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A randomized approximation algorithm for metric triangle packing

Author

Listed:
  • Yong Chen

    (Hangzhou Dianzi University)

  • Zhi-Zhong Chen

    (Tokyo Denki University)

  • Guohui Lin

    (University of Alberta)

  • Lusheng Wang

    (City University of Hong Kong)

  • An Zhang

    (Hangzhou Dianzi University)

Abstract

Given an edge-weighted complete graph G on 3n vertices, the maximum-weight triangle packing problem asks for a collection of n vertex-disjoint triangles in G such that the total weight of edges in these n triangles is maximized. Although the problem has been extensively studied in the literature, it is surprising that prior to this work, no nontrivial approximation algorithm had been designed and analyzed for its metric case, where the edge weights in the input graph satisfy the triangle inequality. In this paper, we design the first nontrivial polynomial-time approximation algorithm for the maximum-weight metric triangle packing problem. Our algorithm is randomized and achieves an expected approximation ratio of $$0.66768 - \epsilon $$ 0.66768 - ϵ for any constant $$\epsilon > 0$$ ϵ > 0 .

Suggested Citation

  • Yong Chen & Zhi-Zhong Chen & Guohui Lin & Lusheng Wang & An Zhang, 2021. "A randomized approximation algorithm for metric triangle packing," Journal of Combinatorial Optimization, Springer, vol. 41(1), pages 12-27, January.
    • Handle: RePEc:spr:jcomop:v:41:y:2021:i:1:d:10.1007_s10878-020-00660-7
    DOI: 10.1007/s10878-020-00660-7
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    References listed on IDEAS

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    1. Esther M. Arkin & Refael Hassin, 1998. "On Local Search for Weighted k -Set Packing," Mathematics of Operations Research, INFORMS, vol. 23(3), pages 640-648, August.
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