From 751f8b5b7ce662f04b1cea4f4612cec7932286e1 Mon Sep 17 00:00:00 2001 From: Beman Dawes Date: Sun, 25 Nov 2007 18:38:02 +0000 Subject: [PATCH] Full merge from trunk at revision 41356 of entire boost-root tree. 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+9,47 @@ project boost/graph : source-location ../src ; -if [ modules.peek : GRAPHVIZ_PARSER ] +local optional_sources ; +local optional_reqs ; + +if [ modules.peek : EXPAT_INCLUDE ] && [ modules.peek : EXPAT_LIBPATH ] { - lib boost_graph - : - graphviz_graph_lex - graphviz_digraph_lex - graphviz_graph_parser - graphviz_digraph_parser - : YY_NO_UNISTD_H - ; + local EXPAT_INCLUDE = [ modules.peek : EXPAT_INCLUDE ] ; + local EXPAT_LIBPATH = [ modules.peek : EXPAT_LIBPATH ] ; - obj graphviz_graph_lex : graphviz_lex.ll - : bgl_undir_ GRAPHVIZ_DIRECTED=0 - graphviz_graph_parser ; - obj graphviz_graph_parser : graphviz_parser.yy - : bgl_undir_ GRAPHVIZ_DIRECTED=0 ; + if --debug-configuration in [ modules.peek : ARGV ] + { + ECHO "Expat include directory: $(EXPAT_INCLUDE)" ; + ECHO "Expat library directory: $(EXPAT_LIBPATH)" ; + } - - obj graphviz_digraph_lex : graphviz_lex.ll - : bgl_dir_ GRAPHVIZ_DIRECTED=1 - graphviz_digraph_parser ; - obj graphviz_digraph_parser : graphviz_parser.yy - : bgl_dir_ GRAPHVIZ_DIRECTED=1 ; + optional_sources += graphml.cpp ; + optional_reqs += $(EXPAT_INCLUDE) + $(EXPAT_LIBPATH) + expat + ; } else { - lib boost_graph - : - read_graphviz_spirit.cpp - : - BOOST_GRAPH_NO_LIB=1 - shared:BOOST_GRAPH_DYN_LINK=1 - # # Intel compiler ICEs if we turn optimization on - intel-vc71-win-9.1:off - # Without these flags, MSVC 7.1 and 8.0 crash - msvc-7.1:-GR- - msvc-8.0:-GR- - ; + ECHO "warning: Graph library does not contain optional GraphML reader." ; + ECHO "note: to enable GraphML support, set EXPAT_INCLUDE and EXPAT_LIBPATH to the" ; + ECHO "note: directories containing the Expat headers and libraries, respectively." ; } + +lib boost_graph + : + read_graphviz_spirit.cpp + $(optional_sources) + : + BOOST_GRAPH_NO_LIB=1 + shared:BOOST_GRAPH_DYN_LINK=1 + # # Intel compiler ICEs if we turn optimization on + intel-vc71-win-9.1:off + # Without these flags, MSVC 7.1 and 8.0 crash + msvc-7.1:-GR- + msvc-8.0:-GR- + # Requirements for any "optional" sources + $(optional_reqs) + ; + +boost-install boost_graph ; \ No newline at end of file diff --git a/doc/AddEdgeVisitor.html b/doc/AddEdgeVisitor.html new file mode 100644 index 00000000..f263ed92 --- /dev/null +++ b/doc/AddEdgeVisitor.html @@ -0,0 +1,130 @@ + + + +AddEdgeVisitor Concept + + + +C++ Boost + +
+ +

AddEdgeVisitor Concept

+ +The AddEdgeVisitor concept exists to allow for some indirection in algorithms +that modify graphs by adding edges. In such algorithms, it may be convenient +to perform additional operations (such as updating an edge index map) at +points in the algorithm where an edge addition occurs. Replacing calls to +to add_edge with calls to AddEdgeVisitor::visit_vertex_pair +allows for such operations to be defined independently from the algorithm. + +

Notation

+ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
Visitor is a type that models the AddEdgeVisitor concept
vis is an object of type Visitor
Graph is the type of a graph
u,v are objects of type graph_traits<Graph>::vertex_descriptor +
e is an object of type graph_traits<Graph>::edge_descriptor +
v is an object of type graph_traits<Graph>::vertex_descriptor +
+ +
+ + +

