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International Conference on Variable Neighborhood Search

ICVNS 2018: Variable Neighborhood Search pp 114–124Cite as

Finding Balanced Bicliques in Bipartite Graphs Using Variable Neighborhood Search

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Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 11328))

Abstract

The Maximum Balanced Biclique Problem (MBBP) consists of identifying a complete bipartite graph, or biclique, of maximum size within an input bipartite graph. This combinatorial optimization problem is solvable in polynomial time when the balance constraint is removed. However, it becomes \(\mathcal {NP}\)–hard when the induced subgraph is required to have the same number of vertices in each layer. Biclique graphs have been proven to be useful in several real-life applications, most of them in the field of biology, and the MBBP in particular can be applied in the design of programmable logic arrays or nanoelectronic systems. Most of the approaches found in literature for this problem are heuristic algorithms based on the idea of removing vertices from the input graph until a feasible solution is obtained; and more recently in the state of the art an evolutionary algorithm (MA/SM) has been proposed. As stated in previous works it is difficult to propose an effective local search method for this problem. Therefore, we propose the use of Reduced Variable Neighborhood Search (RVNS). This methodology is based on a random exploration of the considered neighborhoods and it does not require a local search.

This work has been partially founded by Ministerio de Economía y Competitividad with grant ref. TIN2015-65460-C2-2-P.

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Authors and Affiliations

  1. Department of Computer Sciences, Universidad Rey Juan Carlos, Móstoles, Spain

    Juan David Quintana, Jesús Sánchez-Oro & Abraham Duarte

Authors
  1. Juan David Quintana
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  2. Jesús Sánchez-Oro
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  3. Abraham Duarte
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Corresponding author

Correspondence to Jesús Sánchez-Oro .

Editor information

Editors and Affiliations

  1. University of Macedonia, Thessaloniki, Greece

    Angelo Sifaleras

  2. University of Kent, Canterbury, UK

    Said Salhi

  3. Royal Military College of Canada, Kingston, ON, Canada

    Jack Brimberg

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Quintana, J.D., Sánchez-Oro, J., Duarte, A. (2019). Finding Balanced Bicliques in Bipartite Graphs Using Variable Neighborhood Search. In: Sifaleras, A., Salhi, S., Brimberg, J. (eds) Variable Neighborhood Search. ICVNS 2018. Lecture Notes in Computer Science(), vol 11328. Springer, Cham. https://doi.org/10.1007/978-3-030-15843-9_10

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  • DOI: https://doi.org/10.1007/978-3-030-15843-9_10

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-030-15842-2

  • Online ISBN: 978-3-030-15843-9

  • eBook Packages: Computer ScienceComputer Science (R0)

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