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A Randomized Approximation Algorithm for Metric Triangle Packing

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Combinatorial Optimization and Applications (COCOA 2019)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 11949))

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Abstract

Given an edge-weighted complete graph G on 3n vertices, the maximum-weight triangle packing problem (MWTP for short) 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 MWTP 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 (denoted by MMWTP), 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 MMWTP. Our algorithm is randomized and achieves an expected approximation ratio of \(0.66745 - \epsilon \) for any constant \(\epsilon > 0\).

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Acknowledgements

YC and AZ are supported by the NSFC Grants 11971139, 11771114 and 11571252; and supported by the CSC Grants 201508330054 and 201908330090, respectively. ZZC is supported by in part by the Grant-in-Aid for Scientific Research of the Ministry of Education, Science, Sports and Culture of Japan, under Grant No. 18K11183. GL is supported by the NSERC Canada. LW is supported by a grant for Hong Kong Special Administrative Region, China (CityU 11210119).

Author information

Authors and Affiliations

  1. Department of Mathematics, Hangzhou Dianzi University, Hangzhou, China

    Yong Chen & An Zhang

  2. Division of Information System Design, Tokyo Denki University, Saitama, Japan

    Zhi-Zhong Chen

  3. Department of Computing Science, University of Alberta, Edmonton, Canada

    Guohui Lin

  4. Department of Computer Science, City University of Hong Kong, Kowloon, Hong Kong SAR

    Lusheng Wang

Authors
  1. Yong Chen
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  2. Zhi-Zhong Chen
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  3. Guohui Lin
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  4. Lusheng Wang
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  5. An Zhang
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Corresponding authors

Correspondence to Zhi-Zhong Chen or Guohui Lin .

Editor information

Editors and Affiliations

  1. Georgia State University, Atlanta, GA, USA

    Yingshu Li

  2. Florida Atlantic University, Boca Raton, FL, USA

    Mihaela Cardei

  3. Kennesaw State University, Marietta, GA, USA

    Yan Huang

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Chen, Y., Chen, ZZ., Lin, G., Wang, L., Zhang, A. (2019). A Randomized Approximation Algorithm for Metric Triangle Packing. In: Li, Y., Cardei, M., Huang, Y. (eds) Combinatorial Optimization and Applications. COCOA 2019. Lecture Notes in Computer Science(), vol 11949. Springer, Cham. https://doi.org/10.1007/978-3-030-36412-0_10

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  • DOI: https://doi.org/10.1007/978-3-030-36412-0_10

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-030-36411-3

  • Online ISBN: 978-3-030-36412-0

  • eBook Packages: Computer ScienceComputer Science (R0)

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