diff --git a/doc/figs/planar_vertex_coloring_with_5.png b/doc/figs/planar_vertex_coloring_with_5.png new file mode 100644 index 000000000..729083cf1 Binary files /dev/null and b/doc/figs/planar_vertex_coloring_with_5.png differ diff --git a/doc/planar_vertex_six_coloring.html b/doc/planar_vertex_six_coloring.html new file mode 100644 index 000000000..15465b1ef --- /dev/null +++ b/doc/planar_vertex_six_coloring.html @@ -0,0 +1,101 @@ + + + + + Boost Graph Library: Planar Vertex Six Coloring + + + + C++ Boost +

planar_vertex_six_coloring

+ +

+ 

+template<class VertexListGraph, class ColorMap>
+typename property_traits<ColorMap>::value_type
+planar_vertex_six_coloring(const VertexListGraph& g, ColorMap color);
+
+ +

Computes a vertex coloring for +the vertices in the planar graph in linear time, using at most 6 colors.
+Planar graphs can always be vertex colored with 4 colors, there +is a quadratic time algorithm.
+Boost sequential_vertex_coloring can be forced to use any number k of colors for a crafted planar graph (first test graph). + +

Here is the vertex coloring with 5 colors determined for icosahedron. + +

+ +

Planar graphs with n vertices have at most 3n-6 edges. Therefore always a vertex of degree ≤5 exists. Algorithm removes such "small" vertices until the graph becomes empty. Then the vertices are colored in reverse order they were removed, with the smallest color different to its at most 5 neighbors when it was removed. Therefore at most 6 colors are needed. + +

Where Defined

+boost/graph/planar_vertex_six_coloring.hpp + +

Parameters

+IN: const Graph& g +
+ The graph object on which the algorithm will be applied. The type + Graph must be a model of Vertex List Graph and Adjacency Graph.
+
+ +OUT: ColorMap color +
+ This property map records the colors of each vertex. It must be a + model of + Writeable + Property Map whose key type is the same as the vertex descriptor + type of the graph and whose value type is an integral type that can + store all values of the graph's vertices_size_type.
+
+ +

Complexity

+ +The time complexity is O(V), where V is the +number of vertices of the planar graph.
+This runtime is only possible using undirected_graph_constant_time_edge_add_and_remove providing O(1) remove_edge(). + +

Example

+boost/graph/example/planar_vertex_six_coloring.cpp + +
+  template< class graph >  void simple_maximal_planar_random_graph(graph& g, int n);  // see example
+  typedef adjacency_list< listS, vecS, undirectedS > Graph;
+  typedef graph_traits< Graph >::vertices_size_type vertices_size_type;
+
+  Graph g;
+  simple_maximal_planar_random_graph(g, 1000000);
+
+  std::vector< vertices_size_type > color_vec(num_vertices(g));
+  auto color = make_container_vertex_map(color_vec, g);
+  vertices_size_type num_colors = planar_vertex_six_coloring(g, color);
+
+ +

Test

+boost/graph/test/planar_vertex_six_coloring.cpp test determines vertex coloring for three planar graphs: +
    +
  1. "Fibonacci graph" (for k=15), with fib(k+1) vertices and fib(k+2)-2 edges +
  2. boost/graph/test/planar_input_graphs/pentakis_dodecahedron.leda +
  3. boost/graph/test/planar_input_graphs/maximal_planar_1000.leda +
+With 15/5/6 colors used by sequential_vertex_coloring() and 6/4/6 colors used by planar_vertex_six_coloring(). + +
+ + + +
Copyright © 2024 +Hermann Stamm-Wilbrandt (hermann@stamm-wilbrandt.de) +
+ + + diff --git a/doc/table_of_contents.html b/doc/table_of_contents.html index 5eb527ac1..8fe5d98e2 100644 --- a/doc/table_of_contents.html +++ b/doc/table_of_contents.html @@ -104,6 +104,9 @@

Table of Contents: the Boost Graph Library
  1. directed_graph
  2. undirected_graph
    3. +
      +
    1. undirected_graph_constant_time_edge_add_and_remove
      2. +
  • adjacency_matrix
  • compressed_sparse_row_graph
    • @@ -286,6 +289,8 @@

