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Open AccessArticle

Scale Reduction Techniques for Computing Maximum Induced Bicliques

Sabre Corporation, Southlake, TX 76092, USA
Department of Computer Science and Engineering, The University of Texas at Arlington, Arlington, TX 76019, USA
Department of Statistics and Data Science, The University of Texas at Austin, Austin, TX 78712, USA
Department of Industrial and Systems Engineering, Texas A&M University, College Station, TX 77843, USA
Author to whom correspondence should be addressed.
Algorithms 2017, 10(4), 113;
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)
PDF [288 KB, uploaded 10 October 2017]


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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