Associated Types

+ +None + +

Valid Expressions

+ +

+ + + + + + + + + + + + +
NameExpressionReturn TypeDescription
Add an Edge vis.visit_vertex_pair(u, v, g) void Invoked every time an edge between vertices u and v + should be added to the graph g. +
+ +

Models

+ +Two models of this concept are defined in the file + +add_edge_visitors.hpp: + +
    +
  • default_add_edge_visitor: The constructor of this class takes +no arguments.visit_vertex_pair(u, v, g) is just a dispatch to +add_edge(u, v, g). +
  • edge_index_update_visitor: The constructor of this class takes +two arguments: the first, an EdgeIndexMap, +is a +ReadWritePropertyMap that maps each edge in the associated graph +g to a distinct integer in the range [0, num_edges(g)). +The second argument is the number of edges in the underlying graph, which +serves as the "next available index" counter within the visitor. +For example, in the case the graph used has an initialized interior +edge index, the edge_index_update_visitor constructor should be +called with get(edge_index, g) as the edge index and +num_edges(g) as the next available index. When +visit_vertex_pair(u, v, g) is called, the +edge_index_update_visitor will add the edge (u,v) to the graph +and update the edge index for the newly created edge. +
+ +

+ +
+

+Copyright © 2007 Aaron Windsor ( +aaron.windsor@gmail.com) + + \ No newline at end of file diff --git a/doc/PlanarEmbedding.html b/doc/PlanarEmbedding.html new file mode 100644 index 00000000..7e3739f5 --- /dev/null +++ b/doc/PlanarEmbedding.html @@ -0,0 +1,178 @@ + +Planar Embedding Concept + + +C++ Boost + +
+ +

Planar Embedding Concept

+ + +A planar embedding is an important intermediate representation of a drawing +of a planar graph. Instead of specifying the absolute positions of the vertices +and edges in the plane, a planar embedding specifies their positions relative +to one another. A planar embedding consists of a sequence, for each vertex in +the graph, of all of the edges incident on that vertex in the order in which +they are to be drawn around that vertex. +

+A planar embedding is a refinement of +LValuePropertyMap that +places additional restrictions the value_type used in the property +map. + +

Notation

+ + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
Embedding is a type that models the Planar Embedding concept.
embedding is an object of type Embedding.
Graph is the type of the underlying graph.
e is an object of type graph_traits<Graph>::edge_descriptor. +
v is an object of type graph_traits<Graph>::vertex_descriptor +.
+ +
+ + +

Associated Types

+ + + + + + + + + +
Const Iterator boost::property_traits<Embedding>::value_type::const_iterator + + The iterator type used to iterate over the ordering of the edges in the +planar embedding of a particular vertex +
+ +

Valid Expressions

+ +

+ + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
ExpressionReturn TypeDescription
embedding[v].begin() boost::property_traits<Embedding>::value_type::const_iterator + Returns an iterator to the beginning of the range of edges in the + embedding around vertex v
embedding[v].end() boost::property_traits<Embedding>::value_type::const_iterator + Returns an iterator to the end of the range of edges in the + embedding around vertex v
embedding[v].clear() void Clears all edges in the embedding around a vertex v
embedding[v].push_back(e) void Adds an edge e to the end of the sequence of embedded edges + around the vertex v
+ +

Complexity Guarantees

+ +Starting with an empty embedding, any mixed sequence of n calls to a +particular vertex's push_back and clear should take +O(n) time. + +

Models

+ +Any LValue property map that maps vertices to a std::vector, +std::list, or std::deque models this +concept. Below is an example of using this approach to create a model of +PlanarEmbedding: + +
+#include <boost/property_map.hpp>
+#include <vector>
+
+...
+
+// Assume a graph type "Graph" defined somewhere above and
+// an instance of Graph in a variable g.
+
+// A typedef for the storage - a vector of vectors of edge descriptors
+typedef 
+    std::vector< std::vector< graph_traits<Graph>::edge_descriptor > >
+    planar_embedding_storage_t;
+
+// A typedef for the iterator property map, assuming the graph has
+// an interior vertex index map
+typedef
+    boost::iterator_property_map< planar_embedding_storage_t::iterator,
+                                  property_map<Graph, vertex_index_t>::type
+                                >
+    planar_embedding_t;
+
+// Create an instance of the storage and the property map
+planar_embedding_storage_t planar_embedding_storage(num_vertices(g));
+planar_embedding_t planar_embedding(planar_embedding_storage.begin(),
+                                    get(vertex_index, g)
+                                    );
+
+// planar_embedding can now be passed to any function expecting a model
+// of PlanarEmbedding.
+
+ +

