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    National Tsing Hua University Institutional Repository > 歷任校長 > 李家同 (1993-1994) > 期刊論文  >  The Approximability of the Weighted Hamiltonian Path Completion Problem on a Tree


    Please use this identifier to cite or link to this item: http://nthur.lib.nthu.edu.tw/dspace/handle/987654321/80810


    Title: The Approximability of the Weighted Hamiltonian Path Completion Problem on a Tree
    Authors: Wu, Q.;Lu, C. L.;Lee, R. C. T.
    教師: 李家同
    Date: 2005
    Publisher: Elsevier
    Relation: THEORETICAL COMPUTER SCIENCE, Elsevier, Volume 341, Issue 1-3, SEP 5 2005, Pages 385-397
    Keywords: Trees
    Hamiltonian path completion problem
    Strongly NP-hard
    Approximation algorithm
    Fully polynomial-time approximation scheme
    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 observed that this problem is strongly NP-hard, so it does not 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.
    Relation Link: http://www.elsevier.com/wps/find/homepage.cws_home
    URI: http://nthur.lib.nthu.edu.tw/dspace/handle/987654321/80810
    Appears in Collections:[李家同 (1993-1994)] 期刊論文
    [資訊工程學系] 期刊論文

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