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

  • Q. S. Wu
  • C. L. Lu
  • R. C. T. Lee
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 1969)

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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Copyright information

© Springer-Verlag Berlin Heidelberg 2000

Authors and Affiliations

  • Q. S. Wu
    • 1
  • C. L. Lu
    • 2
  • R. C. T. Lee
    • 3
  1. 1.Dept. of Computer ScienceNational Tsing Hua UniversityHsinchuTaiwan, R.O.C.
  2. 2.National Center for High-Performance ComputingHsinchuTaiwan, R.O.C.
  3. 3.National Chi-Nan UniversityNantou HsienTaiwan, R.O.C.

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