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A multi-start iterated greedy algorithm for the minimum weight vertex cover P3 problem

Author

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  • Zhang, Wenjie
  • Tu, Jianhua
  • Wu, Lidong

Abstract

Given a vertex-weighted graph G=(V,E) and a positive integer k ≥ 2, the minimum weight vertex cover Pk (MWVCPk) problem is to find a vertex subset F ⊆ V with minimum total weight such that every path of order k in G contains at least one vertex in F. For any integer k ≥ 2, the MWVCPk problem for general graphs is NP-hard. In this paper, we restrict our attention to the MWVCP3 problem and present a multi-start iterated greedy algorithm to solve the MWVCP3 problem. The experiments are carried out on randomly generated instances with up to 1000 vertices and 250000 edges. Our work is the first one to adopt heuristic algorithms to solve the MWVCP3 problem, and the experimental results show that our algorithm performs reasonably well in practice.

Suggested Citation

  • Zhang, Wenjie & Tu, Jianhua & Wu, Lidong, 2019. "A multi-start iterated greedy algorithm for the minimum weight vertex cover P3 problem," Applied Mathematics and Computation, Elsevier, vol. 349(C), pages 359-366.
    • Handle: RePEc:eee:apmaco:v:349:y:2019:i:c:p:359-366
    DOI: 10.1016/j.amc.2018.12.067
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    References listed on IDEAS

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    1. Hannes Moser & Rolf Niedermeier & Manuel Sorge, 2012. "Exact combinatorial algorithms and experiments for finding maximum k-plexes," Journal of Combinatorial Optimization, Springer, vol. 24(3), pages 347-373, October.
    2. Shyong Shyu & Peng-Yeng Yin & Bertrand Lin, 2004. "An Ant Colony Optimization Algorithm for the Minimum Weight Vertex Cover Problem," Annals of Operations Research, Springer, vol. 131(1), pages 283-304, October.
    3. Jianhua Tu & Lidong Wu & Jing Yuan & Lei Cui, 2017. "On the vertex cover $$P_3$$ P 3 problem parameterized by treewidth," Journal of Combinatorial Optimization, Springer, vol. 34(2), pages 414-425, August.
    4. Taoqing Zhou & Zhipeng Lü & Yang Wang & Junwen Ding & Bo Peng, 2016. "Multi-start iterated tabu search for the minimum weight vertex cover problem," Journal of Combinatorial Optimization, Springer, vol. 32(2), pages 368-384, August.
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    More about this item

    Keywords

    Iterated greedy algorithm; Minimum weight vertex cover P3 problem; Heuristic algorithms; Combinatorial optimization problems;
    All these keywords.

    JEL classification:

    • P3 - Political Economy and Comparative Economic Systems - - Socialist Institutions and Their Transitions

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