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<IMG SRC="../../../boost.png" NAME="Grafik1" ALT="C++ Boost" ALIGN=BOTTOM WIDTH=277 HEIGHT=86 BORDER=0>
</P>
<table align="center" width="75%" style="border:1px solid; border-spacing: 10pt">
<tr>
<td style="vertical-align: top"><img src="figs/warning.png"></td>
<td>
<b>Warning!</b> This header and its contents are <em>deprecated</em> and
will be removed in a future release. Please update your program to use
<a href="boykov_kolmogorov_max_flow.html"> <tt>boykov_kolmogorov_max_flow</tt></a>
instead. Note that only the name of the algorithm has changed. The template
and function parameters will remain the same.
</td>
</tr>
</table>
<H1><A NAME="sec:kolmogorov_max_flow"></A><TT>kolmogorov_max_flow</TT>
</H1>
<PRE><I>// named parameter version</I>
template &lt;class Graph, class P, class T, class R&gt;
typename property_traits&lt;typename property_map&lt;Graph, edge_capacity_t&gt;::const_type&gt;::value_type
kolmogorov_max_flow(Graph&amp; g,
typename graph_traits&lt;Graph&gt;::vertex_descriptor src,
typename graph_traits&lt;Graph&gt;::vertex_descriptor sink,
const bgl_named_params&lt;P, T, R&gt;&amp; params = <I>all defaults</I>)
<I>// non-named parameter version</I>
template &lt;class Graph, class CapacityEdgeMap, class ResidualCapacityEdgeMap, class ReverseEdgeMap,
class PredecessorMap, class ColorMap, class DistanceMap, class IndexMap&gt;
typename property_traits&lt;CapacityEdgeMap&gt;::value_type
kolmogorov_max_flow(Graph&amp; g,
CapacityEdgeMap cap,
ResidualCapacityEdgeMap res_cap,
ReverseEdgeMap rev_map,
PredecessorMap pre_map,
ColorMap color,
DistanceMap dist,
IndexMap idx,
typename graph_traits &lt;Graph&gt;::vertex_descriptor src,
typename graph_traits &lt;Graph &gt;::vertex_descriptor sink)</PRE><P>
<FONT SIZE=3>Additional overloaded versions for non-named parameters
are provided (without DistanceMap/ColorMap/DistanceMap; for those
iterator_property_maps with the provided index map are used)</FONT></P>
<P>The <TT>kolmogorov_max_flow()</TT> function calculates the maximum
flow of a network. See Section <A HREF="graph_theory_review.html#sec:network-flow-algorithms">Network
Flow Algorithms</A> for a description of maximum flow. The calculated
maximum flow will be the return value of the function. The function
also calculates the flow values <I>f(u,v)</I> for all <I>(u,v)</I> in
<I>E</I>, which are returned in the form of the residual capacity
<I>r(u,v) = c(u,v) - f(u,v)</I>.
</P>
<P><B>Requirements:</B><BR>The directed graph <I>G=(V,E)</I> that
represents the network must include a reverse edge for every edge in
<I>E</I>. That is, the input graph should be <I>G<SUB>in</SUB> =
(V,{E U E<SUP>T</SUP>})</I>. The <TT>ReverseEdgeMap</TT> argument <TT>rev</TT>
must map each edge in the original graph to its reverse edge, that is
<I>(u,v) -&gt; (v,u)</I> for all <I>(u,v)</I> in <I>E</I>.
</P>
<P>Remarks: While the push-relabel method states that each edge in <I>E<SUP>T</SUP></I>
has to have capacity of 0, the reverse edges for this algorithm ARE
allowed to carry capacities. If there are already reverse edges in
the input Graph <I><FONT FACE="Courier New, monospace">G</FONT></I>,
those can be used. This can halve the amount of edges and will
noticeably increase the performance.<BR><BR><B>Algorithm
description:</B><BR>Kolmogorov's algorithm is a variety of the
augmenting-path algorithm. Standard augmenting path algorithms find
shortest paths from source to sink vertex and augment them by
substracting the bottleneck capacity found on that path from the
residual capacities of each edge and adding it to the total flow.
