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Educational Programme
Final Grade
Year of Graduation
Albina Zamaletdinova
Search For Maximal Quasi - Triclique Using Mixed Integer Programming
The problem of finding a maximum gamma-quasi-triclique is considered. Given a

tripartite undirected graph and a constant gamma, gamma from 0 to 1, a subset of

vertices is called a gamma-quasi-triclique if vertex induced subgraph has

dnsity at least gamma for a fixed gamma.

gamma-quasi-triclique can be countered as a relaxaion of a well-known triclique concept

for gamma = 1. This problem is NP-hard. In this work a maximum gamma-quasi-triclique

greedy algorithm was developed and tested. Also this problem was formulated

in the context of mixed integer programming and solved using IMB CPLEX

software. The results of two different approaches were compared on several realworld

datasets. While greedy algorithm finds optimal gamma-quasi-triclique in a shorter

time, the size of the triclique is always smaller than the one found by the mixed

integer programming approach.

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