NP-hard problems in hierarchical-tree clustering
Acta Informatica
A new approach to the maximum-flow problem
Journal of the ACM (JACM)
A general method to speed up fixed-parameter-tractable algorithms
Information Processing Letters
Substitution Decomposition on Chordal Graphs and Applications
ISA '91 Proceedings of the 2nd International Symposium on Algorithms
Graph-Modeled Data Clustering: Exact Algorithms for Clique Generation
Theory of Computing Systems
A more effective linear kernelization for cluster editing
Theoretical Computer Science
Going weighted: Parameterized algorithms for cluster editing
Theoretical Computer Science
Bounded-Degree Techniques Accelerate Some Parameterized Graph Algorithms
Parameterized and Exact Computation
A 2k Kernel for the cluster editing problem
COCOON'10 Proceedings of the 16th annual international conference on Computing and combinatorics
Even faster parameterized cluster deletion and cluster editing
Information Processing Letters
Fixed-parameter tractability of multicut parameterized by the size of the cutset
Proceedings of the forty-third annual ACM symposium on Theory of computing
On making directed graphs transitive
Journal of Computer and System Sciences
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The Cluster Editing problem asks to transform a graph by at most k edge modifications into a disjoint union of cliques. The problem is NP-complete, but several parameterized algorithms are known. We present a novel search tree algorithm for the problem, which improves running time from O*(1.76k) to O*(1.62k). In detail, we can show that we can always branch with branching vector (2,1) or better, resulting in the golden ratio as the base of the search tree size. Our algorithm uses a well-known transformation to the integer-weighted counterpart of the problem. To achieve our result, we combine three techniques: First, we show that zero-edges in the graph enforce structural features that allow us to branch more efficiently. Second, by repeatedly branching we can isolate vertices, releasing costs. Finally, we use a known characterization of graphs with few conflicts.