article

On the Minimum Feedback Vertex Set Problem: Exact and Enumeration Algorithms

Authors:

Fedor V. Fomin,

Artem V. Pyatkin,

Igor RazgonAuthors Info & Claims

Algorithmica, Volume 52, Issue 2

Pages 293 - 307

Published: 01 October 2008 Publication History

Abstract

We present a time $\mathcal {O}(1.7548^{n})$ algorithm finding a minimum feedback vertex set in an undirected graph on n vertices. We also prove that a graph on n vertices can contain at most 1.8638n minimal feedback vertex sets and that there exist graphs having 105n/10ź1.5926n minimal feedback vertex sets.

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Cited By

Kolay SPanolan FSaurabh S(2019)Communication Complexity and Graph FamiliesACM Transactions on Computation Theory10.1145/331323411:2(1-28)Online publication date: 15-Mar-2019
https://dl.acm.org/doi/10.1145/3313234
Fomin FGaspers SLokshtanov DSaurabh S(2019)Exact Algorithms via Monotone Local SearchJournal of the ACM10.1145/328417666:2(1-23)Online publication date: 8-Mar-2019
https://dl.acm.org/doi/10.1145/3284176
Misra NPanolan FRai ARaman VSaurabh S(2019)Parameterized Algorithms for Max Colorable Induced Subgraph Problem on Perfect GraphsAlgorithmica10.1007/s00453-018-0431-881:1(26-46)Online publication date: 1-Jan-2019
https://dl.acm.org/doi/10.1007/s00453-018-0431-8
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Index Terms

On the Minimum Feedback Vertex Set Problem: Exact and Enumeration Algorithms
1. Mathematics of computing
  1. Discrete mathematics
    1. Graph theory
      1. Graph algorithms
2. Theory of computation
  1. Design and analysis of algorithms
  2. Randomness, geometry and discrete structures

Index terms have been assigned to the content through auto-classification.

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Published In

cover image Algorithmica

Algorithmica Volume 52, Issue 2

October 2008

195 pages

ISSN:0178-4617

Issue’s Table of Contents

Copyright © Copyright © 2008 Springer Science+Business Media, LLC.

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Springer-Verlag

Berlin, Heidelberg

Publication History

Published: 01 October 2008

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Cited By

Kolay SPanolan FSaurabh S(2019)Communication Complexity and Graph FamiliesACM Transactions on Computation Theory10.1145/331323411:2(1-28)Online publication date: 15-Mar-2019
https://dl.acm.org/doi/10.1145/3313234
Fomin FGaspers SLokshtanov DSaurabh S(2019)Exact Algorithms via Monotone Local SearchJournal of the ACM10.1145/328417666:2(1-23)Online publication date: 8-Mar-2019
https://dl.acm.org/doi/10.1145/3284176
Misra NPanolan FRai ARaman VSaurabh S(2019)Parameterized Algorithms for Max Colorable Induced Subgraph Problem on Perfect GraphsAlgorithmica10.1007/s00453-018-0431-881:1(26-46)Online publication date: 1-Jan-2019
https://dl.acm.org/doi/10.1007/s00453-018-0431-8
Xiao MTan H(2017)Exact algorithms for Maximum Induced MatchingInformation and Computation10.1016/j.ic.2017.07.006256:C(196-211)Online publication date: 1-Oct-2017
https://dl.acm.org/doi/10.1016/j.ic.2017.07.006
Fomin FGaspers SLokshtanov DSaurabh SWichs DMansour Y(2016)Exact algorithms via monotone local searchProceedings of the forty-eighth annual ACM symposium on Theory of Computing10.1145/2897518.2897551(764-775)Online publication date: 19-Jun-2016
https://dl.acm.org/doi/10.1145/2897518.2897551
Golovach PHeggernes PKratsch D(2016)Enumerating minimal connected dominating sets in graphs of bounded chordalityTheoretical Computer Science10.1016/j.tcs.2016.03.026630:C(63-75)Online publication date: 30-May-2016
https://dl.acm.org/doi/10.1016/j.tcs.2016.03.026
Bliznets IFomin FPilipczuk MVillanger Y(2016)Largest Chordal and Interval Subgraphs Faster than $$2^n$$2nAlgorithmica10.1007/s00453-015-0054-276:2(569-594)Online publication date: 1-Oct-2016
https://dl.acm.org/doi/10.1007/s00453-015-0054-2
Fomin FTodinca IVillanger Y(2015)Large Induced Subgraphs via Triangulations and CMSOSIAM Journal on Computing10.1137/14096480144:1(54-87)Online publication date: 12-Feb-2015
https://dl.acm.org/doi/10.1137/140964801
Couturier JLetourneur RLiedloff M(2015)On the number of minimal dominating sets on some graph classesTheoretical Computer Science10.1016/j.tcs.2014.11.006562:C(634-642)Online publication date: 11-Jan-2015
https://dl.acm.org/doi/10.1016/j.tcs.2014.11.006
Xiao MNagamochi H(2015)An improved exact algorithm for undirected feedback vertex setJournal of Combinatorial Optimization10.1007/s10878-014-9737-x30:2(214-241)Online publication date: 1-Aug-2015
https://dl.acm.org/doi/10.1007/s10878-014-9737-x
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