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Efficient Algorithms for the Hamiltonian Problem on Distance-Hereditary Graphs

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Computing and Combinatorics (COCOON 2002)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 2387))

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Abstract

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 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 on a PRAM model M d . We also 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.

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Author information

Authors and Affiliations

  1. Department of Computer Science and Information Engineering, National Cheng Kung University, Tainan, Taiwan

    Sun-yuan Hsieh

  2. Department of Computer Science and Information Engineering, National Central University, Chung-Li, Taiwan

    Chin-wen Ho

  3. Institute of Information Science, Academia Sinica, Taipei, Taiwan

    Tsan-sheng Hsu & Ming-tat Ko

Authors
  1. Sun-yuan Hsieh
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  2. Chin-wen Ho
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  3. Tsan-sheng Hsu
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  4. Ming-tat Ko
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Editor information

Editors and Affiliations

  1. Department of Computer Science, University of California, Santa Barbara, California, 93106, USA

    Oscar H. Ibarra

  2. Department of Mathematics, National University of Singapore, Singapore, Singapore, 117543

    Louxin Zhang

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© 2002 Springer-Verlag Berlin Heidelberg

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Hsieh, Sy., Ho, Cw., Hsu, Ts., Ko, Mt. (2002). Efficient Algorithms for the Hamiltonian Problem on Distance-Hereditary Graphs. In: Ibarra, O.H., Zhang, L. (eds) Computing and Combinatorics. COCOON 2002. Lecture Notes in Computer Science, vol 2387. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-45655-4_10

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  • DOI: https://doi.org/10.1007/3-540-45655-4_10

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-43996-7

  • Online ISBN: 978-3-540-45655-1

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