Parameterized Algorithms for Partitioning Graphs into Highly Connected Clusters

TL;DR

This paper introduces parameterized algorithms for partitioning graphs into highly connected clusters, aiming to minimize edge deletions, with applications in bioinformatics and network analysis.

Contribution

It develops new algorithms for graph partitioning into highly connected clusters that optimize edge deletions, extending prior methods like HCS clustering.

Findings

Algorithms effectively minimize edge deletions in cluster partitioning

Applications include bioinformatics and network analysis

Improved theoretical bounds on cluster connectivity

Abstract

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.