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.2019.27
URN: urn:nbn:de:0030-drops-109714
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2019/10971/
Bessy, Stéphane ;
Bougeret, Marin ;
Krithika, R. ;
Sahu, Abhishek ;
Saurabh, Saket ;
Thiebaut, Jocelyn ;
Zehavi, Meirav
Packing Arc-Disjoint Cycles in Tournaments
Abstract
A tournament is a directed graph in which there is a single arc between every pair of distinct vertices. Given a tournament T on n vertices, we explore the classical and parameterized complexity of the problems of determining if T has a cycle packing (a set of pairwise arc-disjoint cycles) of size k and a triangle packing (a set of pairwise arc-disjoint triangles) of size k. We refer to these problems as Arc-disjoint Cycles in Tournaments (ACT) and Arc-disjoint Triangles in Tournaments (ATT), respectively. Although the maximization version of ACT can be seen as the linear programming dual of the well-studied problem of finding a minimum feedback arc set (a set of arcs whose deletion results in an acyclic graph) in tournaments, surprisingly no algorithmic results seem to exist for ACT. We first show that ACT and ATT are both NP-complete. Then, we show that the problem of determining if a tournament has a cycle packing and a feedback arc set of the same size is NP-complete. Next, we prove that ACT and ATT are fixed-parameter tractable, they can be solved in 2^{O(k log k)} n^{O(1)} time and 2^{O(k)} n^{O(1)} time respectively. Moreover, they both admit a kernel with O(k) vertices. We also prove that ACT and ATT cannot be solved in 2^{o(sqrt{k})} n^{O(1)} time under the Exponential-Time Hypothesis.
BibTeX - Entry
@InProceedings{bessy_et_al:LIPIcs:2019:10971,
author = {St{\'e}phane Bessy and Marin Bougeret and R. Krithika and Abhishek Sahu and Saket Saurabh and Jocelyn Thiebaut and Meirav Zehavi},
title = {{Packing Arc-Disjoint Cycles in Tournaments}},
booktitle = {44th International Symposium on Mathematical Foundations of Computer Science (MFCS 2019)},
pages = {27:1--27:14},
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/2019/10971},
URN = {urn:nbn:de:0030-drops-109714},
doi = {10.4230/LIPIcs.MFCS.2019.27},
annote = {Keywords: arc-disjoint cycle packing, tournaments, parameterized algorithms, kernelization}
}
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Keywords: |
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arc-disjoint cycle packing, tournaments, parameterized algorithms, kernelization |
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Collection: |
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44th International Symposium on Mathematical Foundations of Computer Science (MFCS 2019) |
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Issue Date: |
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2019 |
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Date of publication: |
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20.08.2019 |
