License: Creative Commons Attribution 3.0 Unported license (CC BY 3.0)
When quoting this document, please refer to the following
DOI: 10.4230/LIPIcs.MFCS.2019.74
URN: urn:nbn:de:0030-drops-110188
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2019/11018/
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Gaspers, Serge ; Li, Ray

Enumeration of Preferred Extensions in Almost Oriented Digraphs

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LIPIcs-MFCS-2019-74.pdf (0.5 MB)

Abstract

In this paper, we present enumeration algorithms to list all preferred extensions of an argumentation framework. This task is equivalent to enumerating all maximal semikernels of a directed graph. For directed graphs on n vertices, all preferred extensions can be enumerated in O^*(3^{n/3}) time and there are directed graphs with Omega(3^{n/3}) preferred extensions. We give faster enumeration algorithms for directed graphs with at most 0.8004 * n vertices occurring in 2-cycles. In particular, for oriented graphs (digraphs with no 2-cycles) one of our algorithms runs in time O(1.2321^n), and we show that there are oriented graphs with Omega(3^{n/6}) > Omega(1.2009^n) preferred extensions.
A combination of three algorithms leads to the fastest enumeration times for various proportions of the number of vertices in 2-cycles. The most innovative one is a new 2-stage sampling algorithm, combined with a new parameterized enumeration algorithm, analyzed with a combination of the recent monotone local search technique (STOC 2016) and an extension thereof (ICALP 2017).

BibTeX - Entry

@InProceedings{gaspers_et_al:LIPIcs:2019:11018,
  author =	{Serge Gaspers and Ray Li},
  title =	{{Enumeration of Preferred Extensions in Almost Oriented Digraphs}},
  booktitle =	{44th International Symposium on Mathematical Foundations of Computer Science (MFCS 2019)},
  pages =	{74:1--74:15},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-117-7},
  ISSN =	{1868-8969},
  year =	{2019},
  volume =	{138},
  editor =	{Peter Rossmanith and Pinar Heggernes and Joost-Pieter Katoen},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{http://drops.dagstuhl.de/opus/volltexte/2019/11018},
  URN =		{urn:nbn:de:0030-drops-110188},
  doi =		{10.4230/LIPIcs.MFCS.2019.74},
  annote =	{Keywords: abstract argumentation, exact algorithms, exponential time algorithms, parameterized algorithms, enumeration algorithms, semikernels in digraphs}
}

Keywords: abstract argumentation, exact algorithms, exponential time algorithms, parameterized algorithms, enumeration algorithms, semikernels in digraphs
Collection: 44th International Symposium on Mathematical Foundations of Computer Science (MFCS 2019)
Issue Date: 2019
Date of publication: 20.08.2019

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