A Fast Branching Algorithm for Cluster Vertex Deletion

Abstract

AbstractIn the family of clustering problems we are given a set of objects (vertices of the graph), together with some observed pairwise similarities (edges). The goal is to identify clusters of similar objects by slightly modifying the graph to obtain a cluster graph (disjoint union of cliques).Hüffner et al. [LATIN 2008, Theory Comput. Syst. 2010] initiated the parameterized study of Cluster Vertex Deletion, where the allowed modification is vertex deletion, and presented an elegant \(\mathcal{O}(2^k k^9 + nm)\)-time fixed-parameter algorithm, parameterized by the solution size. In the last 5 years, this algorithm remained the fastest known algorithm for Cluster Vertex Deletion and, thanks to its simplicity, became one of the textbook examples of an application of the iterative compression principle. In our work we break the 2k-barrier for Cluster Vertex Deletion and present an \(\mathcal{O}(1.9102^k (n+m))\)-time branching algorithm.KeywordsVertex CoverMinimum SolutionCluster GraphAuxiliary GraphMinimum Vertex CoverThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.