Additionally the minimum capacity is added to the residual capacity
of the reverse edges. If no more paths in the residual-edge tree are
found, the algorithm terminates. Instead of finding a new shortest
path from source to sink in the graph in each iteration, Kolmogorov's
version keeps the already found paths as follows:</P>
<P>The algorithm builds up two search trees, a source-tree and a
sink-tree. Each vertex has a label (stored in <I>ColorMap</I>) to
which tree it belongs and a status-flag if this vertex is active or
passive. In the beginning of the algorithm only the source and the
sink are colored (source==black, sink==white) and have active status.
All other vertices are colored gray. The algorithm consists of three
phases:</P>
<P><I>grow-phase</I>: In this phase active vertices are allowed to
acquire neighbor vertices that are connected through an edge that has
a capacity-value greater than zero. Acquiring means that those vertices
become active and belong now to the search tree of the current
active vertex. If there are no more valid connections to neighbor
vertices, the current vertex becomes passive and the grow phase
continues with the next active vertex. The grow phase terminates if
there are no more active vertices left or a vertex discovers a vertex
from the other search tree through an unsaturated edge. In this case
a path from source to sink is found.</P>
<P><I>augment-phase</I>: This phase augments the path that was found
in the grow phase. First it finds the bottleneck capacity of the
found path, and then it updates the residual-capacity of the edges
from this path by substracting the bottleneck capacity from the
residual capacity. Furthermore the residual capacity of the reverse
edges are updated by adding the bottleneck capacity. This phase can
destroy the built up search trees, as it creates at least one
saturated edge. That means, that the search trees collapse to
forests, because a condition for the search trees is, that each
vertex in them has a valid (=non-saturated) connection to a terminal.</P>
<P><I>adoption-phase</I>: Here the search trees are reconstructed. A
simple solution would be to mark all vertices coming after the first
orphan in the found path free vertices (gray). A more sophisticated
solution is to give those orphans new parents: The neighbor vertices
are checked if they have a valid connection to the same terminal like
this vertex had (a path with unsaturated edges). If there is one,
this vertex becomes the new parent of the current orphan and this
forest is re-included into the search tree. If no new valid parent is
found, this vertex becomes a free vertex (marked gray), and it's
children become orphans. The adoption phase terminates if there are
no more orphans.</P>
<P><IMG SRC="figs/kolmogorov_max_flow.gif" NAME="Grafik2" ALIGN=LEFT WIDTH=827 HEIGHT=311 BORDER=0><BR CLEAR=LEFT><B>Details:</B></P>
<UL>
<LI><P>Marking heuristics: A timestamp is stored for each vertex
which shows in which iteration of the algorithm the distance to the
corresponding terminal was calculated.
</P>
<UL>
<LI><P>This distance is used and gets calculated in the
adoption-phase. In order to find a valid new parent for an orphan,
the possible parent is checked for a connection to the terminal to
which tree it belongs. If there is such a connection, the path is
tagged with the current time-stamp, and the distance value. If
another orphan has to find a parent and it comes across a vertex
with a current timestamp, this information is used.</P>
<LI><P>The distance is also used in the grow-phase. If a vertex
comes across another vertex of the same tree while searching for
new vertices, the other's distance is compared to its distance. If
it is smaller, that other vertex becomes the new parent of the
current. This can decrease the length of the search paths, and so
amount of adoptions.</P>
</UL>
<LI><P>Ordering of orphans: As described above, the augment-phase
and the adoption phase can create orphans. The orphans the
augment-phase generates, are ordered according to their distance to
the terminals (smallest first). This combined with the
distance/timestamp heuristics results in the possibility for not
having to recheck terminal-connections too often. New orphans which
are generated in adoption phase are processed before orphans from
the main queue for the same reason.</P>
</UL>
<P><BR><B>Implementation notes:</B></P>
<P>The algorithm is mainly implemented as described in the PhD thesis
of Kolmogorov. Few changes were made for increasing performance:</P>
<UL>
<LI><P>initialization: the algorithm first augments all paths from
source-&gt;sink and all paths from source-&gt;VERTEX-&gt;sink. This
improves especially graph-cuts used in image vision where nearly
each vertex has a source and sink connect. During this step, all
vertices that have an unsaturated connection from source are added
to the active vertex list and so the source is not.
