Integer and combinatorial optimization
Integer and combinatorial optimization
Efficient identification of Web communities
Proceedings of the sixth ACM SIGKDD international conference on Knowledge discovery and data mining
Mining market data: a network approach
Computers and Operations Research
A novel approach to phylogenetic trees: d-Dimensional geometric Steiner trees
Networks - Special Issue on Trees
Mathematical models to reconstruct phylogenetic trees under the minimum evolution criterion
Networks - Special Issue on Trees
Extended and discretized formulations for the maximum clique problem
Computers and Operations Research
Clique Relaxations in Social Network Analysis: The Maximum k-Plex Problem
Operations Research
Algorithms for the maximum k-club problem in graphs
Journal of Combinatorial Optimization
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Given an undirected graph, the k -club problem seeks a maximum cardinality subset of nodes that induces a subgraph with diameter at most k. We present two new formulations for the 3-club problem: one is compact and the other has a nonpolynomial number of constraints. By defining an integer compact relaxation of the second formulation, we obtain a new upper bound on the 3-club optimum that improves on the 3-clique number bound. We derive new families of valid inequalities for the 3-club polytope and use them to strengthen the LP relaxations of the new models. The computational study is performed on 120 graphs with up to 200 nodes and edge densities reported in the literature to produce difficult instances of the 3-club problem. The results show that the new compact formulation is competitive with the exact solution methods reported in the literature, and that a large proportion of the LP gap is bridged with the new valid inequalities. © 2012 Wiley Periodicals, Inc. NETWORKS, 2012 © 2012 Wiley Periodicals, Inc.