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DOI: 10.4230/LIPIcs.MFCS.2019.74
URN: urn:nbn:de:0030-drops-110188
URL: https://drops.dagstuhl.de/opus/volltexte/2019/11018/
Gaspers, Serge ; Li, Ray
Enumeration of Preferred Extensions in Almost Oriented Digraphs
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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 | |
| Seminar: | 44th International Symposium on Mathematical Foundations of Computer Science (MFCS 2019) | |
| Issue date: | 2019 | |
| Date of publication: | 20.08.2019 |