</P>
<LI><P>active vertices: Kolmogorov uses two lists for active nodes
and states that new active vertices are added to the rear of the
second. Fetching an active vertex is done from the beginning of the
first list. If the first list is empty, it is exchanged by the
second. This implementation uses just one list.</P>
<LI><P>grow-phase: In the grow phase the first vertex in the
active-list is taken and all outgoing edges are checked if they are
unsaturated. This decreases performance for graphs with high-edge
density. This implementation stores the last accessed edge and
continues with it, if the first vertex in the active-list is the
same one as during the last grow-phase.</P>
</UL>
<P>This algorithm [<A HREF="bibliography.html#kolmogorov03">68</a>, <a href="bibliography.html#boykov-kolmogorov04">69</a>] was developed by Boykov and Kolmogorov.
</P>
<H3>Where Defined</H3>
<P><TT><A HREF="../../../boost/graph/kolmogorov_max_flow.hpp">boost/graph/kolmogorov_max_flow.hpp</A></TT>
</P>
<H3>Parameters</H3>
<P>IN: <TT>Graph&amp; g</TT>
</P>
<BLOCKQUOTE>A directed graph. The graph's type must be a model of
<A HREF="VertexListGraph.html">Vertex List Graph</A>, <A HREF="EdgeListGraph.html">Edge
List Graph</A> and <A HREF="IncidenceGraph.html">Incidence Graph</A>.
For each edge <I>(u,v)</I> in the graph, the reverse edge <I>(v,u)</I>
must also be in the graph. Performance of the algorithm will be slightly
improved if the graph type also models <a href="AdjacencyMatrix.html">Adjacency
Matrix</a>.
</BLOCKQUOTE>
<P>IN: <TT>vertex_descriptor src</TT>
</P>
<BLOCKQUOTE>The source vertex for the flow network graph.
</BLOCKQUOTE>
<P>IN: <TT>vertex_descriptor sink</TT>
</P>
<BLOCKQUOTE>The sink vertex for the flow network graph.
</BLOCKQUOTE>
<H3>Named Parameters</H3>
<P>IN: <TT>edge_capacity(EdgeCapacityMap cap)</TT>
</P>
<BLOCKQUOTE>The edge capacity property map. The type must be a model
of a constant <A HREF="../../property_map/doc/LvaluePropertyMap.html">Lvalue
Property Map</A>. The key type of the map must be the graph's edge
descriptor type.<BR><B>Default:</B> <TT>get(edge_capacity, g)</TT>
</BLOCKQUOTE>
<P>OUT: <TT>edge_residual_capacity(ResidualCapacityEdgeMap res)</TT>
</P>
<BLOCKQUOTE>The edge residual capacity property map. The type must be
a model of a mutable <A HREF="../../property_map/doc/LvaluePropertyMap.html">Lvalue
Property Map</A>. The key type of the map must be the graph's edge
descriptor type.<BR><B>Default:</B> <TT>get(edge_residual_capacity,
g)</TT>
</BLOCKQUOTE>
