A More Relaxed Model for Graph-Based Data Clustering: s-Plex Editing

Abstract

We introduce the s -Plex Editing problem generalizing the well-studied Cluster Editing problem, both being NP-hard and both being motivated by graph-based data clustering. Instead of transforming a given graph by a minimum number of edge modifications into a disjoint union of cliques ( Cluster Editing ), the task in the case of s -Plex Editing is now to transform a graph into a disjoint union of so-called s -plexes. Herein, an s -plex denotes a vertex set inducing a (sub)graph where every vertex has edges to all but at most s vertices in the s -plex. Cliques are 1-plexes. The advantage of s -plexes for s *** 2 is that they allow to model a more relaxed cluster notion (s -plexes instead of cliques), which better reflects inaccuracies of the input data. We develop a provably efficient and effective preprocessing based on data reduction (yielding a so-called problem kernel), a forbidden subgraph characterization of s -plex cluster graphs, and a depth-bounded search tree which is used to find optimal edge modification sets. Altogether, this yields efficient algorithms in case of moderate numbers of edge modifications.