article

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

Authors:

Fedor V. Fomin,

Serge Gaspers,

Artem V. Pyatkin,

Igor RazgonAuthors Info & Claims

Algorithmica, Volume 52, Issue 2

Pages 293 - 307

Published: 25 August 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 105^n/10≈1.5926ⁿ minimal feedback vertex sets.

Cited By

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Ganian RHaan RKanj ISzeider S(2020)On Existential MSO and Its Relation to ETHACM Transactions on Computation Theory10.1145/341775912:4(1-32)Online publication date: 30-Sep-2020
https://dl.acm.org/doi/10.1145/3417759
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
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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. Combinatorics
      1. Combinatorial algorithms
    2. Graph theory
  2. Mathematical analysis
    1. Numerical analysis
      1. Computations in finite fields
2. Theory of computation
  1. Randomness, geometry and discrete structures

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

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Finding a minimum feedback vertex set in time O(1.7548ⁿ)
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We present an $\mathcal{O} (1.7548^n)$ algorithm finding a minimum feedback vertex set in a graph on n vertices.

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Published In

Algorithmica Volume 52, Issue 2

Parameterized and Exact Algorithms

August 2008

62 pages

ISSN:0178-4617

Issue’s Table of Contents

Publisher

Springer-Verlag

Berlin, Heidelberg

Publication History

Published: 25 August 2008

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Cited By

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Ganian RHaan RKanj ISzeider S(2020)On Existential MSO and Its Relation to ETHACM Transactions on Computation Theory10.1145/341775912:4(1-32)Online publication date: 30-Sep-2020
https://dl.acm.org/doi/10.1145/3417759
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
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