    Table of Contents: the Boost Graph Library make_biconnected_planar
  • make_maximal_planar +
  • + planar_vertex_six_coloring
  • Miscellaneous Algorithms diff --git a/doc/undirected_graph_constant_time_edge_add_and_remove.html b/doc/undirected_graph_constant_time_edge_add_and_remove.html new file mode 100644 index 000000000..332651f95 --- /dev/null +++ b/doc/undirected_graph_constant_time_edge_add_and_remove.html @@ -0,0 +1,91 @@ + + + +Boost Graph Library: Undirected Graph with constant time edge add and remove + +C++ Boost + +
    + +

    +
    +undirected_graph_constant_time_edge_add_and_remove<VertexProp, EdgeProp, GraphProp>
+
    +

    + + +

    +The undirected_graph_constant_time_edge_add_and_remove class template is derived from BGL undirected graph. This class is provided only for constant time edge remove, in case that is not needed use undirected graph instead. + +

    Example

    + +An example of using an undirected_graph_constant_time_edge_add_and_remove is available here libs/graph/example/undirected_graph_constant_time_edge_add and_remove.cpp. It demonstrates that undirected_graph takes quadratic time while undirected_graph_constant_time_edge_and_remove takes only linear time for clearing all outer vertices of wheel graph Wn. +

    + + +

    +  typedef boost::undirected_graph_constant_time_edge_add_and_remove<
+    boost::no_property, boost::no_property, boost::no_property > Graph;
+  Graph g;
+  typedef typename Graph::vertex_descriptor vertex_descriptor;
+  typedef typename Graph::edge_descriptor edge_descriptor;
+
+  vertex_descriptor v0 = g.add_vertex();
+  vertex_descriptor v1 = g.add_vertex();
+  edge_descriptor e = g.add_edge(v0, v1).first;
+  g.remove_edge(e);
+
    + +

    Template Parameters

    + +

    + + + + + + + + + + + + + + + + + + + + + +
    ParameterDescriptionDefault
    VertexPropA property map for the graph vertices. 
    EdgePropA property map for the graph edges. 
    GraphPropA property map for the graph itself.
    +

