Inspired by methods and theoretical results from parameterised algorithmics, we improve the state of the art in solving Cluster Editing, a prominent NP-hard clustering problem with applications in computational biology and beyond. In particular, we demonstrate that an extension of a certain preprocessing algorithm, called the (k + 1)-data reduction rule in parameterised algorithmics, embedded in a sophisticated branch-&-bound algorithm, improves over the performance of existing algorithms based

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... on Integer Linear Programming (ILP) and branch-&-bound. Furthermore, our version of the (k + 1)-rule outperforms the theoretically most effective preprocessing algorithm, which yields a 2k-vertex kernel. Notably, this 2k-vertex kernel is analysed empirically for the first time here. Our new algorithm was developed by integrating Programming by Optimisation into the classical algorithm engineering cycle -an approach which we expect to be successful in many other contexts. Introduction Cluster Editing is a prominent NP-hard combinatorial problem with important applications in computational biology, e.g. to cluster proteins or genes (see the recent survey by Böcker and Baumbach [6]). In machine learning and data mining, weighted variants of Cluster Editing are known as Correlation Clustering [4] and have been the subject of several recent studies (see, e.g., [8, 12] ). Here, we study the unweighted variant of the problem, with the goal of improving the state of the art in empirically solving it. Formally, as a decision problem it reads as follows: Cluster Editing Input: An undirected graph G = (V, E) and a positive integer k ∈ N. Question: Is there a set of at most k edge insertions and deletions that transform G into a cluster graph, that is, a graph in which each connected component is a complete graph? Major parts of this work were done during a research visit of SH at the University of British Columbia in Vancouver (Canada), supported by a "DFG Forschungsstipendium" (HA 7296/1-1).