Journal
NETWORKS
Volume 71, Issue 2, Pages 136-152Publisher
WILEY
DOI: 10.1002/net.21791
Keywords
degree-based quasi-clique; quasi-clique; k-core; clique; clique relaxation; branch-and-bound; mixed integer programming
Funding
- Air Force Research Laboratory (AFRL) Mathematical Modeling and Optimization Institute
- Defense Threat Reduction Agency (DTRA) [HDTRA1-14-1-0065]
- Air Force [FA8651-16-2-0009, FA8651-08-D-0108]
- National Science Foundation [EFRI-1441231]
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We consider the problem of finding a degree-based -quasi-clique of maximum cardinality in a given graph for some fixed (0,1]. A degree-based -quasi-clique (often referred to as simply a quasi-clique) is a subgraph, where the degree of each vertex is at least times the maximum possible degree of a vertex in the subgraph. A degree-based -quasi-clique is a relative clique relaxation model, where the case of =1 corresponds to the well-known concept of a clique. In this article, we first prove that the problem is NP-hard for any fixed (0,1], which addresses one of the open questions in the literature. More importantly, we also develop new exact solution methods for solving the problem and demonstrate their advantages and limitations in extensive computational experiments with both random and real-world networks. Finally, we outline promising directions of future research including possible functional generalizations of the considered clique relaxation model. (c) 2017 Wiley Periodicals, Inc. NETWORKS, Vol. 71(2), 136-152 2018
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