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An Approximate Algorithm for the Weighted Hamiltonian Path Completion Problem on a Tree

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Algorithms and Computation (ISAAC 2000)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 1969))

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Abstract

Given a graph, the Hamiltonian path completion problem is to find an augmenting edge set such that the augmented graph has a Hamiltonian path. In this paper, we show that the Hamiltonian path completion problem will unlikely have any constant ratio approximation algorithm unless NP = P. This problem remains hard to approximate even when the given subgraph is a tree. Moreover, if the edge weights are restricted to be either 1 or 2, the Hamiltonian path completion problem on a tree is still NP-hard. Then it is shown that this problem will unlikely have any fully polynomial-time approximation scheme (FPTAS) unless NP=P. When the given tree is a k-tree, we give an approximation algorithm with performance ratio 1.5.

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Author information

Authors and Affiliations

  1. Dept. of Computer Science, National Tsing Hua University, 300, Hsinchu, Taiwan, R.O.C.

    Q. S. Wu

  2. National Center for High-Performance Computing, P.O. Box 19-136, 300, Hsinchu, Taiwan, R.O.C.

    C. L. Lu

  3. National Chi-Nan University, Puli, 545, Nantou Hsien, Taiwan, R.O.C.

    R. C. T. Lee

Authors
  1. Q. S. Wu
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  2. C. L. Lu
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  3. R. C. T. Lee
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Editor information

Editors and Affiliations

  1. Karlsruhe University, Germany

    Gerhard Goos

  2. Cornell University, NY, USA

    Juris Hartmanis

  3. Utrecht University, The Netherlands

    Jan van Leeuwen

  4. Academia Sinica, Institute of Information Science, 128 Academia Road, Section 2, Nankang, 115, Taipei, Taiwan, R.O.C.

    D. T. Lee

  5. Department of Computer Science and Akamai Technologies, University of Illinois at Urbana Champaign, 500 Technology Square, 02139, Cambridge, MA, USA

    Shang-Hua Teng

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© 2000 Springer-Verlag Berlin Heidelberg

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Wu, Q.S., Lu, C.L., Lee, R.C.T. (2000). An Approximate Algorithm for the Weighted Hamiltonian Path Completion Problem on a Tree. In: Goos, G., Hartmanis, J., van Leeuwen, J., Lee, D.T., Teng, SH. (eds) Algorithms and Computation. ISAAC 2000. Lecture Notes in Computer Science, vol 1969. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-40996-3_14

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  • DOI: https://doi.org/10.1007/3-540-40996-3_14

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-41255-7

  • Online ISBN: 978-3-540-40996-0

  • eBook Packages: Springer Book Archive

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