The Hamiltonian problem on distance-hereditary graphs

Authors:
Sun-Yuan Hsieh;Chin-Wen Ho;Tsan-Sheng Hsu;Ming-Tat Ko
Affiliations:
Department of Computer Science and Information Engineering, National Cheng Kung University, Tainan, Taiwan;Department of Computer Science and Information Engineering, National Central University, Chung-Li, Taiwan;Institute of Information Science, Academia Sinica, Taipei, Taiwan;Institute of Information Science, Academia Sinica, Taipei, Taiwan
Venue:
Discrete Applied Mathematics
Year:
2006

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Abstract

In this paper, we first present an O(n+m)-time sequential algorithm to solve the Hamiltonian problem on a distance-hereditary graph G, where n and m are the number of vertices and edges of G, respectively. This algorithm is faster than the previous best known algorithm for the problem which takes O(n^2) time. We also give an efficient parallel implementation of our sequential algorithm. Moreover, if G is represented by its decomposition tree form, the problem can be solved optimally in O(logn) time using O((n+m)/logn) processors on an EREW PRAM.