+ +
+

+Copyright © 2007 Aaron Windsor ( +aaron.windsor@gmail.com) + + \ No newline at end of file diff --git a/doc/PlanarFaceVisitor.html b/doc/PlanarFaceVisitor.html new file mode 100644 index 00000000..3fa3ab59 --- /dev/null +++ b/doc/PlanarFaceVisitor.html @@ -0,0 +1,148 @@ + + + +Planar Face Visitor Concept + + +C++ Boost + +
+ +

Planar Face Visitor Concept

+ +This concept defines the visitor interface for +planar_face_traversal. +Users can define a class with the Planar Face Visitor interface and pass an +object of the class to planar_face_traversal, thereby augmenting the +actions taken during the traversal. Note that objects passed to +planar_face_traversal are passed by reference. + +

Notation

+ + + + + + + + + + + + + + + + + + + + + + + + + + + +
VA type that is a model of Planar Face Visitor.
visAn object of type V.
GA type that is a model of Graph.
eAn object of type boost::graph_traits<G>::edge_descriptor. +
vAn object of type boost::graph_traits<G>::vertex_descriptor. +
+ + +

Valid Expressions

+ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
NameExpressionReturn TypeDescription
Begin Traversalvis.begin_traversal()void +This is invoked once per traversal, before the traversal begins. +
Begin Facevis.begin_face()void +This is invoked once for each face, before any vertices or edges on the face +are visited. +
Next Vertexvis.next_vertex(v)void +This is invoked when a vertex is encountered while traversing a face. +
Next Edgevis.next_edge(e)void +This is invoked when an edge is encountered while traversing a face. +
End Facevis.end_face()void +This is invoked once for each face, after all vertices and edges on the face +are visited. +
End Traversalvis.end_traversal()void +This is invoked once per traversal, after the traversal ends. +
+ +

Models

+ +
    +
  • The file +planar_face_traversal.hpp contains a class +planar_face_traversal_visitor that implements empty actions for +all event points of a Planar Face Visitor. In the case where only a few of the +event points of Planar Face Visitor need to be implemented, one can derive from +planar_face_traversal_visitor and only implement the necessary event +points.
  • The implementation of +make_maximal_planar uses a triangulation_visitor that is +a model of Planar Face Visitor. +
    • +
+ +
+
+Copyright © 2007 Aaron Windsor ( +aaron.windsor@gmail.com) + + diff --git a/doc/adjacency_list.html b/doc/adjacency_list.html index 48404d43..f4e04811 100644 --- a/doc/adjacency_list.html +++ b/doc/adjacency_list.html @@ -354,7 +354,7 @@ align=center>OKOK
and
-adjacency_list_traits<OutEdgeList, VertexList, Directed>::vertex_descriptor +adjacency_list_traits<OutEdgeList, VertexList, Directed, EdgeList>::vertex_descriptor

The type for the vertex descriptors associated with the adjacency_list. @@ -363,7 +363,7 @@ The type for the vertex descriptors associated with the graph_traits<adjacency_list>::edge_descriptor
and
-adjacency_list_traits<OutEdgeList, VertexList, Directed>::edge_descriptor +adjacency_list_traits<OutEdgeList, VertexList, Directed, EdgeList>::edge_descriptor

The type for the edge descriptors associated with the adjacency_list. @@ -424,7 +424,7 @@ as out_edge_iterator. graph_traits<adjacency_list>::directed_category
and
-adjacency_list_traits<OutEdgeList, VertexList, Directed>::directed_category +adjacency_list_traits<OutEdgeList, VertexList, Directed, EdgeList>::directed_category

Provides information about whether the graph is directed (directed_tag) or undirected @@ -434,7 +434,7 @@ directed (directed_tag) or undirected graph_traits<adjacency_list>::edge_parallel_category
and
-adjacency_list_traits<OutEdgeList, VertexList, Directed>::edge_parallel_category +adjacency_list_traits<OutEdgeList, VertexList, Directed, EdgeList>::edge_parallel_category

