The parallel complexity of elimination ordering procedures

Abstract

We prove that lexicographic breadth-first search is P-complete and that a variant of the parallel perfect elimination procedure of P. Klein [11] is powerful enough to compute a semi-perfect elimination ordering in sense of [10] if certain induced subgraphs are forbidden. We present an efficient parallel breadth first search algorithm for all graphs which have no cycle of length greater four and no house as an induced subgraph. A side result is that a maximal clique can be computed in polylogarithmic time using a linear number of processors.