Solving the maximum clique problem using a tabu search approach
Annals of Operations Research - Special issue on Tabu search
Computers and Operations Research
New methods to color the vertices of a graph
Communications of the ACM
Toward Self-Integrating Software Applications for Supply Chain Management
Information Systems Frontiers
A fast algorithm for the maximum clique problem
Discrete Applied Mathematics - Sixth Twente Workshop on Graphs and Combinatorial Optimization
Variable neighborhood search for the maximum clique
Discrete Applied Mathematics - The fourth international colloquium on graphs and optimisation (GO-IV)
An efficient variable neighborhood search heuristic for very large scale vehicle routing problems
Computers and Operations Research
Neighborhood structures for the container loading problem: a VNS implementation
Journal of Heuristics
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Given a simple undirected graph G, a k-club is a subset of vertices inducing a subgraph of diameter at most k. The maximum k-club problem (MkCP) is to find a k-club of maximum cardinality in G. These structures, originally introduced to model cohesive subgroups in social network analysis, are of interest in network-based data mining and clustering applications. The maximum k-club problem is NP-hard, moreover, determining whether a given k-club is maximal (by inclusion) is NP-hard as well. This paper first provides a sufficient condition for testing maximality of a given k-club. Then it proceeds to develop a variable neighborhood search (VNS) heuristic and an exact algorithm for MkCP that uses the VNS solution as a lower bound. Computational experiments with test instances available in the literature show that the proposed algorithms are very effective on sparse instances and outperform the existing methods on most dense graphs from the testbed.