Coarse grained parallel algorithms for graph matching
Parallel Computing
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Chordal graphs are graphs with the property that each cycle of length greater than 3 has two non consecutive vertices that are joined by an edge. An important subclass of chordal graphs are strongly chordal graphs \cite{Fa1}. Chordal graphs appear for example in the design of acyclic data base schemes \cite{BMFY}. In this paper we study the computational complexity (both sequential and parallel) of the maximum matching problem for chordal and strongly chordal graphs. We show that there is a linear time greedy algorithm for a maximum matching in a strongly chordal graph provided a strongly perfect elimination ordering is known. This algorithm can be also turned into a parallel algorithm. The technique used can be also extended for the multidimensional matching for chordal and strongly chordal graphs yielding the first polynomial time algorithms for these classes of graphs (the multidimensional matching is NP-complete in general).