  Clustering is a well-known and important problem with numerous applications.
The graph-based model is one of the typical cluster models. In the graph model,
clusters are generally defined as cliques. However, such an approach might be
too restrictive as in some applications, not all objects from the same cluster
must be connected. That is why different types of cliques relaxations often
considered as clusters.
  In our work, we consider a problem of partitioning graph into clusters and a
problem of isolating cluster of a special type whereby cluster we mean highly
connected subgraph. Initially, such clusterization was proposed by Hartuv and
Shamir. And their HCS clustering algorithm was extensively applied in practice.
It was used to cluster cDNA fingerprints, to find complexes in protein-protein
interaction data, to group protein sequences hierarchically into superfamily
and family clusters, to find families of regulatory RNA structures. The HCS
algorithm partitions graph in highly connected subgraphs. However, it is
achieved by deletion of not necessarily the minimum number of edges. In our
work, we try to minimize the number of edge deletions. We consider problems
from the parameterized point of view where the main parameter is a number of
allowed edge deletions.
