#include <boost/limits.hpp>
#ifdef BOOST_NO_TEMPLATED_ITERATOR_CONSTRUCTORS
-# include <iterator>
+#include <iterator>
#endif
/* This algorithm is to find coloring of a graph
- Algorithm:
+ Algorithm:
Let G = (V,E) be a graph with vertices (somehow) ordered v_1, v_2, ...,
v_n. For k = 1, 2, ..., n the sequential algorithm assigns v_k to the
- smallest possible color.
+ smallest possible color.
Reference:
Thomas F. Coleman and Jorge J. More, Estimation of sparse Jacobian
matrices and graph coloring problems. J. Numer. Anal. V20, P187-209, 1983
- v_k is stored as o[k] here.
+ v_k is stored as o[k] here.
The color of the vertex v will be stored in color[v].
i.e., vertex v belongs to coloring color[v] */
-namespace boost {
- template <class VertexListGraph, class OrderPA, class ColorMap>
- typename property_traits<ColorMap>::value_type
- sequential_vertex_coloring(const VertexListGraph& G, OrderPA order,
- ColorMap color)
- {
- typedef graph_traits<VertexListGraph> GraphTraits;
+namespace boost
+{
+template < class VertexListGraph, class OrderPA, class ColorMap >
+typename property_traits< ColorMap >::value_type sequential_vertex_coloring(
+ const VertexListGraph& G, OrderPA order, ColorMap color)
+{
+ typedef graph_traits< VertexListGraph > GraphTraits;
typedef typename GraphTraits::vertex_descriptor Vertex;
- typedef typename property_traits<ColorMap>::value_type size_type;
-
+ typedef typename property_traits< ColorMap >::value_type size_type;
+
size_type max_color = 0;
const size_type V = num_vertices(G);
// for each color. The length of mark is the
// number of vertices since the maximum possible number of colors
// is the number of vertices.
- std::vector<size_type> mark(V,
- std::numeric_limits<size_type>::max BOOST_PREVENT_MACRO_SUBSTITUTION());
-
- //Initialize colors
+ std::vector< size_type > mark(V,
+ std::numeric_limits< size_type >::max
+ BOOST_PREVENT_MACRO_SUBSTITUTION());
+
+ // Initialize colors
typename GraphTraits::vertex_iterator v, vend;
for (boost::tie(v, vend) = vertices(G); v != vend; ++v)
- put(color, *v, V-1);
-
- //Determine the color for every vertex one by one
- for ( size_type i = 0; i < V; i++) {
- Vertex current = get(order,i);
- typename GraphTraits::adjacency_iterator v, vend;
-
- //Mark the colors of vertices adjacent to current.
- //i can be the value for marking since i increases successively
- for (boost::tie(v,vend) = adjacent_vertices(current, G); v != vend; ++v)
- mark[get(color,*v)] = i;
-
- //Next step is to assign the smallest un-marked color
- //to the current vertex.
- size_type j = 0;
-
- //Scan through all useable colors, find the smallest possible
- //color that is not used by neighbors. Note that if mark[j]
- //is equal to i, color j is used by one of the current vertex's
- //neighbors.
- while ( j < max_color && mark[j] == i )
- ++j;
-
- if ( j == max_color ) //All colors are used up. Add one more color
- ++max_color;
-
- //At this point, j is the smallest possible color
- put(color, current, j); //Save the color of vertex current
+ put(color, *v, V - 1);
+
+ // Determine the color for every vertex one by one
+ for (size_type i = 0; i < V; i++)
+ {
+ Vertex current = get(order, i);
+ typename GraphTraits::adjacency_iterator v, vend;
+
+ // Mark the colors of vertices adjacent to current.
+ // i can be the value for marking since i increases successively
+ for (boost::tie(v, vend) = adjacent_vertices(current, G); v != vend;
+ ++v)
+ mark[get(color, *v)] = i;
+
+ // Next step is to assign the smallest un-marked color
+ // to the current vertex.
+ size_type j = 0;
+
+ // Scan through all useable colors, find the smallest possible
+ // color that is not used by neighbors. Note that if mark[j]
+ // is equal to i, color j is used by one of the current vertex's
+ // neighbors.
+ while (j < max_color && mark[j] == i)
+ ++j;
+
+ if (j == max_color) // All colors are used up. Add one more color
+ ++max_color;
+
+ // At this point, j is the smallest possible color
+ put(color, current, j); // Save the color of vertex current
}
-
+
return max_color;
- }
-
- template<class VertexListGraph, class ColorMap>
- typename property_traits<ColorMap>::value_type
- sequential_vertex_coloring(const VertexListGraph& G, ColorMap color)
- {
- typedef typename graph_traits<VertexListGraph>::vertex_descriptor
- vertex_descriptor;
- typedef typename graph_traits<VertexListGraph>::vertex_iterator
- vertex_iterator;
-
- std::pair<vertex_iterator, vertex_iterator> v = vertices(G);
+}
+
+template < class VertexListGraph, class ColorMap >
+typename property_traits< ColorMap >::value_type sequential_vertex_coloring(
+ const VertexListGraph& G, ColorMap color)
+{
+ typedef typename graph_traits< VertexListGraph >::vertex_descriptor
+ vertex_descriptor;
+ typedef typename graph_traits< VertexListGraph >::vertex_iterator
+ vertex_iterator;
+
+ std::pair< vertex_iterator, vertex_iterator > v = vertices(G);
#ifndef BOOST_NO_TEMPLATED_ITERATOR_CONSTRUCTORS
- std::vector<vertex_descriptor> order(v.first, v.second);
+ std::vector< vertex_descriptor > order(v.first, v.second);
#else
- std::vector<vertex_descriptor> order;
+ std::vector< vertex_descriptor > order;
order.reserve(std::distance(v.first, v.second));
- while (v.first != v.second) order.push_back(*v.first++);
+ while (v.first != v.second)
+ order.push_back(*v.first++);
#endif
- return sequential_vertex_coloring
- (G,
- make_iterator_property_map
- (order.begin(), identity_property_map(),
- graph_traits<VertexListGraph>::null_vertex()),
- color);
- }
+ return sequential_vertex_coloring(G,
+ make_iterator_property_map(order.begin(), identity_property_map(),
+ graph_traits< VertexListGraph >::null_vertex()),
+ color);
+}
}
#endif
projects / ceph.git / blobdiff