On the complexity of approximating the independent set problem
Information and Computation
Relations between average case complexity and approximation complexity
STOC '02 Proceedings of the thiry-fourth annual ACM symposium on Theory of computing
Computers and Intractability: A Guide to the Theory of NP-Completeness
Computers and Intractability: A Guide to the Theory of NP-Completeness
A fast algorithm for the maximum clique problem
Discrete Applied Mathematics - Sixth Twente Workshop on Graphs and Combinatorial Optimization
Branch-And-Price: Column Generation for Solving Huge Integer Programs
Operations Research
The maximum edge biclique problem is NP-complete
Discrete Applied Mathematics
Biclustering Algorithms for Biological Data Analysis: A Survey
IEEE/ACM Transactions on Computational Biology and Bioinformatics (TCBB)
Inapproximability of maximum weighted edge biclique and its applications
TAMC'08 Proceedings of the 5th international conference on Theory and applications of models of computation
Finding maximum edge bicliques in convex bipartite graphs
COCOON'10 Proceedings of the 16th annual international conference on Computing and combinatorics
Biclique completion problems for multicast network design
Discrete Optimization
An exact algorithm for IP column generation
Operations Research Letters
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A biclique is a complete bipartite graph. Given an (L,R)-bipartite graph G=(V,E) and a positive integer k, the maximum edge biclique packing (mebp) problem consists in finding a set of at most k bicliques, subgraphs of G, such that the bicliques are vertex disjoint with respect to a subset of vertices S, where S@?{V,L,R}, and the number of edges inside the bicliques is maximized. The maximum edge biclique (meb) problem is a special case of the mebp problem in which k=1. Several applications of the meb problem have been studied and, in this paper, we describe applications of the mebp problem in metabolic networks and product bundling. In these applications the input graphs are very unbalanced (i.e., |R| is considerably greater than |L|), thus we consider carefully this property in our models. We introduce a new formulation for the meb problem and a branch-and-price scheme, using the classical branch rule by Ryan and Foster, for the mebp problem. Finally, we present computational experiments with instances that come from the described applications and also with randomly generated instances.