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

  • Authors:

  • Q. S. Wu;Chin Lung Lu;Richard C. T. Lee

  • Affiliations:

  • -;-;-

  • Venue:
  • ISAAC '00 Proceedings of the 11th International Conference on Algorithms and Computation
  • Year:
  • 2000

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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.