    + +

    Where Defined

    + +

    +boost/graph/undirected_graph_constant_time_edge_add_and_remove.hpp + +

    + +
    +

    + + +
    Copyright © 2024 +Hermann Stamm-Wilbrandt (hermann@stamm-wilbrandt.de) +
    + + + diff --git a/example/planar_vertex_six_coloring.cpp b/example/planar_vertex_six_coloring.cpp new file mode 100644 index 000000000..3f7deb514 --- /dev/null +++ b/example/planar_vertex_six_coloring.cpp @@ -0,0 +1,90 @@ +//======================================================================= +// Copyright 2024 +// Author: Hermann Stamm-Wilbrandt +// +// 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) +//======================================================================= +#include +#include +#include + +using namespace boost; + +// => ../test/planar_vertex_six_coloring.cpp for application to other planar graphs +// +template< class graph > void simple_maximal_planar_random_graph(graph& g, int n); + + +// time measurements +clock_t start_; +#define _(blk) std::cerr << #blk << " "; start_ = clock(); blk \ + std::cerr << (clock()-start_)*1.0/CLOCKS_PER_SEC << "s" << std::endl; + + +int main(int argc, char *argv[]) { + typedef adjacency_list< listS, vecS, undirectedS > Graph; + typedef graph_traits< Graph >::vertices_size_type vertices_size_type; + Graph g; + + _(simple_maximal_planar_random_graph(g, argc < 2 ? 333335 : atoi(argv[1]));) + + std::vector< vertices_size_type > color_vec(num_vertices(g)); + auto color = make_container_vertex_map(color_vec, g); + + std::cout << num_vertices(g) << " vertices" << std::endl; + std::cout << num_edges(g) << " egdes" << std::endl; + + _(vertices_size_type num_colors = planar_vertex_six_coloring(g, color);) + std::cout << num_colors << " colors" << std::endl; + + BGL_FORALL_EDGES(e, g, Graph) + { BOOST_ASSERT(get(color, source(e, g)) != get(color, target(e, g))); } + + std::cout << "vertex coloring verified" << std::endl; + + return 0; +} + + +/* +https://www.researchgate.net/publication/360912158_A_simple_linear_time_algorithm_for_embedding_maximal_planar_graphs_1 + +"simple_maximal_planar_random_graph()" implements only type==3 of chapter 8. +With type==4 and type==5 added it would be full blown "maximal_planar_random_graph()". + + + triangular face T[t] transformation, t chosen randomly: + + T[t][0] T[t][0] + +--#--+ +--#--+ + | | | | | + | | | | | + | | ==> | i | + | | | / \ | + | | |/ \| + #-----# #-----# + T[t][1] T[t][2] T[t][1] T[t][2] +*/ +template< class graph > void simple_maximal_planar_random_graph(graph& g, int n) +{ + BOOST_ASSERT(n > 2); + g.clear(); + std::vector< typename graph::vertex_descriptor> V; V.reserve(n); + V[0] = add_vertex(g); V[1] = add_vertex(g); V[2] = add_vertex(g); + add_edge(V[0], V[1], g); add_edge(V[0], V[2], g); add_edge(V[1], V[2], g); + std::vector> T; + // start with inside and outside face of complete graph on 3 vertices + T.reserve(2*n-4); T.push_back({0, 1, 2}); T.push_back({0, 1, 2}); + for (int i=3; i < n; ++i) + { + unsigned t = random() % T.size(); + V[i] = add_vertex(g); + unsigned v; + BOOST_FOREACH(v, T[t]) { add_edge(V[v], V[i], g); } + T.push_back(T[t]); T.back()[0] = i; + T.push_back(T[t]); T.back()[1] = i; + T[t][2] = i; + } +} diff --git a/example/undirected_graph_constant_time_edge_add_and_remove.cpp b/example/undirected_graph_constant_time_edge_add_and_remove.cpp new file mode 100644 index 000000000..1b93fb02f --- /dev/null +++ b/example/undirected_graph_constant_time_edge_add_and_remove.cpp @@ -0,0 +1,103 @@ +//======================================================================= +// Copyright 2024 +// Author: Hermann Stamm-Wilbrandt +// +// 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) +//======================================================================= +#include +#include +#include +#include +#include + +typedef