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A new approximate cluster deletion algorithm for diamond-free graphs

Author

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  • Sabrine Malek

    (University of Sfax)

  • Wady Naanaa

    (University of Tunis El Manar)

Abstract

The cluster deletion problem (CD) asks for transforming a given graph into a disjoint union of cliques by removing as few edges as possible. CD is among the most studied combinatorial optimization problem and, for general graphs, it is NP-hard. In the present paper, we identify a new polynomially solvable CD subproblem. We specifically propose a two-phase polynomial-time algorithm that optimally solves CD on the class of (butterfly,diamond)-free graphs. For this latter class of graphs, our two-phase algorithm provides optimal solutions even for another clustering variant, namely, cluster editing. Then, we propose a 2-optimal CD algorithm dedicated to the super-class of diamond-free graphs. For this class, we also show that CD, when parameterised by the number of deleted edges, admits a quadratic-size kernel. Finally, we report the results of experiments carried out on numerous diamond-free graphs, showing the effectiveness of the proposed approximate algorithm in terms of solution quality.

Suggested Citation

  • Sabrine Malek & Wady Naanaa, 2020. "A new approximate cluster deletion algorithm for diamond-free graphs," Journal of Combinatorial Optimization, Springer, vol. 39(2), pages 385-411, February.
    • Handle: RePEc:spr:jcomop:v:39:y:2020:i:2:d:10.1007_s10878-019-00477-z
    DOI: 10.1007/s10878-019-00477-z
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