<P>IN: <TT>edge_reverse(ReverseEdgeMap rev)</TT>
</P>
<BLOCKQUOTE>An edge property map that maps every edge <I>(u,v)</I> in
the graph to the reverse edge <I>(v,u)</I>. The map must be a model
of constant <A HREF="../../property_map/doc/LvaluePropertyMap.html">Lvalue
Property Map</A>. The key type of the map must be the graph's edge
descriptor type.<BR><B>Default:</B> <TT>get(edge_reverse, g)</TT>
</BLOCKQUOTE>
<P>UTIL: <TT>vertex_predecessor(PredecessorMap pre_map)</TT>
</P>
<BLOCKQUOTE>A vertex property map that stores the edge to the vertex'
predecessor. The map must be a model of mutable <A HREF="../../property_map/doc/LvaluePropertyMap.html">Lvalue
Property Map</A>. The key type of the map must be the graph's vertex
descriptor type.<BR><B>Default:</B> <TT>get(vertex_predecessor, g)</TT>
</BLOCKQUOTE>
<P>OUT/UTIL: <TT>vertex_color(ColorMap color)</TT>
</P>
<BLOCKQUOTE>A vertex property map that stores a color for edge
vertex. If the color of a vertex after running the algorithm is black
the vertex belongs to the source tree else it belongs to the
sink-tree (used for minimum cuts). The map must be a model of mutable
<A HREF="../../property_map/doc/LvaluePropertyMap.html">Lvalue Property
Map</A>. The key type of the map must be the graph's vertex
descriptor type.<BR><B>Default:</B> <TT>get(vertex_color, g)</TT>
</BLOCKQUOTE>
<P>UTIL: <TT>vertex_distance(DistanceMap dist)</TT>
</P>
<BLOCKQUOTE>A vertex property map that stores the distance to the
corresponding terminal. It's a utility-map for speeding up the
algorithm. The map must be a model of mutable <A HREF="../../property_map/doc/LvaluePropertyMap.html">Lvalue
Property Map</A>. The key type of the map must be the graph's vertex
descriptor type.<BR><B>Default:</B> <TT>get(vertex_distance, g)</TT>
</BLOCKQUOTE>
<P>IN: <TT>vertex_index(VertexIndexMap index_map)</TT>
</P>
<BLOCKQUOTE>Maps each vertex of the graph to a unique integer in the
range <TT>[0, num_vertices(g))</TT>. The map must be a model of
constant <A HREF="../../property_map/doc/LvaluePropertyMap.html">LvaluePropertyMap</A>.
The key type of the map must be the graph's vertex descriptor
type.<BR><B>Default:</B> <TT>get(vertex_index, g)</TT>
</BLOCKQUOTE>
<H3>Example</H3>
<P>This reads an example maximum flow problem (a graph with edge
capacities) from a file in the DIMACS format (<TT><A HREF="../example/max_flow.dat">example/max_flow.dat</A></TT>).
The source for this example can be found in
<TT><A HREF="../example/boykov_kolmogorov-eg.cpp">example/boykov_kolmogorov-eg.cpp</A></TT>.