This describes whether the graph class allows the insertion of parallel edges (edges with the same source and target). The two tags @@ -445,13 +445,17 @@ parallel edges while the others allow parallel edges.
-graph_traits<adjacency_list>::vertices_size_type +graph_traits<adjacency_list>::vertices_size_type
+and
+adjacency_list_traits<OutEdgeList, VertexList, Directed_list, EdgeList>::vertices_size_type


The type used for dealing with the number of vertices in the graph.
-graph_traits<adjacency_list>::edge_size_type +graph_traits<adjacency_list>::edge_size_type
+and
+adjacency_list_traits<OutEdgeList, VertexList, Directed_list, EdgeList>::edge_size_type


The type used for dealing with the number of edges in the graph. diff --git a/doc/astar_search.html b/doc/astar_search.html index eec058c3..eaf1e630 100644 --- a/doc/astar_search.html +++ b/doc/astar_search.html @@ -439,7 +439,7 @@ The time complexity is O((E + V) log V). is invoked on edge (u,v) if d[u] + w(u,v) < d[v].
  • vis.edge_not_relaxed(e, g) is invoked if the edge is not relaxed (see above). -
  • vis.black_target(u, g) +
  • vis.black_target(e, g) is invoked when a vertex that is on the CLOSED list is "rediscovered" via a more efficient path, and is re-added to the OPEN list. diff --git a/doc/bibliography.html b/doc/bibliography.html index 938ad768..da96b674 100644 --- a/doc/bibliography.html +++ b/doc/bibliography.html @@ -401,6 +401,37 @@ Morgan Kaufmann Publishers, San Fransisco, 1997. Modern Compiler Implementation in JAVA
    Cambridge University Press, 1998. +

    68 +
    Vladimir Kolmogorov
    +Graph Based Algorithms for Scene Reconstruction from Two or More Views
    +PhD thesis, Cornell University, September 2003. + +

    69 +
    Yuri Boykov and Vladimir Kolmogorov
    + An Experimental Comparison of Min-Cut/Max-Flow Algorithms for Energy Minimization in Vision
    + In IEEE Transactions on Pattern Analysis and Machine Intelligence, vol. 26, no. 9, pp. 1124-1137, Sept. 2004. + +

    70 +
    John M. Boyer and Wendy J. Myrvold
    + +On the Cutting Edge: Simplified O(n) Planarity by Edge Addition +
    +Journal of Graph Algorithms and Applications, 8(2): 241-273, 2004. + +

    71 +
    M. Chrobak, T. Payne
    + +A Linear-time Algorithm for Drawing a Planar Graph on the Grid +
    +Information Processing Letters 54: 241-246, 1995. + +

    72 +
    H. de Fraysseix, J. Pach, R. Pollack
    + +How to Draw a Planar Graph on a Grid +
    +Combinatorica 10: 41-51, 1990. +
    diff --git a/doc/boyer_myrvold.html b/doc/boyer_myrvold.html new file mode 100644 index 00000000..69569e98 --- /dev/null +++ b/doc/boyer_myrvold.html @@ -0,0 +1,259 @@ + + + +Boost Graph Library: Boyer-Myrvold Planarity Testing/Embedding + +C++ Boost + +
    + +

    Boyer-Myrvold Planarity Testing/Embedding

    + +

    +A graph is planar if it can +be drawn in two-dimensional space without any of its edges crossing. Such a +drawing of a planar graph is called a +plane drawing. Each +plane drawing belongs to an equivalence class called a planar embedding +[1] that is defined by the clockwise ordering of adjacent +edges around each vertex in the graph. A planar embedding is a convenient +intermediate representation of an actual drawing of a planar graph, and many +planar graph drawing algorithms are formulated as functions mapping a planar +embedding to a plane drawing. +
    +
    + + + + + +
    A planar graph (top left), along with a planar +embedding of that graph (bottom left) can be used to create a plane drawing +(right) by embedding edges around each vertex in the order in which they +appear in the planar embedding. +
    + +
    +
    +

    +The function boyer_myrvold_planarity_test implements the planarity +testing/embedding algorithm of Boyer and Myrvold +[70]. +boyer_myrvold_planarity_test returns true if the input graph +is planar and false otherwise. As a side-effect of this test, a planar +embedding can be constructed if the graph is planar or a minimal set of edges +that form a Kuratowski +subgraph can be found if the graph is not planar. +boyer_myrvold_planarity_test uses named parameter arguments (courtesy +of the Boost.Parameter +library) to specify what the function actually does. Some examples are: + +

