Abstract
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 ( P d (| 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 | 3 ) sequential algorithm.
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