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Declawing a graph: polyhedra and Branch-and-Cut algorithms

Author

Listed:
  • Felipe C. Fragoso

    (Universidade Federal da Paraíba (UFPB))

  • Gilberto F. Sousa Filho

    (Universidade Federal da Paraíba (UFPB))

  • Fábio Protti

    (Universidade Federal Fluminense (UFF))

Abstract

The complete bipartite graph $$K_{1,3}$$ K 1 , 3 is called a claw. A graph is said to be claw-free if it contains no induced subgraph isomorphic to a claw. Given a graph G, the NP-hard Graph Declawing Problem (GDP) consists of finding a minimum set $$S\subseteq V(G)$$ S ⊆ V ( G ) such that $$G-S$$ G - S is claw-free. This work develops a polyhedral study of the GDP polytope, expliciting its full dimensionality, proposing and testing five families of facets: trivial inequalities, claw inequalities, star inequalities, lantern inequalities, and binary star inequalities. In total, four Branch-and-Cut algorithms with separation heuristics have been developed to test the computational benefits of each proposed family on random graph instances and random interval graph instances. Our results show that the model that uses a separation heuristics proposed for star inequalities achieves better results on both set of instances in almost all cases.

Suggested Citation

  • Felipe C. Fragoso & Gilberto F. Sousa Filho & Fábio Protti, 2021. "Declawing a graph: polyhedra and Branch-and-Cut algorithms," Journal of Combinatorial Optimization, Springer, vol. 42(1), pages 85-124, July.
    • Handle: RePEc:spr:jcomop:v:42:y:2021:i:1:d:10.1007_s10878-021-00736-y
    DOI: 10.1007/s10878-021-00736-y
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    References listed on IDEAS

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    1. Lucas Bastos & Luiz Satoru Ochi & Fábio Protti & Anand Subramanian & Ivan César Martins & Rian Gabriel S. Pinheiro, 2016. "Efficient algorithms for cluster editing," Journal of Combinatorial Optimization, Springer, vol. 31(1), pages 347-371, January.
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    Cited by:

    1. Camur, Mustafa C. & Sharkey, Thomas C. & Vogiatzis, Chrysafis, 2023. "The stochastic pseudo-star degree centrality problem," European Journal of Operational Research, Elsevier, vol. 308(2), pages 525-539.

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