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Cluster Editing: Kernelization Based on Edge Cuts [chapter]

Yixin Cao, Jianer Chen
2010 Lecture Notes in Computer Science  
Our techniques are based on the study of the relationship between cluster editing and graph edge-cuts.  ...  Thus far most kernelization algorithms for this problem are based on the concept of critical cliques.  ...  The above results that reveal the relations between the structures of the cluster editing problem and graph edge cuts not only form the basis for our kernelization results presented in the current paper  ... 
doi:10.1007/978-3-642-17493-3_8 fatcat:dea5flr4rnfy7jvz3gsvydiycq

Exact Algorithms for Cluster Editing: Evaluation and Experiments

Sebastian Böcker, Sebastian Briesemeister, Gunnar W. Klau
2009 Algorithmica  
We present empirical results for the Cluster Editing problem using exact methods from fixed-parameter algorithmics and linear programming.  ...  In addition to the fastest known fixed-parameter branching strategy for the problem, we investigate an integer linear program (ILP) formulation of the problem using a cutting plane approach.  ...  Integer Linear Programming and Branch-and-Cut In this section we describe an algorithm for Weighted Cluster Editing, which is based on mathematical optimization.  ... 
doi:10.1007/s00453-009-9339-7 fatcat:nk6t7ouz6beetjoj6v3ht6a4su

Even faster parameterized cluster deletion and cluster editing

Sebastian Böcker, Peter Damaschke
2011 Information Processing Letters  
Cluster Deletion and Cluster Editing ask to transform a graph by at most k edge deletions or edge edits, respectively, into a cluster graph, i.e., disjoint union of cliques.  ...  Even faster parameterized cluster deletion and cluster editing.  ...  Acknowledgment The second author has been supported by the Swedish Research Council (Vetenskapsrådet), grant 2007-6437, "Combinatorial inference algorithms -parameterization and clustering".  ... 
doi:10.1016/j.ipl.2011.05.003 fatcat:7gguo5pwgnf3do2vebdlr75rmq

Cluster Editing with Locally Bounded Modifications Revisited [chapter]

Peter Damaschke
2013 Lecture Notes in Computer Science  
For Cluster Editing where both the number of clusters and the edit degree are bounded, we speed up the kernelization by almost a factor n compared to Komusiewicz and Uhlmann (2012) , at cost of a marginally  ...  worse kernel size bound.  ...  Another difference to [6] is that the "old" reduction rules are only based on the (d, t)-constraints, whereas we find edit-optimal clusters, as defined below. Definition 1.  ... 
doi:10.1007/978-3-642-45278-9_38 fatcat:jecsuoqwvngg3nbprs4y647whq

Cluster editing with locally bounded modifications

Christian Komusiewicz, Johannes Uhlmann
2012 Discrete Applied Mathematics  
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  ...  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.  ...  Our algorithms for these problems are based on simple data reduction rules that produce in O(|V | 3 ) time a problem kernel consisting of at most 4dt vertices (in the case of Cluster Editing) and 2dt vertices  ... 
doi:10.1016/j.dam.2012.05.019 fatcat:355xaizmhffllamz45kci6qrri

Subexponential fixed-parameter tractability of cluster editing [article]

Fedor V. Fomin and Stefan Kratsch and Marcin Pilipczuk and Michał Pilipczuk and Yngve Villanger
2013 arXiv   pre-print
In the Correlation Clustering, also known as Cluster Editing, we are given an undirected n-vertex graph G and a positive integer k.  ...  The task is to decide if G can be transformed into a cluster graph, i.e., a disjoint union of cliques, by changing at most k adjacencies, i.e. by adding/deleting at most k edges.  ...  We thank Christian Komusiewicz for pointing us to the recent results on Cluster Editing [8, 31] and his thesis [30] .  ... 
arXiv:1112.4419v4 fatcat:wrwtz2givvfyjfzefdluoq3n7u

A more effective linear kernelization for cluster editing

Jiong Guo
2009 Theoretical Computer Science  
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.  ...  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.  ...  Based on these two data reduction rules, we achieve a problem kernel of 4k vertices for Cluster Editing. Theorem 2.  ... 
doi:10.1016/j.tcs.2008.10.021 fatcat:ty2rxhhkb5fg7chymuxk5us4fu

A More Relaxed Model for Graph-Based Data Clustering: s-Plex Cluster Editing

Jiong Guo, Christian Komusiewicz, Rolf Niedermeier, Johannes Uhlmann
2010 SIAM Journal on Discrete Mathematics  
We develop a provably effective preprocessing based on data reduction (yielding a so-called problem kernel), a forbidden subgraph characterization of s-plex cluster graphs, and a depth-bounded search tree  ...  We introduce the s-Plex Cluster Editing problem as a generalization of the wellstudied Cluster Editing problem, both being NP-hard and both being motivated by graph-based data clustering.  ...  We are grateful to Falk Hüffner for inspiring discussions in the early phase of this research and anonymous referees of SIAM Journal on Discrete Mathematics for detailed feedback improving our presentation  ... 
doi:10.1137/090767285 fatcat:dnkgz4fpgnf3lmcuenkg3p6kxe