boost::undirected_graph_constant_time_edge_add_and_remove< + boost::no_property, boost::no_property, boost::no_property > ugraph_o1; + +typedef boost::undirected_graph< + boost::no_property, boost::no_property, boost::no_property > ugraph; + + +/* + Wheel graphs W5 4 W7 6---1 + /|\ / \ / \ + / | \ 5---0---2 + 3--0--1 \ / \ / + \ | / 4---3 + \|/ + 2 +*/ +template< class Graph > void wheel(Graph& g, int n); + + +/* + Demo function removing the edges for all but central vertex of + wheel graph Wn, showing roughly linear time for ugraph_01 + [because of O(1) remove_edge()] and quadratic time for ugraph. + + Very simplified version of what planar_vertex_six_coloring() does. + Proof that boost::undirected_graph_constant_time_edge_add_and_remove + class is essential for linear runtime of that vertex coloring algorithm. +*/ +template< class Graph > float clear_vertices(Graph& g, int n) +{ + wheel(g, n); + + std::vector< typename Graph::vertex_descriptor > vec; + vec.reserve(num_vertices(g)); + + BGL_FORALL_VERTICES_T(v, g, Graph) { vec.push_back(v); } + + clock_t start = clock(); + + typename Graph::vertex_descriptor u; + BOOST_REVERSE_FOREACH(u, vec) { g.clear_vertex(u); } + + return (clock()-start)*1.0/CLOCKS_PER_SEC; +} + + +int main(int argc, char*argv[]) { + int n = argc < 2 ? 2000 : atoi(argv[1]); + ugraph_o1 UO1; + ugraph U; + + std::cout << "Wn ugraph_o1 ugraph runtimes [s]" << std::endl; + + for (int i=0; i <= 4; ++i, n*=2) + { + std::cout << n << " " + << clear_vertices(UO1, n) << " " + << clear_vertices(U, n) << std::endl; + } + + return 0; +} + + +template< class Graph > +void wheel(Graph& g, int n) +{ + typedef typename Graph::vertex_descriptor vertex_descriptor; + + BOOST_ASSERT(n > 3); + + g = Graph(); + + vertex_descriptor v = add_vertex(g); + vertex_descriptor w = add_vertex(g); + g.add_edge(v, w); + + vertex_descriptor x = w; + + for (int i=3; i <= n; ++i) + { + vertex_descriptor y = add_vertex(g); + g.add_edge(v, y); + g.add_edge(x, y); + x = y; + } + + g.add_edge(x, w); +} diff --git a/include/boost/graph/detail/adjacency_list.hpp b/include/boost/graph/detail/adjacency_list.hpp index ed5a1d483..f80ed8fba 100644 --- a/include/boost/graph/detail/adjacency_list.hpp +++ b/include/boost/graph/detail/adjacency_list.hpp @@ -797,6 +797,32 @@ namespace detail } g.m_edges.erase(edge_iter_to_erase); } + + // O(1) + template < class OutEdgeList_iterator, class Config > + static void apply(OutEdgeList_iterator iter1, + OutEdgeList_iterator iter2, + undirected_graph_helper< Config >& g_, StoredProperty&) + { + typedef typename Config::global_edgelist_selector EdgeListS; + BOOST_STATIC_ASSERT((is_same< EdgeListS, listS >::value)); + + typedef typename Config::graph_type graph_type; + graph_type& g = static_cast< graph_type& >(g_); + typename Config::edge_descriptor e = *iter1; + typename Config::edge_descriptor f = *iter2; + BOOST_ASSERT(source(e, g) == target(f, g)); + BOOST_ASSERT(source(f, g) == target(e, g)); + + typename Config::OutEdgeList& out_el + = g.out_edge_list(source(e, g)); + typename Config::EdgeIter edge_iter_to_erase; + edge_iter_to_erase = (*iter1.base()).get_iter(); + out_el.erase(iter1.base()); + typename Config::OutEdgeList& in_el = g.out_edge_list(target(e, g)); + in_el.erase(iter2.base()); + g.m_edges.erase(edge_iter_to_erase); + } }; template <> struct remove_undirected_edge_dispatch< no_property > @@ -833,6 +859,32 @@ namespace detail } g.m_edges.erase(edge_iter_to_erase); } + + // O(1) + template < class OutEdgeList_iterator, class Config > + static void apply(OutEdgeList_iterator iter1, + OutEdgeList_iterator iter2, + undirected_graph_helper< Config >& g_, no_property&) + { + typedef typename Config::global_edgelist_selector EdgeListS; + BOOST_STATIC_ASSERT((is_same< EdgeListS, listS >::value)); + + typedef typename Config::graph_type graph_type; + graph_type& g = static_cast< graph_type& >(g_); + typename Config::edge_descriptor