      +
    • Testing whether or not a graph is planar: +
      +bool is_planar = boyer_myrvold_planarity_test(g);
+
      + +
    • Computing a planar embedding for a graph if it is planar, otherwise finding +a set of edges that forms an obstructing Kuratowski subgraph: +
      +if (boyer_myrvold_planarity_test(boyer_myrvold_params::graph = g, 
+                                 boyer_myrvold_params::embedding = embedding_pmap,  
+                                 boyer_myrvold_params::kuratowski_subgraph = out_itr
+                                 )
+    )
+{
+  //do something with the embedding in embedding_pmap
+}
+else
+{
+  //do something with the kuratowski subgraph output to out_itr
+}
+
      +
    + +

    +The parameters passed to boyer_myrvold_planarity_test in the examples +above do more than just carry the data structures used for input and output - +the algorithm is optimized at compile time based on which parameters are +present. A complete list of parameters accepted and their interactions are +described below. +

    +boyer_myrvold_planarity_test accepts as input any undirected graph, +even those with self-loops and multiple edges. +However, many planar graph drawing algorithms make additional restrictions +on the structure of the input graph - for example, requiring that the input +graph is connected, biconnected, or even maximal planar (triangulated.) +Fortunately, any planar graph on n vertices that lacks one of these +properties can be augmented with additional edges so that it satisfies that +property in O(n) time - the functions +make_connected, +make_biconnected_planar, +and make_maximal_planar +exist for this purpose. If the graph drawing algorithm you're using requires, +say, a biconnected graph, then you must make your input graph biconnected +before passing it into boyer_myrvold_planarity_test so that the +computed planar embedding includes these additional edges. This may require +more than one call to boyer_myrvold_planarity_test depending on the +structure of the graph you begin with, since both +make_biconnected_planar and make_maximal_planar require a +planar embedding of the existing graph as an input parameter. + +

    +The named parameters accepted by boyer_myrvold_planarity_test are: + +

      +
    • graph : The input graph - this is the only required +parameter. +
    • vertex_index_map : A mapping from vertices of the input +graph to indexes in the range [0..num_vertices(g)). If this parameter +is not provided, the vertex index map is assumed to be available as an interior +property of the graph, accessible by calling get(vertex_index, g). +
    • edge_index_map: A mapping from the edges of the input graph +to indexes in the range [0..num_edges(g)). This parameter is only +needed if the kuratowski_subgraph argument is provided. If the +kuratowski_subgraph argument is provided and this parameter is not +provided, the EdgeIndexMap is assumed to be available as an interior property +accessible by calling get(edge_index, g). +
    • embedding : If the graph is planar, this will be populated +with a mapping from vertices to the clockwise order of neighbors in the planar +embedding. +
    • kuratowski_subgraph : If the graph is not planar, a minimal +set of edges that form the obstructing Kuratowski subgraph will be written to +this iterator. +
    + +These named parameters all belong to the namespace +boyer_myrvold_params. See below for more information on the concepts +required for these arguments. + +

    Verifying the output

    + +Whether or not the input graph is planar, boyer_myrvold_planarity_test +can produce a certificate that can be automatically checked to verify that the +function is working properly. +

    +If the graph is planar, a planar embedding can be produced. The +planar embedding can be verified by passing it to a plane drawing routine +(such as +chrobak_payne_straight_line_drawing) and using the function +is_straight_line_drawing +to verify that the resulting graph is planar. +

    +If the graph is not planar, a set of edges that forms a Kuratowski subgraph in +the original graph can be produced. This set of edges can be passed to the +function is_kuratowski_subgraph + to verify that they can be contracted into a K5 or +K3,3. boyer_myrvold_planarity_test chooses the set +of edges forming the Kuratowski subgraph in such a way that the contraction to +a K5 or K3,3 can be done by a simple +deterministic process which is described in the documentation to +is_kuratowski_subgraph. + +

