Cluster Editing with Locally Bounded Modifications Revisited

Cluster editing with locally bounded modifications

Given an undirected graph G = (V,E) and a nonnegative integer k, the NPhard Cluster Editing problem asks whether G can be transformed into a disjoint union of cliques by modifying at most k edges. In this work, we study how “local degree bounds” influence the complexity of Cluster Editing and of the related Cluster Deletion problem which allows only edge deletions. We show that even for graphs ...

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

We introduce the s-Plex Cluster Editing problem as a generalization of the wellstudied 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 (this is Cluster Editing), the task in the case of s-Plex Cluster Editing is to transform a grap...

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

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...

A Parameterized View on Multi-Layer Cluster Editing

In classical Cluster Editing we seek to transform a given graph into a disjoint union of cliques, called a cluster graph, using the fewest number of edge modifications (deletions or additions). Motivated by recent applications, we propose and study Cluster Editing in multi-layer graphs. A multi-layer graph consists of a set of simple graphs, called layers, that all have the same vertex set. In ...

Some Results on Boundedness in Locally Convex Cones