Efficient Algorithms for the Hamiltonian Problem on Distance-Hereditary Graphs

In this paper, we first present an O(|V| + |E|)-time sequential algorithm to solve the Hamiltonian problem on a distance-hereditary graph G = (V, E). This algorithm is faster than the previous best result which takes O(|V|2) time. Let Td(|V|, |E|) and Pd(|V|, |E|) denote the parallel time and processor complexities, respectively, required to construct a decomposition tree of a distance-hereditary graph on a PRAM model Md. We also show that this problem can be solved in O(Td(|V|, |E|) + log |V|) time using O(Pd(|V|, |E|) + (|V| + |E|)/ log |V|) processors on Md. 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.

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