</P>
<PRE>#include &lt;boost/config.hpp&gt;
#include &lt;iostream&gt;
#include &lt;string&gt;
#include &lt;boost/graph/kolmogorov_max_flow.hpp&gt;
#include &lt;boost/graph/adjacency_list.hpp&gt;
#include &lt;boost/graph/read_dimacs.hpp&gt;
#include &lt;boost/graph/graph_utility.hpp&gt;
int
main()
{
using namespace boost;
typedef adjacency_list_traits &lt; vecS, vecS, directedS &gt; Traits;
typedef adjacency_list &lt; vecS, vecS, directedS,
property &lt; vertex_name_t, std::string,
property &lt; vertex_index_t, long,
property &lt; vertex_color_t, boost::default_color_type,
property &lt; vertex_distance_t, long,
property &lt; vertex_predecessor_t, Traits::edge_descriptor &gt; &gt; &gt; &gt; &gt;,
property &lt; edge_capacity_t, long,
property &lt; edge_residual_capacity_t, long,
property &lt; edge_reverse_t, Traits::edge_descriptor &gt; &gt; &gt; &gt; Graph;
Graph g;
property_map &lt; Graph, edge_capacity_t &gt;::type
capacity = get(edge_capacity, g);
property_map &lt; Graph, edge_residual_capacity_t &gt;::type
residual_capacity = get(edge_residual_capacity, g);
property_map &lt; Graph, edge_reverse_t &gt;::type rev = get(edge_reverse, g);
Traits::vertex_descriptor s, t;
read_dimacs_max_flow(g, capacity, rev, s, t);
std::vector&lt;default_color_type&gt; color(num_vertices(g));
std::vector&lt;long&gt; distance(num_vertices(g));
long flow = kolmogorov_max_flow(g ,s, t);
std::cout &lt;&lt; "c The total flow:" &lt;&lt; std::endl;
std::cout &lt;&lt; "s " &lt;&lt; flow &lt;&lt; std::endl &lt;&lt; std::endl;
std::cout &lt;&lt; "c flow values:" &lt;&lt; std::endl;
graph_traits &lt; Graph &gt;::vertex_iterator u_iter, u_end;
graph_traits &lt; Graph &gt;::out_edge_iterator ei, e_end;
for (tie(u_iter, u_end) = vertices(g); u_iter != u_end; ++u_iter)
for (tie(ei, e_end) = out_edges(*u_iter, g); ei != e_end; ++ei)
if (capacity[*ei] &gt; 0)
std::cout &lt;&lt; "f " &lt;&lt; *u_iter &lt;&lt; " " &lt;&lt; target(*ei, g) &lt;&lt; " "
&lt;&lt; (capacity[*ei] - residual_capacity[*ei]) &lt;&lt; std::endl;
return EXIT_SUCCESS;
}</PRE><P>
The output is:
</P>
<PRE>c The total flow:
s 13
c flow values:
f 0 6 3
f 0 1 0
f 0 2 10
f 1 5 1
f 1 0 0
f 1 3 0
f 2 4 4
f 2 3 6
f 2 0 0
f 3 7 5
f 3 2 0
f 3 1 1
f 4 5 4
f 4 6 0
f 5 4 0
f 5 7 5
f 6 7 3
f 6 4 0
f 7 6 0
f 7 5 0</PRE><H3>
See Also</H3>
<P STYLE="margin-bottom: 0cm"><TT><A HREF="edmonds_karp_max_flow.html">edmonds_karp_max_flow()</A></TT>,<BR><TT><A HREF="push_relabel_max_flow.html">push_relabel_max_flow()</A></TT>.
</P>
<HR>
<TABLE CELLPADDING=2 CELLSPACING=2>
<TR VALIGN=TOP>
<TD>
<P>Copyright &copy; 2006</P>
</TD>
<TD>
<P>Stephan Diederich, University
Mannheim(<A HREF="mailto:diederich@ti.uni-manheim.de">diederich@ti.uni-manheim.de</A>)</P>
</TD>
</TR>
</TABLE>
<P><BR><BR>
</P>
</BODY>
</HTML>

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@@ -201,11 +201,6 @@
<OL>
<LI><A href="edmonds_karp_max_flow.html"><tt>edmonds_karp_max_flow</tt></A>
<LI><A href="push_relabel_max_flow.html"><tt>push_relabel_max_flow</tt></A>
<li>
<a href="kolmogorov_max_flow.html"><tt>kolmogorov_max_flow</tt></a> (<em>Deprecated</em>.
Use <a href="boykov_kolmogorov_max_flow.html"><tt>boykov_kolmogorov_max_flow</tt></a>
instead.)
</li>
<li><a href="boykov_kolmogorov_max_flow.html"><tt>boykov_kolmogorov_max_flow</tt></a></li>
<LI><A href="maximum_matching.html"><tt>edmonds_maximum_cardinality_matching</tt></A>
</OL>

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include/boost/graph/detail/is_same.hpp
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@@ -1,48 +0,0 @@
//=======================================================================
// Copyright 1997, 1998, 1999, 2000 University of Notre Dame.
