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Subexponential parameterized algorithms on graphs of boundedgenus and Hminorfree Graphs
"... ... Building on these results, we develop subexponential fixedparameter algorithms for dominating set, vertex cover, and set cover in any class of graphs excluding a fixed graph H as a minor. Inparticular, this general category of graphs includes planar graphs, boundedgenus graphs, singlecrossing ..."
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Cited by 63 (22 self)
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... Building on these results, we develop subexponential fixedparameter algorithms for dominating set, vertex cover, and set cover in any class of graphs excluding a fixed graph H as a minor. Inparticular, this general category of graphs includes planar graphs, boundedgenus graphs, singlecrossingminorfree graphs, and anyclass of graphs that is closed under taking minors. Specifically, the running time is 2O(pk)nh, where h is a constant depending onlyon H, which is polynomial for k = O(log² n). We introducea general approach for developing algorithms on Hminorfreegraphs, based on structural results about Hminorfree graphs at the
New races in parameterized algorithmics
 IN: PROCEEDINGS OF THE 37TH INTERNATIONAL SYMPOSIUM ON MATHEMATICAL FOUNDATIONS OF COMPUTER SCIENCE (MFCS ’12), LNCS
"... Once having classified an NPhard problem fixedparameter tractable with respect to a certain parameter, the race for the most efficient fixedparameter algorithm starts. Herein, the attention usually focuses on improving the running time factor exponential in the considered parameter, and, in case ..."
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Cited by 10 (7 self)
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Once having classified an NPhard problem fixedparameter tractable with respect to a certain parameter, the race for the most efficient fixedparameter algorithm starts. Herein, the attention usually focuses on improving the running time factor exponential in the considered parameter, and, in case of kernelization algorithms, to improve the bound on the kernel size. Both from a practical as well as a theoretical point of view, however, there are further aspects of efficiency that deserve attention. We discuss several of these aspects and particularly focus on the search for “stronger parameterizations” in developing fixedparameter algorithms.
Cluster editing with locally bounded modifications
 Discrete Applied Mathematics
"... Given an undirected graph G = (V,E) and a nonnegative integer k, the NPhard Cluster Editing problem asks whether G can be transformed into a disjoint unionof cliques by modifying atmost k edges. Inthiswork, westudy how “local degree bounds ” influence the complexity of Cluster Editing andof the rela ..."
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Cited by 9 (4 self)
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Given an undirected graph G = (V,E) and a nonnegative integer k, the NPhard Cluster Editing problem asks whether G can be transformed into a disjoint unionof cliques by modifying atmost k edges. Inthiswork, westudy how “local degree bounds ” influence the complexity of Cluster Editing andof the related Cluster Deletionproblem which allows only edge deletions. We show that even for graphs with constant maximum degree Cluster Editing and Cluster Deletion are NPhard and that this implies NPhardness even if every vertex is incident with only a constant number of edge modifications. We further show that under some complexitytheoretic assumptions both Cluster Editing and Cluster Deletion cannot be solved within a running time that is subexponential in k, V, or E. Finally, we present a problem kernelization for the combined parameter “number d of clusters andmaximumnumber tofmodificationsincident withavertex ” thus showing that Cluster Editing and Cluster Deletion become easier in case the number of clusters is upperbounded. An extended abstract containing some of the results from this work as well as further fixedparameter tractability results for Cluster Editing and Cluster Deletion appeared under the title “Alternative Parameterizations for Cluster Editing ” in the proceedings
A GOLDEN RATIO PARAMETERIZED ALGORITHM FOR CLUSTER EDITING
, 2012
"... The Cluster Editing problem asks to transform a graph by at most k edge modifications into a disjoint union of cliques. The problem is NPcomplete, but several parameterized algorithms are known. We present a novel search tree algorithm for the ..."
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Cited by 8 (0 self)
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The Cluster Editing problem asks to transform a graph by at most k edge modifications into a disjoint union of cliques. The problem is NPcomplete, but several parameterized algorithms are known. We present a novel search tree algorithm for the