NP-hard problems in hierarchical-tree clustering
Acta Informatica
Journal of Algorithms
Fixed-parameter tractability of graph modification problems for hereditary properties
Information Processing Letters
FOCS '02 Proceedings of the 43rd Symposium on Foundations of Computer Science
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
Clustering with qualitative information
Journal of Computer and System Sciences - Special issue: Learning theory 2003
Correlation clustering in general weighted graphs
Theoretical Computer Science - Approximation and online algorithms
Invitation to data reduction and problem kernelization
ACM SIGACT News
Applying modular decomposition to parameterized bicluster editing
IWPEC'06 Proceedings of the Second international conference on Parameterized and Exact Computation
The cluster editing problem: implementations and experiments
IWPEC'06 Proceedings of the Second international conference on Parameterized and Exact Computation
The lost continent of polynomial time: preprocessing and kernelization
IWPEC'06 Proceedings of the Second international conference on Parameterized and Exact Computation
Efficient parameterized preprocessing for cluster editing
FCT'07 Proceedings of the 16th international conference on Fundamentals of Computation Theory
A more effective linear kernelization for Cluster Editing
ESCAPE'07 Proceedings of the First international conference on Combinatorics, Algorithms, Probabilistic and Experimental Methodologies
Fixed-Parameter Algorithms for Graph-Modeled Date Clustering
TAMC '09 Proceedings of the 6th Annual Conference on Theory and Applications of Models of Computation
Complexity issues for the sandwich homogeneous set problem
Discrete Applied Mathematics
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The Correlation Clusteringproblem, also known as the Cluster Editingproblem, seeks to edit a given graph by adding and deleting edges to obtain a collection of vertex-disjoint cliques, such that the editing cost is minimized. The Edge Clique Partitioningproblem seeks to partition the edges of a given graph into edge-disjoint cliques, such that the number of cliques is minimized. Both problems are known to be NP-hard, and they have been previously studied with respect to approximation and fixed parameter tractability. In this paper we study these two problems in a more general setting that we term fuzzy graphs, where the input graphs may have missing information, meaning that whether or not there is an edge between some pairs of vertices of the input graph can be undecided.For fuzzy graphs the Correlation Clusteringand Edge Clique Partitioningproblems have previously been studied only with respect to approximation. Here we give parameterized algorithms based on kernelization for both problems. We prove that the Correlation Clusteringproblem is fixed-parameter tractable on fuzzy graphs when parameterized by (k,r), where kis the editing cost and ris the minimum number of vertices required to cover the undecided edges. In particular we show that it has a polynomial-time reduction to a problem kernel on O(k2+ r) vertices. We provide an analogous result for the Edge Clique Partitioningproblem on fuzzy graphs. Using (k,r) as parameters, where kbounds the size of the partition, and ris the minimum number of vertices required to cover the undecided edges, we describe a polynomial-time kernelization to a problem kernel on O(k4·3r) vertices. This implies fixed-parameter tractability for this parameterization. Furthermore we also show that parameterizing only by the number of cliques k, is not enough to obtain fixed-parameter tractability. The problem remains, in fact, NP-hard for each fixed k 2.