king_ordering
| Graphs: | undirected |
|---|---|
| Properties: | color, degree |
| Complexity: | time: O(m2log(m)|E|) where m = max { degree(v) | v in V } |
(1)
template <class IncidenceGraph, class OutputIterator,
class ColorMap, class DegreeMap, class VertexIndexMap>
OutputIterator
king_ordering(const IncidenceGraph& g,
typename graph_traits<Graph>::vertex_descriptor s,
OutputIterator inverse_permutation,
ColorMap color, DegreeMap degree, VertexIndexMap index_map);
(2)
template <class IncidenceGraph, class OutputIterator>
OutputIterator
king_ordering(const IncidenceGraph& g, OutputIterator inverse_permutation);
template <class IncidenceGraph, class OutputItrator, class VertexIndexMap>
OutputIterator
king_ordering(const IncidenceGraph& g, OutputIterator inverse_permutation,
VertexIndexMap index_map);
template <class VertexListGraph, class OutputIterator,
class ColorMap, class DegreeMap, class VertexIndexMap>
OutputIterator
king_ordering(const VertexListGraph& G, OutputIterator inverse_permutation,
ColorMap color, DegreeMap degree, VertexIndexMap index_map);
(3)
template <class IncidenceGraph, class OutputIterator,
class ColorMap, class DegreeMap, class VertexIndexMap>
OutputIterator
king_ordering(const IncidenceGraph& g,
std::deque< typename
graph_traits<Graph>::vertex_descriptor > vertex_queue,
OutputIterator permutation,
ColorMap color, DegreeMap degree, VertexIndexMap index_map);
The goal of the King ordering
algorithm [62]is to reduce the bandwidth of a graph by reordering the
indices assigned to each vertex. The King ordering algorithm
works by a local minimization of the i-th bandwidths. The vertices are
basically assigned a breadth-first search order, except that at each
step, the adjacent vertices are placed in the queue in order of
increasing pseudo-degree, where pseudo-degree is defined as the number of
outgoing edges with white endpoints (vertices yet to be examined).
Version 1 of the algorithm lets the user choose the ``starting vertex'', version 2 finds a good starting vertex using the pseudo-peripheral pair heuristic (among each component), while version 3 contains the starting nodes for each vertex in the deque. The choice of the ``starting vertex'' can have a significant effect on the quality of the ordering.
The output of the algorithm are the vertices in the new ordering. Storing the output into a vector gives you the permutation from the new ordering to the old ordering.
inv_perm[new_index[u]] == u
Often times, it is the opposite permutation that you want, the permutation from the old index to the new index. This can easily be computed in the following way.
for (size_type i = 0; i != inv_perm.size(); ++i)
perm[old_index[inv_perm[i]]] = i;
| Copyright © 2000-2001 | Jeremy Siek, Indiana University (jsiek@osl.iu.edu) |