e = *iter1; + typename Config::edge_descriptor f = *iter2; + BOOST_ASSERT(source(e, g) == target(f, g)); + BOOST_ASSERT(source(f, g) == target(e, g)); + + typename Config::OutEdgeList& out_el + = g.out_edge_list(source(e, g)); + typename Config::EdgeIter edge_iter_to_erase; + edge_iter_to_erase = (*iter1.base()).get_iter(); + out_el.erase(iter1.base()); + typename Config::OutEdgeList& in_el = g.out_edge_list(target(e, g)); + in_el.erase(iter2.base()); + g.m_edges.erase(edge_iter_to_erase); + } }; // O(E/V) @@ -924,6 +976,17 @@ template < class Config > struct undirected_graph_helper { this->remove_edge(*iter); } + // O(1) + inline void remove_edge(typename Config::out_edge_iterator iter1, + typename Config::out_edge_iterator iter2) + { + typedef typename Config::global_edgelist_selector EdgeListS; + BOOST_STATIC_ASSERT((!is_same< EdgeListS, vecS >::value)); + + typedef typename Config::OutEdgeList::value_type::property_type PType; + detail::remove_undirected_edge_dispatch< PType >::apply( + iter1, iter2, *this, *(PType*)((*iter1).get_property())); + } }; // Had to make these non-members to avoid accidental instantiation @@ -953,6 +1016,17 @@ inline void remove_edge(EdgeOrIter e, undirected_graph_helper< Config >& g_) g_.remove_edge(e); } +// O(1) +template < class OutEdgeIter, class Config > +inline void remove_edge_(OutEdgeIter i1, OutEdgeIter i2, + undirected_graph_helper< Config >& g_) +{ + typedef typename Config::global_edgelist_selector EdgeListS; + BOOST_STATIC_ASSERT((is_same< EdgeListS, listS >::value)); + + g_.remove_edge(i1, i2); +} + // O(E/V) or O(log(E/V)) template < class Config > void remove_edge(typename Config::vertex_descriptor u, diff --git a/include/boost/graph/planar_vertex_six_coloring.hpp b/include/boost/graph/planar_vertex_six_coloring.hpp new file mode 100644 index 000000000..17a374306 --- /dev/null +++ b/include/boost/graph/planar_vertex_six_coloring.hpp @@ -0,0 +1,120 @@ +//======================================================================= +// Copyright 2024 +// Author: Hermann Stamm-Wilbrandt +// +// 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_PLANAR_VERTEX_SIX_COLORING_HPP +#define BOOST_GRAPH_PLANAR_VERTEX_SIX_COLORING_HPP + +#include +#include +#include +#include +#include +#include + +/* This algorithm is to find a vertex six coloring of a planar graph + + Algorithm: + Let G = (V,E) be a planar graph with n vertices. + Planar graphs always have a vertex of degree 5 or less. + Remember its (at most 5) adjacent vertices and remove its edges. + Repeat until all vertices have been processed. + Now color the vertices in reverse order they were removed. + Assign smallest color different to all <=5 remembered vertices to vertex. + Repeat until done. + + The color of the vertex v will be stored in color[v]. + i.e., vertex v belongs to coloring color[v] */ + +namespace boost +{ + enum vertex_back_t { vertex_back }; + BOOST_INSTALL_PROPERTY(vertex, back); + +template < class VertexListGraph, class ColorMap > +typename property_traits< ColorMap >::value_type planar_vertex_six_coloring( + const VertexListGraph& G, ColorMap color) +{ + typedef typename VertexListGraph::vertex_descriptor vertex_descriptor; + + typedef typename property_traits< ColorMap >::value_type size_type; + + typedef undirected_graph_constant_time_edge_add_and_remove< + property< vertex_back_t, vertex_descriptor >, + no_property, no_property > ugraph_o1; + + + std::vector< typename ugraph_o1::vertex_descriptor > + vertex_u(num_vertices(G)); + auto vmap = make_container_vertex_map(vertex_u, G); +// +// get(vmap, _) +// {v,w} in V(G)---------------> +// <---------------V(U) <= {u,t} +// back[_] +// +// Determine copy U of G with linkage +// + ugraph_o1 U; + + auto back = get(vertex_back, U); + + + BGL_FORALL_VERTICES_T(v, G, VertexListGraph) + { put(vmap, v, U.add_vertex(v)); } + + BGL_FORALL_EDGES_T(e, G, VertexListGraph) + { U.add_edge(get(vmap, source(e, G)), get(vmap, target(e, G))); } + +/* + Determine 