2026-07-23T17:25:31Z https://drops.dagstuhl.de/oai

oai:drops-oai.dagstuhl.de:5750 2024-03-06T10:36:59Z ddc:004 open_access

Faster Exact and Parameterized Algorithm for Feedback Vertex Set in Tournaments Kumar, Mithilesh Lokshtanov, Daniel Parameterized algorithms Exact algorithms Feedback vertex set Tour- naments Graph partitions 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. Schloss Dagstuhl – Leibniz-Zentrum für Informatik Mithilesh Kumar and Daniel Lokshtanov 2016 Is Part Of LIPIcs, Volume 47, 33rd Symposium on Theoretical Aspects of Computer Science (STACS 2016) InProceedings Text doc-type:ResearchArticle publishedVersion application/pdf doi:10.4230/LIPIcs.STACS.2016.49 urn:nbn:de:0030-drops-57501 https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2016.49 eng https://creativecommons.org/licenses/by/3.0/legalcode