Skeleton-Based Clustering by Quasi-Threshold Editing

AbstractWe consider the problem of transforming a given graph into a quasi-threshold graph using a minimum number of edge additions and deletions. Building on the previously proposed heuristic Quasi-Threshold Mover (QTM), we present improvements both in terms of running time and quality. We propose a novel, linear-time algorithm that solves the inclusion-minimal variant of this problem, i.e., a set of edge edits such that no subset of them also transforms the given graph into a quasi-threshold graph. In an extensive experimental evaluation, we apply these algorithms to a large set of graphs from different applications and find that they lead QTM to find solutions with fewer edits. Although the inclusion-minimal algorithm needs significantly more edits on its own, it outperforms the initialization heuristic previously proposed for QTM.