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Mixed Integer Programming for Searching Maximum Quasi-Bicliques
- Source :
- Springer Proceedings in Mathematics & Statistics, vol 315. Springer, Cham (2020)
- Publication Year :
- 2020
-
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}.<br />Comment: This paper draft is stored here for self-archiving purposes
Details
- Database :
- arXiv
- Journal :
- Springer Proceedings in Mathematics & Statistics, vol 315. Springer, Cham (2020)
- Publication Type :
- Report
- Accession number :
- edsarx.2002.09880
- Document Type :
- Working Paper
- Full Text :
- https://doi.org/10.1007/978-3-030-37157-9_2