License: Creative Commons Attribution 4.0 International license (CC BY 4.0)
When quoting this document, please refer to the following
DOI: 10.4230/LIPIcs.STACS.2021.37
URN: urn:nbn:de:0030-drops-136823
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2021/13682/
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Golovach, Petr A. ; Komusiewicz, Christian ; Kratsch, Dieter ; Le, Van Bang

Refined Notions of Parameterized Enumeration Kernels with Applications to Matching Cut Enumeration

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Abstract

An enumeration kernel as defined by Creignou et al. [Theory Comput. Syst. 2017] for a parameterized enumeration problem consists of an algorithm that transforms each instance into one whose size is bounded by the parameter plus a solution-lifting algorithm that efficiently enumerates all solutions from the set of the solutions of the kernel. We propose to consider two new versions of enumeration kernels by asking that the solutions of the original instance can be enumerated in polynomial time or with polynomial delay from the kernel solutions. Using the NP-hard Matching Cut problem parameterized by structural parameters such as the vertex cover number or the cyclomatic number of the input graph, we show that the new enumeration kernels present a useful notion of data reduction for enumeration problems which allows to compactly represent the set of feasible solutions.

BibTeX - Entry

@InProceedings{golovach_et_al:LIPIcs.STACS.2021.37,
  author =	{Golovach, Petr A. and Komusiewicz, Christian and Kratsch, Dieter and Le, Van Bang},
  title =	{{Refined Notions of Parameterized Enumeration Kernels with Applications to Matching Cut Enumeration}},
  booktitle =	{38th International Symposium on Theoretical Aspects of Computer Science (STACS 2021)},
  pages =	{37:1--37:18},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-180-1},
  ISSN =	{1868-8969},
  year =	{2021},
  volume =	{187},
  editor =	{Bl\"{a}ser, Markus and Monmege, Benjamin},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/opus/volltexte/2021/13682},
  URN =		{urn:nbn:de:0030-drops-136823},
  doi =		{10.4230/LIPIcs.STACS.2021.37},
  annote =	{Keywords: enumeration problems, polynomial delay, output-sensitive algorithms, kernelization, structural parameterizations, matching cuts}
}

Keywords: enumeration problems, polynomial delay, output-sensitive algorithms, kernelization, structural parameterizations, matching cuts
Collection: 38th International Symposium on Theoretical Aspects of Computer Science (STACS 2021)
Issue Date: 2021
Date of publication: 10.03.2021

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