NP-hard problems in hierarchical-tree clustering
Acta Informatica
A new approach to the maximum-flow problem
Journal of the ACM (JACM)
The Complexity of Multiterminal Cuts
SIAM Journal on Computing
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
Fixed-Parameter Algorithms for Cluster Vertex Deletion
Theory of Computing Systems - Special Section: Algorithmic Game Theory; Guest Editors: Burkhard Monien and Ulf-Peter Schroeder
Alternative parameterizations for cluster editing
SOFSEM'11 Proceedings of the 37th international conference on Current trends in theory and practice of computer science
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
A 2k kernel for the cluster editing problem
Journal of Computer and System Sciences
A More Relaxed Model for Graph-Based Data Clustering: $s$-Plex Cluster Editing
SIAM Journal on Discrete Mathematics
Cluster editing with locally bounded modifications
Discrete Applied Mathematics
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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(1.76^k+m+n) to O(1.62^k+m+n) for m edges and n vertices. 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. This is achieved by keeping track of the parity of merged vertices. Second, by repeatedly branching we can isolate vertices, releasing cost. Third, we use a known characterization of graphs with few conflicts. We then show that Integer-Weighted Cluster Editing remains NP-hard for graphs that have a particularly simple structure: namely, a clique minus the edges of a triangle.