An efficient parallel strategy for the two-fixed-endpoint Hamiltonian path problem on distance-hereditary graphs

In this paper, we solve the two-fixed-endpoint Hamiltonian path problem on distance-hereditary graphs efficiently in parallel. Let T-d(\V\, \E\) and P-d(\V\, \E\) denote the parallel time and processor complexities, respectively, required to construct a decomposition tree of a distance-hereditary graph G = (V, E) on a PRAM model M-d. We show that this problem can be solved in O(T-d(\V\, \E\) + log\V\) time using O(Pd(\V\, \E\) + (\V\ + \E\)/log\V\) processors on M-d. Moreover, if G is represented by its decomposition tree form, the problem can be solved optimally in O(log\V\) time using O((\V\ + \E\)/log\V\) processors on an EREW PRAM. We also obtain a linear-time algorithm which is faster than the previous known O(\V\) sequential algorithm. (C) 2004 Elsevier Inc. All rights reserved.