EFFICIENT PARALLEL ALGORITHMS FOR BIPARTITE PERMUTATION GRAPHS

In this paper, we further study the properties of bipartite permutation graphs. We give first efficient parallel algorithms for several problems on bipartite permutation graphs. These problems include transforming a bipartite graph into a strongly ordered one if it is also a permutation graph; testing isomorphism; finding a Hamiltonian path/cycle; solving a variant of the crossing number problem; and others. All these problems can be solved in O(log2n) time with O(n3) processors on a Common CRCW PRAM. We also show that the minimum fill-in problem for bipartite permutation graphs can be solved efficiently by a randomized parallel algorithm.