,
        IndexMap idx,
        typename graph_traits<Graph>::vertex_descriptor src,
        typename graph_traits<Graph>::vertex_descriptor sink)
   {
     typename graph_traits<Graph>::vertices_size_type n_verts = num_vertices(g);
     std::vector<typename graph_traits<Graph>::edge_descriptor> predecessor_vec(n_verts);
     std::vector<typename graph_traits<Graph>::vertices_size_type> distance_vec(n_verts);

     return kolmogorov_max_flow
         (g, cap, res_cap, rev,
          make_iterator_property_map(predecessor_vec.begin(), idx),
          color,
          make_iterator_property_map(distance_vec.begin(), idx),
          idx, src, sink);
   }
   
  /**
   * named-parameter version, some given
   */
   template <class Graph, class P, class T, class R>
   typename property_traits<typename property_map<Graph, edge_capacity_t>::const_type>::value_type
   kolmogorov_max_flow
       (Graph& g,
        typename graph_traits<Graph>::vertex_descriptor src,
        typename graph_traits<Graph>::vertex_descriptor sink,
        const bgl_named_params<P, T, R>& params)
   {
     return kolmogorov_max_flow(g,
                                choose_const_pmap(get_param(params, edge_capacity), g, edge_capacity),
                                choose_pmap(get_param(params, edge_residual_capacity), g, edge_residual_capacity),
                                choose_const_pmap(get_param(params, edge_reverse), g, edge_reverse),
                                choose_pmap(get_param(params, vertex_predecessor), g, vertex_predecessor),
                                choose_pmap(get_param(params, vertex_color), g, vertex_color),
                                choose_pmap(get_param(params, vertex_distance), g, vertex_distance),
                                choose_const_pmap(get_param(params, vertex_index), g, vertex_index),
                                src, sink);
   }
   
  /**
   * named-parameter version, none given
   */
   template <class Graph>
   typename property_traits<typename property_map<Graph, edge_capacity_t>::const_type>::value_type
   kolmogorov_max_flow
       (Graph& g,
        typename graph_traits<Graph>::vertex_descriptor src,
        typename graph_traits<Graph>::vertex_descriptor sink)
   {
     bgl_named_params<int, buffer_param_t> params(0); // bogus empty param
     return kolmogorov_max_flow(g, src, sink, params);
   }
} // namespace boost

#endif // BOOST_KOLMOGOROV_MAX_FLOW_HPP