5-bounded acyclic orientation + + Marek Chrobak, David Eppstein + "Planar orientations with low out-degree and compaction of adjacency matrices" + Theoretical Computer Science 1991 + https://dl.acm.org/doi/10.1016/0304-3975%2891%2990020-3 +*/ + std::vector< typename ugraph_o1::vertex_descriptor > small, visited; + std::vector< vertex_descriptor > rev; + small.reserve(num_vertices(U)); + visited.reserve(num_vertices(U)); + rev.reserve(num_vertices(U)); + + BGL_FORALL_VERTICES_T(u, U, ugraph_o1) + { if (degree(u, U) <= 5) { small.push_back(u); } } + + + while (!small.empty()) + { + typename ugraph_o1::vertex_descriptor u = small.back(); + small.pop_back(); + + BGL_FORALL_ADJ_T(u, t, U, ugraph_o1) + { + if (degree(t, U) == 6) small.push_back(t); + } + U.clear_vertex(u); + + visited.push_back(u); + } + + BOOST_ASSERT(num_vertices(U) == visited.size()); + +// call sequential_vertex_coloring() +// with reverse order of 5-bounded acyclic orientation determination +// + BOOST_REVERSE_FOREACH(typename ugraph_o1::vertex_descriptor u, visited) + rev.push_back(back[u]); + + return sequential_vertex_coloring( + G, make_container_vertex_map(rev, G), color); +} + +} // namespace boost + +#endif // BOOST_GRAPH_PLANAR_VERTEX_SIX_COLORING_HPP diff --git a/include/boost/graph/undirected_graph.hpp b/include/boost/graph/undirected_graph.hpp index ec1bbbba6..3ec353ef3 100644 --- a/include/boost/graph/undirected_graph.hpp +++ b/include/boost/graph/undirected_graph.hpp @@ -340,6 +340,14 @@ class undirected_graph std::swap(m_max_edge_index, g.m_max_edge_index); } +protected: + void remove_edge_(void *p) + { + auto *q = static_cast< std::pair< out_edge_iterator, out_edge_iterator > * >(p); + boost::remove_edge_(q->first, q->second, m_graph); + --m_num_edges; + } + private: vertices_size_type renumber_vertex_indices( vertex_iterator i, vertex_iterator end, vertices_size_type n) diff --git a/include/boost/graph/undirected_graph_constant_time_edge_add_and_remove.hpp b/include/boost/graph/undirected_graph_constant_time_edge_add_and_remove.hpp new file mode 100644 index 000000000..0c32e3a02 --- /dev/null +++ b/include/boost/graph/undirected_graph_constant_time_edge_add_and_remove.hpp @@ -0,0 +1,122 @@ +//======================================================================= +// Copyright 2024 +// Author: Hermann Stamm-Wilbrandt +// +// 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_UNDIRECTED_GRAPH_CONSTANT_TIME_EDGE_ADD_AND_REMOVE_HPP +#define BOOST_GRAPH_UNDIRECTED_GRAPH_CONSTANT_TIME_EDGE_ADD_AND_REMOVE_HPP + +#include +#include +#include +#include + +enum edge_oeip_t +{ + edge_oeip +}; + +namespace boost +{ +BOOST_INSTALL_PROPERTY(edge, oeip); + + +/** + * The undirected_graph_constant_time_edge_add_and_remove class + * extends undirected_graph class template of the BGL. + * Its only purpose over undirected_graph is to provide + * O(1) time remove_edge() (and add_edge()) functions. + */ +#define GRAPH_TYPE \ + undirected_graph< VP, property< edge_oeip_t, void*, EP >, GP > + +template< class VP, class EP, class GP> +class undirected_graph_constant_time_edge_add_and_remove + : public GRAPH_TYPE +{ + public: + typedef GRAPH_TYPE graph_type; + + typedef typename graph_type::vertices_size_type vertices_size_type; + typedef typename graph_type::vertex_descriptor vertex_descriptor; + typedef typename graph_type::edge_descriptor edge_descriptor; + typedef typename graph_type::out_edge_iterator out_edge_iterator; + typedef typename graph_type::edge_iterator edge_iterator; + + public: + inline undirected_graph_constant_time_edge_add_and_remove() + : graph_type() + , m_map(get(edge_oeip, *this)) + { + } + + // would miss necessary linkage between x and created graph + inline undirected_graph_constant_time_edge_add_and_remove( + graph_type