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A new approximate cluster deletion algorithm for diamond-free graphs

  • Sabrine MalekEmail author
  • Wady Naanaa
Article
  • 32 Downloads

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.

Keywords

Cluster deletion (CD) Polynomial algorithm (Butterfly, diamond)-free graphs Maximal clique Suboptimal algorithm Diamond-free graphs 

Notes

References

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© Springer Science+Business Media, LLC, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Faculty of Economics and Management of SfaxUniversity of SfaxSfaxTunisia
  2. 2.National Engineering School of TunisUniversity of Tunis El ManarTunisTunisia

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