A golden ratio parameterized algorithm for Cluster Editing

Sebastian Böcker
2012 Journal of Discrete Algorithms  
We then show that Integer-Weighted Cluster Editing remains NP-hard for graphs that have a particularly simple structure: namely, a clique minus the edges of a triangle.  ...  The Cluster Editing problem asks to transform a graph by at most k edge modifications into a disjoint union of cliques. The problem is NP-complete, but several parameterized algorithms are known.  ...  Cluster Editing.  ... 
doi:10.1016/j.jda.2012.04.005 fatcat:2iy7cudorfbkpamhzysy6h2nau

Going weighted: Parameterized algorithms for cluster editing

S. Böcker, S. Briesemeister, Q.B.A. Bui, A. Truss
2009 Theoretical Computer Science  
The goal of the Cluster Editing problem is to make the fewest changes to the edge set of an input graph such that the resulting graph is a disjoint union of cliques.  ...  In this paper, we present a number of surprisingly simple search tree algorithms for Weighted Cluster Editing assuming that edge insertion and deletion costs are positive integers.  ...  However, this does not result in a kernel for Weighted Cluster Editing.  ... 
doi:10.1016/j.tcs.2009.05.006 fatcat:56ooabwianculhxhqm3ei5woue

Fixed-Parameter Enumerability of Cluster Editing and Related Problems

Peter Damaschke
2008 Theory of Computing Systems  
The result is based on a property of twin-free graphs. We also give FPT results for problem versions avoiding certain artificial clusterings.  ...  Cluster Editing is transforming a graph by at most k edge insertions or deletions into a disjoint union of cliques. This problem is fixed-parameter tractable (FPT).  ...  Acknowledgements This work was partially supported by the Swedish Research Council (Vetenskapsrådet), grant no. 2007-6437, "Combinatorial inference algorithms -parameterization and clustering".  ... 
doi:10.1007/s00224-008-9130-1 fatcat:zsxnrpedoba35igvstvsndv46i

Programming by Optimisation Meets Parameterised Algorithmics: A Case Study for Cluster Editing [chapter]

Sepp Hartung, Holger H. Hoos
2015 Lecture Notes in Computer Science  
on Integer Linear Programming (ILP) and branch-&-bound.  ...  Question: Is there a set of at most k edge insertions and deletions that transform G into a cluster graph, that is, a graph in which each connected component is a complete graph?  ...  We thank Tomasz Przedmojski who provided, as part of his bachelor thesis, an accelerated implementation of the O(M · k) kernel [20] .  ... 
doi:10.1007/978-3-319-19084-6_5 fatcat:yq65bnk7m5e5zphfjqs2zpmhni

A Golden Ratio Parameterized Algorithm for Cluster Editing [chapter]

Sebastian Böcker
2011 Lecture Notes in Computer Science  
A golden ratio parameterized algorithm for Cluster Editing.  ...  The Cluster Editing problem asks to transform a graph by at most k edge modifications into a disjoint union of cliques. The problem is NP-complete, but several parameterized algorithms are known.  ...  Cluster Editing.  ... 
doi:10.1007/978-3-642-25011-8_7 fatcat:kif6oj3r6bfenlkubucyvnrfoa

Tight bounds for parameterized complexity of Cluster Editing with a small number of clusters

Fedor V. Fomin, Stefan Kratsch, Marcin Pilipczuk, Michał Pilipczuk, Yngve Villanger
2014 Journal of computer and system sciences (Print)  
For more information, please contact the WRAP Team at: publications@warwick.ac.uk Tight bounds for parameterized complexity of Cluster Editing with a small number of clusters $ Abstract In the Cluster  ...  Editing problem, also known as Correlation Clustering, we are given an undirected n-vertex graph G and a positive integer k.  ...  We thank Christian Komusiewicz for pointing us to the recent results on Cluster Editing [7, 35] . We also thank an anonymous referee for suggesting the current, elegant proof of Lemma 10.  ... 
doi:10.1016/j.jcss.2014.04.015 fatcat:hc7pkihgofdrxj5gz7fvgxsptu

A FIXED-PARAMETER APPROACH FOR WEIGHTED CLUSTER EDITING

SEBASTIAN BÖCKER, SEBASTIAN BRIESEMEISTER, QUANG BAO ANH BUI, ANKE TRUB
2007 Proceedings of the 6th Asia-Pacific Bioinformatics Conference  
Several well-known clustering algorithms are based on transforming the input matrix into a weighted graph although the resulting WEIGHTED CLUSTER EDITING problem is computationally hard: here, we transform  ...  the input graph into a disjoint union of cliques such that the sum of weights of all modified edges is minimized.  ...  , WEIGHTED CLUSTER EDITING does not make any prior assumptions on the number of clusters or their structure.  ... 
doi:10.1142/9781848161092_0023 fatcat:j2r3dzfxprdxzdx3hetthxojua
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