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Student
Title
Supervisor
Faculty
Educational Programme
Final Grade
Year of Graduation
Polina Ivanova
Searching for Maximum Quasi-bicliques
Data Science
(Master’s programme)
8
2017
This paper is devoted to the investigation of the problem of finding the maximal quasi-bicliques in a bipartite graph. Quasi-biclique in the graph is called an almost complete subgraph. Relaxation of completeness can be understood variously; in this paper, we assume that the subgraph is a quasi-biclique if it lacks gamma * 100% of the edges to become a clique for fixed gamma. For a bigraph and a fixed gamma, the problem of finding the maximal quasi-biclique consists in finding subsets of the fractions of the graph such that the induced by these subsets subgraph is a quasi-biclique and its size is maximal for a given graph.

In this graduation work, algorithms that use models of mixed integer programming (MIP) to search for a quasi-biclique are constructed and tested for working efficiency.

Also, a model is tested that simultaneously maximizes both the size of the quasi-bicli and its density, using the idea of the TriBox method of triclaster generation in a triadic context narrowed to two-dimensional space.

Keywords: quasi-biclique, problem of finding the maximal quasi-biclik, mixed integer programming, MIP.

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