Coarse grained parallel algorithms for graph matching
Parallel Computing
| Hi-index | 0.00 |
Chordal graphs became interesting as a generalization of interval graphs (see for example \cite{LB}). We call a graph chordal if every cycle of length greater than three has a chord, i.e. an edge that joins two non consecutive vertices of the cycle. Note that interval graphs are not only chordal but strongly chordal as defined in \cite{Fa1}. Strongly chordal graphs are just those chordal graphs having a so called strongly perfect elimination ordering. In this paper we consider the sequential and parallel complexity of the maximum matching problem in chordal and strongly chordal graphs. Note that in general a linear time algorithm for perfect matching is not known. Here we shall show that, provided a strongly perfect elimination ordering is known, a maximum matching in a strongly chordal graph can be found in linear time by a simple greedy algorithm. This algorithm can be turned into a (non optimal) parallel algorithm.