On the complexity of bicoloring clique hypergraphs of graphs
Journal of Algorithms
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)
Applying Modular Decomposition to Parameterized Cluster Editing Problems
Theory of Computing Systems
A more effective linear kernelization for cluster editing
Theoretical Computer Science
Digraphs: Theory, Algorithms and Applications
Digraphs: Theory, Algorithms and Applications
Fixed-Parameter Algorithms for Cluster Vertex Deletion
Theory of Computing Systems - Special Section: Algorithmic Game Theory; Guest Editors: Burkhard Monien and Ulf-Peter Schroeder
Efficient parameterized preprocessing for cluster editing
FCT'07 Proceedings of the 16th international conference on Fundamentals of Computation Theory
Parameterized Complexity
Some Parameterized Problems On Digraphs
The Computer Journal
Efficient algorithms for Eulerian extension
WG'10 Proceedings of the 36th international conference on Graph-theoretic concepts in computer science
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We present the first thorough theoretical analysis of the Transitivity Editing problem on digraphs. Herein, the task is to perform a minimum number of arc insertions or deletions in order to make a given digraph transitive. This problem has recently been identified as important for the detection of hierarchical structure in molecular characteristics of disease. Mixing up Transitivity Editing with the companion problems on undirected graphs, it has been erroneously claimed to be NP-hard. We correct this error by presenting a first proof of NP-hardness, which also extends to the restricted cases where the input digraph is acyclic or has maximum degree four. Moreover, we improve previous fixed-parameter algorithms, now achieving a running time of O (2.57 k + n 3) for an n -vertex digraph if k arc modifications are sufficient to make it transitive. In particular, providing an O (k 2)-vertex problem kernel, we positively answer an open question from the literature. In case of digraphs with maximum degree d , an O (k ·d )-vertex problem kernel can be shown. We also demonstrate that if the input digraph contains no "diamond structure", then one can always find an optimal solution that exclusively performs arc deletions. Most of our results (including NP-hardness) can be transferred to the Transitivity Deletion problem, where only arc deletions are allowed.