### Programming by Optimisation Meets Parameterised Algorithmics: A Case Study for Cluster Editing [chapter]

Sepp Hartung, Holger H. Hoos
2015 Lecture Notes in Computer Science
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
more » ... 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).