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Finding Balanced Bicliques in Bipartite Graphs Using Variable Neighborhood Search

  • Juan David Quintana
  • Jesús Sánchez-OroEmail author
  • Abraham Duarte
Conference paper
First Online:
Part of the Lecture Notes in Computer Science book series (LNCS, 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.

Keywords

Biclique Reduced VNS Bipartite 
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Authors and Affiliations

  1. 1.Department of Computer SciencesUniversidad Rey Juan CarlosMóstolesSpain

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