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.
CITATION STYLE
Hsieh, S. Y., Ho, C. W., Hsu, T. S., & Ko, M. T. (2002). Efficient algorithms for the hamiltonian problem on distance-hereditary graphs. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 2387, pp. 77–86). Springer Verlag. https://doi.org/10.1007/3-540-45655-4_10
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