Machine Learning
FOCS '02 Proceedings of the 43rd Symposium on Foundations of Computer Science
COCOON '02 Proceedings of the 8th Annual International Conference on Computing and Combinatorics
Cluster Graph Modification Problems
WG '02 Revised Papers from the 28th International Workshop on Graph-Theoretic Concepts in Computer Science
Parameterized enumeration, transversals, and imperfect phylogeny reconstruction
Theoretical Computer Science - Parameterized and exact computation
Graph-modeled data clustering: fixed-parameter algorithms for clique generation
CIAC'03 Proceedings of the 5th Italian conference on Algorithms and complexity
Finding k disjoint triangles in an arbitrary graph
WG'04 Proceedings of the 30th international conference on Graph-Theoretic Concepts in Computer Science
Linear kernels in linear time, or how to save k colors in O(n2) steps
WG'04 Proceedings of the 30th international conference on Graph-Theoretic Concepts in Computer Science
Parameterized Complexity
Fixed-parameter tractable generalizations of cluster editing
CIAC'06 Proceedings of the 6th Italian conference on Algorithms and Complexity
The cluster editing problem: implementations and experiments
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
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Cluster Editing is the problem of changing a graph G by at most k edge insertions or deletions into a disjoint union of cliques. The problem is motivated from computational biology and known to be FPT. We study the enumeration of all solutions with a minimal set of edge changes. Enumerations can support efficient decisions between ambiguous solutions. We prove that all minimal solutions differ only on a so-called a full kernel of at most k2/4+O(k) vertices. This bound is tight. For ambiguous edges we get an optimal bound up to a constant factor. Finally we give an algorithm that outputs a compressed enumeration in O*(2.4k) time.