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.STACS.2016.49
URN: urn:nbn:de:0030-drops-57501
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2016/5750/
Kumar, Mithilesh ;
Lokshtanov, Daniel
Faster Exact and Parameterized Algorithm for Feedback Vertex Set in Tournaments
Abstract
A tournament is a directed graph T such that every pair of vertices is connected by an arc. A feedback vertex set is a set S of vertices in T such that T\S is acyclic. In this article we consider the FEEDBACK VERTEX SET problem in tournaments. Here the input is a tournament T and an integer k, and the task is to determine whether T has a feedback vertex set of size at most k. We give a new algorithm for FEEDBACK VERTEX SET IN TOURNAMENTS. The running time of our algorithm is upper-bounded by O(1.6181^k + n^{O(1)}) and by O(1.466^n). Thus our algorithm simultaneously improves over the fastest known parameterized algorithm for the problem by Dom et al. running in time O(2^kk^{O(1)} + n^{O(1)}), and the fastest known exact exponential-time algorithm by Gaspers and Mnich with running time O(1.674^n). On the way to proving our main result we prove a strengthening of a special case of a graph partitioning theorem due to Bollobas and Scott. In particular we show that the vertices of any undirected m-edge graph of maximum degree d can be colored white or black in such a way that for each of the two colors, the number of edges with both endpoints of that color is between m/4-d/2 and m/4+d/2.
BibTeX - Entry
@InProceedings{kumar_et_al:LIPIcs:2016:5750,
author = {Mithilesh Kumar and Daniel Lokshtanov},
title = {{Faster Exact and Parameterized Algorithm for Feedback Vertex Set in Tournaments}},
booktitle = {33rd Symposium on Theoretical Aspects of Computer Science (STACS 2016)},
pages = {49:1--49:13},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-001-9},
ISSN = {1868-8969},
year = {2016},
volume = {47},
editor = {Nicolas Ollinger and Heribert Vollmer},
publisher = {Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
address = {Dagstuhl, Germany},
URL = {http://drops.dagstuhl.de/opus/volltexte/2016/5750},
URN = {urn:nbn:de:0030-drops-57501},
doi = {10.4230/LIPIcs.STACS.2016.49},
annote = {Keywords: Parameterized algorithms, Exact algorithms, Feedback vertex set, Tour- naments, Graph partitions}
}
Keywords: |
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Parameterized algorithms, Exact algorithms, Feedback vertex set, Tour- naments, Graph partitions |
Collection: |
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33rd Symposium on Theoretical Aspects of Computer Science (STACS 2016) |
Issue Date: |
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2016 |
Date of publication: |
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16.02.2016 |