    Where Defined

    + +

    + +boost/graph/boyer_myrvold_planar_test.hpp + + +

    Parameters

    + +IN: Graph& g + +
    +Any undirected graph. The graph type must be a model of +VertexAndEdgeListGraph and +IncidenceGraph. +
    + +OUT PlanarEmbedding embedding + +
    +Must model the PlanarEmbedding concept. +
    + +IN OutputIterator kuratowski_subgraph + +
    +An OutputIterator which accepts values of the type +graph_traits<Graph>::edge_descriptor +
    + +IN VertexIndexMap vm + +
    +A Readable Property Map + that maps vertices from g to distinct integers in the range +[0, num_vertices(g) )
    +Default: get(vertex_index,g)
    +
    + +IN EdgeIndexMap em + +
    +A Readable Property Map + that maps edges from g to distinct integers in the range +[0, num_edges(g) )
    +Default: get(edge_index,g), but this parameter is only used if +the kuratowski_subgraph_iterator is provided.
    +
    + +

    Complexity

    + +Assuming that both the vertex index and edge index supplied take time +O(1) to return an index and there are O(n) +total self-loops and parallel edges in the graph, most combinations of +arguments given to +boyer_myrvold_planarity_test result in an algorithm that runs in time +O(n) for a graph with n vertices and m edges. The only +exception is when Kuratowski subgraph isolation is requested for a dense graph +(a graph with n = o(m)) - the running time will be O(n+m) +[2]. + +

    Examples

    + +

    +

    + +

    See Also

    + +Planar Graphs in the Boost Graph Library + + +

    Notes

    + +

    [1] A planar embedding is also called a combinatorial +embedding. + +

    [2] The algorithm can still be made to run in time O(n) +for this case, if needed. Euler's +formula implies that a planar graph with n vertices can have no more +than 3n - 6 edges, which means that any non-planar graph on n +vertices has a subgraph of only 3n - 5 edges that contains a Kuratowski +subgraph. So, if you need to find a Kuratowski subgraph of a graph with more +than 3n - 5 edges in time O(n), you can create a subgraph of the +original graph consisting of any arbitrary 3n - 5 edges and pass that +graph to boyer_myrvold_planarity_test. + + +
    +

    +Copyright © 2007 Aaron Windsor ( +aaron.windsor@gmail.com) + + diff --git a/doc/cochet-terrasson98numerical.pdf b/doc/cochet-terrasson98numerical.pdf new file mode 100755 index 0000000000000000000000000000000000000000..c0ec550ab4d38200e39057c4aba2688d9bf2bb65 GIT binary patch literal 207767 zcmY!laBfY*C*c`KvwhJ$;TV$Vh`lNRGgX1}qeBQ~# zUeNFG6gfI?zF$y$m7~qh&3g(0V|IPE>k&Sva=7ub0hg_$&$3JN@63$fQ6XI4w?}7k zq}j#(Po;s6gC|x*I`Pkb`*72poG#0MO3C^>XZUAx%}<&4!FAfD&6Ayc1u8oIALqq{ z_t)riDSyuR-&G}2ndy+fN`0fa$Bc6}tHRt}W7ni*d1*fUJEPt(*lYg1{eO4d6!ET+ zSyG@8^~Y>((1$v+uVveAUaJbb&#n4*!un@v(ScHLZ(UoqPAp5+BF#nGV#klPeYZr; z&YNZarDopus(SuXzT-j4%n!tMzs-I7XyYx%SFMJ;zRM4VGdo%|9kCIKoF*6Z>BCPG z4(EhQo5uYWk!$MeHd~q2@XXw)6!Nyy1zE0Y<@@q&T8#`yk%C*ptS-V=g-ezJ^klm$=(~Q%7YlWgoUL)A1y45c>b*6Ba4ZEzk0*9!iLX>Zmmq) zAvxL4NdMFWdl`ww7Yy-dQm%V2yj@&d!?LDSZtu-Vo{+^$Bkr0ugnTfU`V>}wNLz(D z(#`98RQ;6$&)$`k301Cn6#Pf?i&FYIYvSgx3Fyi~$s0DU^lrR;I7dA5(qx`l zIv<$?emrdh(8vpNQ>IpkGd)%1L 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b/doc/edmunds_karp_max_flow.html index 4478c4e4..0bf59675 100644 --- a/doc/edmunds_karp_max_flow.html +++ b/doc/edmunds_karp_max_flow.html @@ -75,6 +75,8 @@ This algorithm provides a very simple and easy to implement solution to the maximum flow problem. However, there are several reasons why this algorithm is not as good as the push_relabel_max_flow() +or the kolmogorov_max_flow() algorithm.