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Item type:Publication, Access status: with files , Linear kernels and linear-time algorithms for finding large cutsThe maximum cut problem in graphs and its generalizations are fundamental combinatorial problems. Several of these cut problems were recently shown to be fixed-parameter tractable and admit polynomial kernels when parameterized above the tight lower bound measured by the size and order of the graph. In this paper we continue this line of research and considerably improve several of those results: – We show that an algorithm by Crowston et al. (Algorithmica 72(3):734–757, 2015) for (Signed) Max- Cut Above Edwards−ErdÖs Bound can be implemented so as to run in linear time 8k ·O(m); this significantly improves the previous analysis with run time 8k · O(n4). – We give an asymptotically optimal kernel for (Signed) Max- Cut Above Edwards−ErdÖs Bound with O(k) vertices, improving a kernel with O(k3) vertices by Crowston et al. (Theor Comput Sci 513:53–64, 2013). – We improve all known kernels for parameterizations above strongly λ-extendible properties (a generalization of the Max- Cut results) by Crowston et al. (Proceedings of FSTTCS 2013, Leibniz international proceedings in informatics,Guwahati, 2013) from O(k3) vertices to O(k) vertices.Publicationtype: Journal Article229 247 - Some of the metrics are blocked by yourconsent settings
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Item type:Publication, Access status: with files , Linear kernels and linear-time algorithms for finding large cuts(Schloss Dagstuhl - Leibniz-Zentrum für Informatik GmbH, Dagstuhl Publishing, 2016-12-01); The maximum cut problem in graphs and its generalizations are fundamental combinatorial problems. Several of these cut problems were recently shown to be fixed-parameter tractable and admit polynomial kernels when parameterized above the tight lower bound measured by the size and order of the graph. In this paper we continue this line of research and considerably improve several of those results: We show that an algorithm by Crowston et al. [ICALP 2012] for (Signed) Max-Cut Above Edwards-Erdös Bound can be implemented in such a way that it runs in linear time 8k · O(m); this significantly improves the previous analysis with run time 8k · O(n4). We give an asymptotically optimal kernel for (Signed) Max-Cut Above Edwards-Erdös Bound with O(k) vertices, improving a kernel with O(k3) vertices by Crowston et al. [COCOON 2013]. We improve all known kernels for strongly λ-extendable properties parameterized above tight lower bound by Crowston et al. [FSTTCS 2013] from O(k3) vertices to O(k) vertices. As a consequence, Max Acyclic Subdigraph parameterized above Poljak-Turzík bound admits a kernel with O(k) vertices and can be solved in time 2O(k) · nO(1); this answers an open question by Crowston et al. [FSTTCS 2012]. All presented kernels can be computed in time O(km).Publicationtype: Conference Paper184 183 - Some of the metrics are blocked by yourconsent settings
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