// Authors: Andrew Lumsdaine, Lie-Quan Lee, Jeremy G. Siek
//
// 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_GRAPH_DETAIL_IS_SAME_HPP
#define BOOST_GRAPH_DETAIL_IS_SAME_HPP
// Deprecate the use of this header.
// TODO: Remove this file from trunk/release in 1.41/1.42.
#if defined(_MSC_VER) || defined(__BORLANDC__) || defined(__DMC__)
# pragma message ("Warning: This header is deprecated. Please use: boost/type_traits/is_same.hpp")
#elif defined(__GNUC__) || defined(__HP_aCC) || defined(__SUNPRO_CC) || defined(__IBMCPP__)
# warning "This header is deprecated. Please use: boost/type_traits/is_same.hpp"
#endif
#include <boost/mpl/if.hpp>
namespace boost {
struct false_tag;
struct true_tag;
namespace graph_detail {
#if !defined BOOST_NO_TEMPLATE_PARTIAL_SPECIALIZATION
template <class U, class V>
struct is_same {
typedef boost::false_tag is_same_tag;
};
template <class U>
struct is_same<U, U> {
typedef boost::true_tag is_same_tag;
};
#else
template <class U, class V>
struct is_same {
enum { Unum = U::num, Vnum = V::num };
typedef typename mpl::if_c< (Unum == Vnum),
boost::true_tag, boost::false_tag>::type is_same_tag;
};
#endif
} // namespace graph_detail
} // namespace boost
#endif

4
include/boost/graph/graph_concepts.hpp
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@@ -342,7 +342,7 @@ typename T::ThereReallyIsNoMemberByThisNameInT vertices(T const&);
}
G g;
typename graph_traits<G>::vertex_descriptor v;
typename vertex_property<G>::type vp;
typename vertex_property_type<G>::type vp;
};
BOOST_concept(EdgeMutablePropertyGraph,(G))
@@ -356,7 +356,7 @@ typename T::ThereReallyIsNoMemberByThisNameInT vertices(T const&);
G g;
std::pair<edge_descriptor, bool> p;
typename graph_traits<G>::vertex_descriptor u, v;
typename edge_property<G>::type ep;
typename edge_property_type<G>::type ep;
};
BOOST_concept(AdjacencyMatrix,(G))

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include/boost/graph/graph_traits.hpp
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@@ -12,6 +12,7 @@
#include <boost/config.hpp>
#include <iterator>
#include <utility> /* Primarily for std::pair */
#include <boost/tuple/tuple.hpp>
#include <boost/mpl/if.hpp>
#include <boost/mpl/bool.hpp>

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include/boost/graph/kolmogorov_max_flow.hpp
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@@ -1,814 +0,0 @@
// 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
// HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY,
// WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING
// 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
#if defined(_MSC_VER) || defined(__BORLANDC__) || defined(__DMC__)
# pragma message ("The kolmogorov_max_flow.hpp header is deprecated and will be removed in Boost 1.47. Use boykov_kolmogorov_max_flow.hpp instead.")
#elif defined(__GNUC__) || defined(__HP_aCC) || defined(__SUNPRO_CC) || defined(__IBMCPP__)
# warning "The kolmogorov_max_flow.hpp header is deprecated and will be removed in Boost 1.47. Use boykov_kolmogorov_max_flow.hpp instead."
#endif
#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>
#include <boost/graph/lookup_edge.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(boost::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(boost::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;
boost::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(boost::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;
boost::tie(to_sink, is_there) = lookup_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(boost::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;
boost::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;
boost::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(boost::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(boost::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(boost::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(boost::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

1
test/astar_search_test.cpp
View File

@@ -15,6 +15,7 @@
#include <boost/graph/adjacency_list.hpp>
#include <boost/graph/random.hpp>
#include <boost/random.hpp>
#include <utility>
#include <vector>
#include <list>
#include <iostream>