Abstract
We present efficient fixed-parameter algorithms for the NP-complete edge modification problems Cluster Editing and Cluster Deletion. Here, the goal is to make the fewest changes to the edge set of an input graph such that the new graph is a vertex-disjoint union of cliques. Allowing up to k edge additions and deletions (Cluster Editing), we solve this problem in O(2.27k + |V|3) time; allowing only up to k edge deletions (Cluster Deletion), we solve this problem in O(1.77k + |V|3) time. The key ingredients of our algorithms are two easy to implement bounded search tree algorithms and an efficient polynomial-time reduction to a problem kernel of size O(k3). This improves and complements previous work. Finally, we discuss further improvements on search tree sizes using computer-generated case distinctions.
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Gramm, J., Guo, J., Hüffner, F. et al. Graph-Modeled Data Clustering: Exact Algorithms for Clique Generation. Theory Comput Syst 38, 373–392 (2005). https://doi.org/10.1007/s00224-004-1178-y
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DOI: https://doi.org/10.1007/s00224-004-1178-y