NP-hard problems in hierarchical-tree clustering
Acta Informatica
Faster scaling algorithms for general graph matching problems
Journal of the ACM (JACM)
Which problems have strongly exponential complexity?
Journal of Computer and System Sciences
Exact algorithms for NP-hard problems: a survey
Combinatorial optimization - Eureka, you shrink!
Machine Learning
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
Parameterized Complexity Theory (Texts in Theoretical Computer Science. An EATCS Series)
Parameterized Complexity Theory (Texts in Theoretical Computer Science. An EATCS Series)
A more effective linear kernelization for cluster editing
Theoretical Computer Science
ICALP '09 Proceedings of the 36th International Colloquium on Automata, Languages and Programming: Part I
Going weighted: Parameterized algorithms for cluster editing
Theoretical Computer Science
Alternative parameterizations for cluster editing
SOFSEM'11 Proceedings of the 37th international conference on Current trends in theory and practice of computer science
Partition into triangles on bounded degree graphs
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
A 2k kernel for the cluster editing problem
Journal of Computer and System Sciences
On making directed graphs transitive
Journal of Computer and System Sciences
A golden ratio parameterized algorithm for Cluster Editing
Journal of Discrete Algorithms
Parameterized Complexity
Hi-index | 0.04 |
Given an undirected graph G=(V,E) and a nonnegative integer k, the NP-hard Cluster Editing problem asks whether G can be transformed into a disjoint union of cliques by modifying at most k edges. In this work, we study how ''local degree bounds'' influence the complexity of Cluster Editing and of the related Cluster Deletion problem which allows only edge deletions. We show that even for graphs with constant maximum degree Cluster Editing and Cluster Deletion are NP-hard and that this implies NP-hardness even if every vertex is incident with only a constant number of edge modifications. We further show that under some complexity-theoretic assumptions both Cluster Editing and Cluster Deletion cannot be solved within a running time that is subexponential in k, |V|, or |E|. Finally, we present a problem kernelization for the combined parameter ''number d of clusters and maximum number t of modifications incident with a vertex'' thus showing that Cluster Editing and Cluster Deletion become easier in case the number of clusters is upper-bounded.