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arXiv · 2002.09880

Mixed Integer Programming for Searching Maximum Quasi-Bicliques

Dmitry I. Ignatov·Polina Ivanova·Albina Zamaletdinova
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Abstract

This paper is related to the problem of finding the maximal quasi-bicliques in a bipartite graph (bigraph). A quasi-biclique in the bigraph is its "almost" complete subgraph. The relaxation of completeness can be understood variously; here, we assume that the subgraph is a $\gamma$-quasi-biclique if it lacks a certain number of edges to form a biclique such that its density is at least $\gamma \in (0,1]$. For a bigraph and fixed $\gamma$, the problem of searching for the maximal quasi-biclique consists of finding a subset of vertices of the bigraph such that the induced subgraph is a quasi-biclique and its size is maximal for a given graph. Several models based on Mixed Integer Programming (MIP) to search for a quasi-biclique are proposed and tested for working efficiency. An alternative model inspired by biclustering is formulated and tested; this model simultaneously maximizes both the size of the quasi-biclique and its density, using the least-square criterion similar to the one exploited by triclustering \textsc{TriBox}.

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BibTeXRIS

Dmitry I. Ignatov, Polina Ivanova, Albina Zamaletdinova. 2020-02-23. Mixed Integer Programming for Searching Maximum Quasi-Bicliques. https://doi.org/10.1007/978-3-030-37157-9_2

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