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 upperbounded 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 exponentialtime 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 medge 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/4d/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 = {49:149:13},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {9783959770019},
ISSN = {18688969},
year = {2016},
volume = {47},
editor = {Nicolas Ollinger and Heribert Vollmer},
publisher = {Schloss DagstuhlLeibnizZentrum fuer Informatik},
address = {Dagstuhl, Germany},
URL = {http://drops.dagstuhl.de/opus/volltexte/2016/5750},
URN = {urn:nbn:de:0030drops57501},
doi = {10.4230/LIPIcs.STACS.2016.49},
annote = {Keywords: Parameterized algorithms, Exact algorithms, Feedback vertex set, Tour naments, Graph partitions}
}
16.02.2016
Keywords: 

Parameterized algorithms, Exact algorithms, Feedback vertex set, Tour naments, Graph partitions 
Seminar: 

33rd Symposium on Theoretical Aspects of Computer Science (STACS 2016)

Issue date: 

2016 
Date of publication: 

16.02.2016 