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Iterated backtrack removal search for finding k-vertex-critical subgraphs

Author

Listed:
  • Wen Sun

    (Université d’Angers)

  • Jin-Kao Hao

    (Université d’Angers
    Institut Universitaire de France)

  • Alexandre Caminada

    (UTBM)

Abstract

Given an undirected graph $$G = (V,E)$$ G = ( V , E ) and a positive integer k, a k-vertex-critical subgraph (k-VCS) of G is a subgraph H such that its chromatic number equals k (i.e., $$\chi (H) = k$$ χ ( H ) = k ), and removing any vertex causes a decrease of $$\chi (H)$$ χ ( H ) . The k-VCS problem (k-VCSP) is to find the smallest k-vertex-critical subgraph $$H^*$$ H ∗ of G. This paper proposes an iterated backtrack-based removal (IBR) heuristic to find k-VCS for a given graph G. IBR extends the popular removal strategy that is intensification-oriented. The proposed extensions include two new diversification-oriented search components—a backtracking mechanism to reconsider some removed vertices and a perturbation strategy to escape local optima traps. Computational results on 80 benchmark graphs show that IBR is very competitive in terms of solution quality and run-time efficiency compared with state-of-the-art algorithms in the literature. Specifically, IBR improves the best-known solutions for 9 graphs and matches the best results for other 70 instances. We investigate the interest of the key components of the proposed algorithm.

Suggested Citation

  • Wen Sun & Jin-Kao Hao & Alexandre Caminada, 2019. "Iterated backtrack removal search for finding k-vertex-critical subgraphs," Journal of Heuristics, Springer, vol. 25(4), pages 565-590, October.
    • Handle: RePEc:spr:joheur:v:25:y:2019:i:4:d:10.1007_s10732-017-9358-5
    DOI: 10.1007/s10732-017-9358-5
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    References listed on IDEAS

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    Cited by:

    1. Alex Gliesch & Marcus Ritt, 2022. "A new heuristic for finding verifiable k-vertex-critical subgraphs," Journal of Heuristics, Springer, vol. 28(1), pages 61-91, February.

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