  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}.
