NP-hard problems in hierarchical-tree clustering
Acta Informatica
Substitution Decomposition on Chordal Graphs and Applications
ISA '91 Proceedings of the 2nd International Symposium on Algorithms
Polynomial-time data reduction for dominating set
Journal of the ACM (JACM)
Machine Learning
Cluster graph modification problems
Discrete Applied Mathematics - Discrete mathematics & data mining (DM & DM)
Aggregating inconsistent information: ranking and clustering
Proceedings of the thirty-seventh annual ACM symposium on Theory of computing
Graph-Modeled Data Clustering: Exact Algorithms for Clique Generation
Theory of Computing Systems
Correlation clustering with a fixed number of clusters
SODA '06 Proceedings of the seventeenth annual ACM-SIAM symposium on Discrete algorithm
Clustering with qualitative information
Journal of Computer and System Sciences - Special issue: Learning theory 2003
Parameterized Complexity Theory (Texts in Theoretical Computer Science. An EATCS Series)
Parameterized Complexity Theory (Texts in Theoretical Computer Science. An EATCS Series)
Invitation to data reduction and problem kernelization
ACM SIGACT News
Parametric Duality and Kernelization: Lower Bounds and Upper Bounds on Kernel Size
SIAM Journal on Computing
Exact algorithms for cluster editing: evaluation and experiments
WEA'08 Proceedings of the 7th international conference on Experimental algorithms
Extending the tractability border for closest leaf powers
WG'05 Proceedings of the 31st international conference on Graph-Theoretic Concepts in Computer Science
Applying modular decomposition to parameterized bicluster editing
IWPEC'06 Proceedings of the Second international conference on Parameterized and Exact Computation
A more effective linear kernelization for Cluster Editing
ESCAPE'07 Proceedings of the First international conference on Combinatorics, Algorithms, Probabilistic and Experimental Methodologies
Parameterized Complexity
Fixed-Parameter Algorithms for Graph-Modeled Date Clustering
TAMC '09 Proceedings of the 6th Annual Conference on Theory and Applications of Models of Computation
A More Relaxed Model for Graph-Based Data Clustering: s-Plex Editing
AAIM '09 Proceedings of the 5th International Conference on Algorithmic Aspects in Information and Management
Graph-Based Data Clustering with Overlaps
COCOON '09 Proceedings of the 15th Annual International Conference on Computing and Combinatorics
On Making Directed Graphs Transitive
WADS '09 Proceedings of the 11th International Symposium on Algorithms and Data Structures
Going weighted: Parameterized algorithms for cluster editing
Theoretical Computer Science
A Linear Vertex Kernel for Maximum Internal Spanning Tree
ISAAC '09 Proceedings of the 20th International Symposium on Algorithms and Computation
Editing Graphs into Disjoint Unions of Dense Clusters
ISAAC '09 Proceedings of the 20th International Symposium on Algorithms and Computation
Iterative compression and exact algorithms
Theoretical Computer Science
A 2k Kernel for the cluster editing problem
COCOON'10 Proceedings of the 16th annual international conference on Computing and combinatorics
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
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
Kernelization of packing problems
Proceedings of the twenty-third annual ACM-SIAM symposium on Discrete Algorithms
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
A polynomial kernel for feedback arc set on bipartite tournaments
ISAAC'11 Proceedings of the 22nd international conference on Algorithms and Computation
Graph-based data clustering with overlaps
Discrete Optimization
Cluster editing with locally bounded modifications
Discrete Applied Mathematics
A golden ratio parameterized algorithm for Cluster Editing
Journal of Discrete Algorithms
A linear vertex kernel for maximum internal spanning tree
Journal of Computer and System Sciences
Clustering with local restrictions
Information and Computation
A Polynomial Kernel for Feedback Arc Set on Bipartite Tournaments
Theory of Computing Systems
Hi-index | 5.23 |
In the NP-hard Cluster Editing problem, we have as input an undirected graph G and an integer k=0. The question is whether we can transform G, by inserting and deleting at most k edges, into a cluster graph, that is, a union of disjoint cliques. We first confirm a conjecture by Michael Fellows [IWPEC 2006] that there is a polynomial-time kernelization for Cluster Editing that leads to a problem kernel with at most 6k vertices. More precisely, we present a cubic-time algorithm that, given a graph G and an integer k=0, finds a graph G^' and an integer k^'@?k such that G can be transformed into a cluster graph by at most k edge modifications iff G^' can be transformed into a cluster graph by at most k^' edge modifications, and the problem kernel G^' has at most 6k vertices. So far, only a problem kernel of 24k vertices was known. Second, we show that this bound for the number of vertices of G^' can be further improved to 4k vertices. Finally, we consider the variant of Cluster Editing where the number of cliques that the cluster graph can contain is stipulated to be a constant d0. We present a simple kernelization for this variant leaving a problem kernel of at most (d+2)k+d vertices.