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Linear kernels and linear-time algorithms for finding large cuts
Citation Link: https://doi.org/10.15480/882.2624
Publikationstyp
Journal Article
Date Issued
2017-10-25
Sprache
English
Author(s)
TORE-DOI
TORE-URI
Journal
Volume
80
Issue
9
Start Page
2574
End Page
2615
Citation
Algorithmica (2018)
Publisher DOI
Publisher
Springer
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. (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.
– 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.
Subjects
Max-cut
Kernelization
Linear-time algorithms
DDC Class
004: Informatik
More Funding Information
Supported by ERC Starting Grant 306465 (BeyondWorstCase).
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