const& x) = delete; + + // would miss necessary linkage between graphs + inline undirected_graph_constant_time_edge_add_and_remove( + vertices_size_type n, GP const& p = GP()) = delete; + + template < typename EdgeIterator > + inline undirected_graph_constant_time_edge_add_and_remove(EdgeIterator f, + EdgeIterator l, + typename GRAPH_TYPE::vertices_size_type n, + typename GRAPH_TYPE::edges_size_type m = 0, + GP const& p = GP()) = delete; + + // too slow + std::pair< edge_descriptor, bool > add_edge( + vertex_descriptor u, vertex_descriptor v, EP const& p) = delete; + + // O(1) + inline std::pair< edge_descriptor, bool > + add_edge(vertex_descriptor u, vertex_descriptor v) + { + std::pair< edge_descriptor, bool > et = graph_type::add_edge(u, v); + BOOST_ASSERT(et.second); + + storage.push_back(std::make_pair(--out_edges(u, *this).second, + --out_edges(v, *this).second)); + m_map[et.first] = reinterpret_cast(&storage.back()); + return et; + } + + // too slow + void remove_edge(vertex_descriptor u, vertex_descriptor v) = delete; + + // O(1) + void remove_edge(edge_iterator i) { remove_edge(*i); } + + // O(1) + inline void remove_edge(edge_descriptor e) + { + graph_type::remove_edge_(m_map[e]); + } + + // O(degree(v)) + inline void clear_vertex(vertex_descriptor v) + { + while (true) + { + out_edge_iterator ei, ei_end; + boost::tie(ei, ei_end) = out_edges(v, *this); + if (ei == ei_end) + break; + this->remove_edge(*ei); + } + } + + private: + typename property_map< graph_type, edge_oeip_t >::type m_map; + std::list< std::pair< out_edge_iterator, out_edge_iterator > > storage; +}; + +} /* namespace boost */ + + +#endif diff --git a/test/Jamfile.v2 b/test/Jamfile.v2 index b2656eb07..0e065d677 100644 --- a/test/Jamfile.v2 +++ b/test/Jamfile.v2 @@ -84,7 +84,8 @@ alias graph_test_regular : [ compile reverse_graph_cc.cpp ] [ run sequential_vertex_coloring.cpp ] - + [ run planar_vertex_six_coloring.cpp ] + # TODO: Merge these into a single test framework. 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+26 15 0 +26 16 0 +27 3 0 +27 4 0 +27 15 0 +27 16 0 +27 17 0 +28 8 0 +28 9 0 +28 16 0 +28 17 0 +28 18 0 +29 4 0 +29 5 0 +29 17 0 +29 18 0 +29 19 0 +30 9 0 +30 10 0 +30 18 0 +30 19 0 +30 20 0 +31 1 0 +31 5 0 +31 11 0 +31 19 0 +31 20 0 +32 6 0 +32 10 0 +32 11 0 +32 12 0 +32 20 0 diff --git a/test/planar_vertex_six_coloring.cpp b/test/planar_vertex_six_coloring.cpp new file mode 100644 index 000000000..9b11a7087 --- /dev/null +++ b/test/planar_vertex_six_coloring.cpp @@ -0,0 +1,216 @@ +//======================================================================= +// Copyright 2024 +// Authors: Hermann Stamm-Wilbrandt +// +// Use, modification and distribution is subject to 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) +//======================================================================= +// +// Demonstrates sequential_vertex_coloring() forced to take 15 colors +// on graph built with "create(15, g)", and planar_vertex_six_coloring() +// taking 6 colors only (both linear time algorithms). +// +#include +#include +#include +#include +#include +#include +#include +#include +#include + +using namespace boost; + +typedef adjacency_list< listS, vecS, undirectedS > Graph; +typedef graph_traits< Graph >::vertices_size_type vertices_size_type; +typedef graph_traits< Graph >::vertex_descriptor vertex_descriptor; +typedef graph_traits< Graph >::edge_descriptor edge_descriptor; + + +edge_descriptor create(Graph& g, int k); +void read_leda_graph(Graph& g, const char* gname); + +// time measurements +clock_t start_; +#define __(blk) if (output) std::cerr << #blk << " "; start_ = clock(); blk \ + if (output) std::cerr << (clock()-start_)*1.0/CLOCKS_PER_SEC << std::endl; + + +int main(int argc, char*argv[]) +{ + unsigned int k = (argc < 2) ? 