On the existence of an efficient parallel algorithm for a graph theoretic problem

Abstract

The problem of computing the relation ⊖ among edges of a graph is an important step in algorithms for several graph theoretic problems such as embedding graphs in Cartesian products, decomposing a graph into a product or deciding whether a graph is a binary Hamming graph. By an efficient parallel algorithm we mean one that takes polylogarithmic time using a polynomial number of processors. In this paper we show that there are efficient parallel algorithms for computing the relation ⊖, for computing the equivalence classes of its transitive closure $\hat \Theta$ and for deciding whether a graph is a binary Hamming graph.

On leave from Inštitut Jožef Stefan, Ljubljana. This work was done while the author was visiting the Institut für Mathematik und Angewandte Geometrie at the Montanuniversität Leoben, Austria, supported by the Research Council of Slovenia.