Beyond the flow decomposition barrier
Journal of the ACM (JACM)
Cluster graph modification problems
Discrete Applied Mathematics - Discrete mathematics & data mining (DM & DM)
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 Enumerability of Cluster Editing and Related Problems
Theory of Computing Systems
The cluster editing problem: implementations and experiments
IWPEC'06 Proceedings of the Second international conference on Parameterized and Exact Computation
On making directed graphs transitive
Journal of Computer and System Sciences
A golden ratio parameterized algorithm for cluster editing
IWOCA'11 Proceedings of the 22nd international conference on Combinatorial Algorithms
Cluster editing with locally bounded modifications
Discrete Applied Mathematics
A golden ratio parameterized algorithm for Cluster Editing
Journal of Discrete Algorithms
Hi-index | 0.89 |
Cluster Deletion and Cluster Editing ask to transform a graph by at most k edge deletions or edge edits, respectively, into a cluster graph, i.e., disjoint union of cliques. Equivalently, a cluster graph has no conflict triples, i.e., two incident edges without a transitive edge. We solve the two problems in time O^@?(1.415^k) and O^@?(1.76^k), respectively. These results round off our earlier work by considerably improved time bounds. For Cluster Deletion we use a technique that cuts away small connected components that do no longer contribute to the exponential part of the time complexity. As this idea is simple and versatile, it may lead to improvements for several other parameterized graph problems. The improvement for Cluster Editing is achieved by using the full power of an earlier structure theorem for graphs where no edge is in three conflict triples.