The maximum independent union of cliques problem: complexity and exact approaches

Zeynep Ertem (), Eugene Lykhovyd (), Yiming Wang () and Sergiy Butenko ()
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Zeynep Ertem: The University of Texas at Austin
Eugene Lykhovyd: Texas A&M University
Yiming Wang: Texas A&M University
Sergiy Butenko: Texas A&M University

Journal of Global Optimization, 2020, vol. 76, issue 3, No 8, 545-562

Abstract: Abstract Given a simple graph, the maximum independent union of cliques problem is to find a maximum-cardinality subset of vertices such that each connected component of the corresponding induced subgraph is a complete graph. This recently introduced problem allows both cliques and independent sets as feasible solutions and is of significant theoretical and applied interest. This paper establishes the complexity of the problem on several classes of graphs (planar, claw-free, and bipartite graphs), and develops an integer programming formulation and an exact combinatorial branch-and-bound algorithm for solving it. Results of numerical experiments with numerous benchmark instances are also reported.

Keywords: Clique; Independent set; Independent union of cliques; Network clustering; Cluster vertex deletion (search for similar items in EconPapers)
Date: 2020
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DOI: 10.1007/s10898-018-0694-2

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