15 : atoi(argv[1]); + bool output = argc > 2; + + Graph g; + edge_descriptor e; + + __(create(g, k);) + + BOOST_TEST(num_vertices(g) == 987); // fib(k+1) + BOOST_TEST(num_edges(g) == 1595); // fib(k+2)-2 + + std::vector< vertices_size_type > color_vec(num_vertices(g)); + auto color = make_container_vertex_map(color_vec, g); + + __(vertices_size_type num_colors = sequential_vertex_coloring(g, color);) + + BOOST_TEST(num_colors == k); + BGL_FORALL_EDGES(e, g, Graph) + { BOOST_ASSERT(get(color, source(e, g)) != get(color, target(e, g))); } + + __(vertices_size_type num_color6 = planar_vertex_six_coloring(g, color);) + + BOOST_TEST(num_color6 == 6); + BGL_FORALL_EDGES(e, g, Graph) + { BOOST_ASSERT(get(color, source(e, g)) != get(color, target(e, g))); } + + if (output) + { + std::cerr << num_vertices(g) << "/" << num_edges(g) + << " vertices/edges" << std::endl; + std::cerr << num_colors << "/" << num_color6 + << " colors used" << std::endl; + } + + + __(read_leda_graph(g, "planar_input_graphs/pentakis_dodecahedron.leda");) + + color_vec.resize(num_vertices(g)); + color = make_container_vertex_map(color_vec, g); + + BOOST_TEST(num_vertices(g) == 32); + BOOST_TEST(num_edges(g) == 3*32-6); + + __(num_colors = sequential_vertex_coloring(g, color);) + + BOOST_TEST(num_colors == 5); + BGL_FORALL_EDGES(e, g, Graph) + { BOOST_ASSERT(get(color, source(e, g)) != get(color, target(e, g))); } + + __(num_color6 = planar_vertex_six_coloring(g, color);) + + BOOST_TEST(num_color6 == 4); + BGL_FORALL_EDGES(e, g, Graph) + { BOOST_ASSERT(get(color, source(e, g)) != get(color, target(e, g))); } + + if (output) + { + std::cerr << num_vertices(g) << "/" << num_edges(g) + << " vertices/edges" << std::endl; + std::cerr << num_colors << "/" << num_color6 + << " colors used" << std::endl; + } + + + __(read_leda_graph(g, "planar_input_graphs/maximal_planar_1000.leda");) + + color_vec.resize(num_vertices(g)); + color = make_container_vertex_map(color_vec, g); + + BOOST_TEST(num_vertices(g) == 1000); + BOOST_TEST(num_edges(g) == 3*1000-6); + + __(num_colors = sequential_vertex_coloring(g, color);) + + BOOST_TEST(num_colors == 6); + BGL_FORALL_EDGES(e, g, Graph) + { BOOST_ASSERT(get(color, source(e, g)) != get(color, target(e, g))); } + + __(num_color6 = planar_vertex_six_coloring(g, color);) + + BOOST_TEST(num_color6 == 6); + BGL_FORALL_EDGES(e, g, Graph) + { BOOST_ASSERT(get(color, source(e, g)) != get(color, target(e, g))); } + + if (output) + { + std::cerr << num_vertices(g) << "/" << num_edges(g) + << " vertices/edges" << std::endl; + std::cerr << num_colors << "/" << num_color6 + << " colors used" << std::endl; + } + + + return boost::report_errors(); +} + + +/* + creating C6 + + -5- + /|\ +... + from C5 + / + ---4 + / /|\ / + plus C3 / / | 3 + / / / |/|\ + plus C1 2 / / 2 | \ + / / \ / / / / \| \ + 0 0---1 0--1 0---1 0 +*/ +edge_descriptor create(Graph& g, int k) +{ + if (k < 4) + { + BOOST_ASSERT(k > 1); + + vertex_descriptor v = add_vertex(g); + vertex_descriptor w = add_vertex(g); + auto e = add_edge(v, w, g); + if (k == 2) return e.first; + + vertex_descriptor x = add_vertex(g); + add_edge(v, x, g); + return add_edge(w, x, g).first; + } + + std::vector es; + while (--k > 1) { es.push_back(create(g, k--)); } + + vertex_descriptor v = add_vertex(g); + if (k == 1) + { + vertex_descriptor w = add_vertex(g); + add_edge(v, w, g); + v = w; + } + + edge_descriptor e; + for (auto ei = es.rbegin(); ei != es.rend(); ++ei) + { + add_edge(source(*ei, g), v, g); + e = add_edge(target(*ei, g), v, g).first; + } + return e; +} + + +void read_leda_graph(Graph& g, const char* gname) +{ + int n, m; + std::string line; + + std::ifstream in(gname); + BOOST_ASSERT(in); + + std::getline(in, line); + in >> line >> line >> n; + + g = Graph(n); + + for (int i=1; i <= n; ++i) { + in >> line; + } + + in >> m; + for (int i=1; i <= m; ++i) { + int s, t, v; + in >> s >> t >> v; + add_edge(s-1, t-1, g); + } +}