research-article

A fixed-parameter algorithm for the directed feedback vertex set problem

Authors:

Barry O'Sullivan,

Igor RazgonAuthors Info & Claims

STOC '08: Proceedings of the fortieth annual ACM symposium on Theory of computing

Pages 177 - 186

https://doi.org/10.1145/1374376.1374404

Published: 17 May 2008 Publication History

Abstract

The (parameterized) feedback vertex set problem on directed graphs, which we refer to as the dfvs problem, is defined as follows: given a directed graph G and a parameter k, either construct a feedback vertex set of at most k vertices in G or report that no such set exists. Whether or not the dfvs problem is fixed-parameter tractable has been a well-known open problem in parameterized computation and complexity, i.e., whether the problem can be solved in time f(k)n^O(1) for some function f. In this paper we develop new algorithmic techniques that result in an algorithm with running time 4^k k! n^O(1) for the dfvs problem, thus showing that this problem is fixed-parameter tractable.

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Xiong ZZhou YXiao MKhoussainov B(2024)Finding small feedback arc sets on large graphsComputers and Operations Research10.1016/j.cor.2024.106724169:COnline publication date: 1-Sep-2024
https://dl.acm.org/doi/10.1016/j.cor.2024.106724
Dirks JGerhard EGrobler MMouawad ASiebertz S(2024)Data Reduction for Directed Feedback Vertex Set on Graphs Without Long Induced CyclesSOFSEM 2024: Theory and Practice of Computer Science10.1007/978-3-031-52113-3_13(183-197)Online publication date: 7-Feb-2024
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Index Terms

A fixed-parameter algorithm for the directed feedback vertex set problem
1. Mathematics of computing
  1. Discrete mathematics
    1. Graph theory
2. Theory of computation
  1. Design and analysis of algorithms

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cover image ACM Conferences

STOC '08: Proceedings of the fortieth annual ACM symposium on Theory of computing

May 2008

712 pages

ISBN:9781605580470

DOI:10.1145/1374376

General Chair:
Richard Ladner
University of Washington
,
Program Chair:
Cynthia Dwork
Microsoft Research, Silicon Valley

Copyright © 2008 ACM.

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Published: 17 May 2008

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parameterized complexity

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May 17 - 20, 2008

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https://doi.org/10.1109/TAC.2023.3344871
Xiong ZZhou YXiao MKhoussainov B(2024)Finding small feedback arc sets on large graphsComputers and Operations Research10.1016/j.cor.2024.106724169:COnline publication date: 1-Sep-2024
https://dl.acm.org/doi/10.1016/j.cor.2024.106724
Dirks JGerhard EGrobler MMouawad ASiebertz S(2024)Data Reduction for Directed Feedback Vertex Set on Graphs Without Long Induced CyclesSOFSEM 2024: Theory and Practice of Computer Science10.1007/978-3-031-52113-3_13(183-197)Online publication date: 7-Feb-2024
https://doi.org/10.1007/978-3-031-52113-3_13
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