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Algorithms 2017, 10(4), 113; https://doi.org/10.3390/a10040113

Scale Reduction Techniques for Computing Maximum Induced Bicliques

1
Sabre Corporation, Southlake, TX 76092, USA
2
Department of Computer Science and Engineering, The University of Texas at Arlington, Arlington, TX 76019, USA
3
Department of Statistics and Data Science, The University of Texas at Austin, Austin, TX 78712, USA
4
Department of Industrial and Systems Engineering, Texas A&M University, College Station, TX 77843, USA
*
Author to whom correspondence should be addressed.
Received: 16 June 2017 / Revised: 19 September 2017 / Accepted: 27 September 2017 / Published: 4 October 2017
(This article belongs to the Special Issue Algorithms for Community Detection in Complex Networks)
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Abstract

Given a simple, undirected graph G, a biclique is a subset of vertices inducing a complete bipartite subgraph in G. In this paper, we consider two associated optimization problems, the maximum biclique problem, which asks for a biclique of the maximum cardinality in the graph, and the maximum edge biclique problem, aiming to find a biclique with the maximum number of edges in the graph. These NP-hard problems find applications in biclustering-type tasks arising in complex network analysis. Real-life instances of these problems often involve massive, but sparse networks. We develop exact approaches for detecting optimal bicliques in large-scale graphs that combine effective scale reduction techniques with integer programming methodology. Results of computational experiments with numerous real-life network instances demonstrate the performance of the proposed approach. View Full-Text
Keywords: maximum biclique; biclustering; complex networks; community detection maximum biclique; biclustering; complex networks; community detection
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Shahinpour, S.; Shirvani, S.; Ertem, Z.; Butenko, S. Scale Reduction Techniques for Computing Maximum Induced Bicliques. Algorithms 2017, 10, 113.

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