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Algorithmica

, Volume 52, Issue 2, pp 293–307 | Cite as

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

  • Fedor V. Fomin
  • Serge GaspersEmail author
  • Artem V. Pyatkin
  • Igor Razgon
Article

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 1.8638 n minimal feedback vertex sets and that there exist graphs having 105 n/10≈1.5926 n minimal feedback vertex sets.

Keywords

Minimum feedback vertex set Maximum induced forest Exact exponential algorithm Number of minimal feedback vertex sets 

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Copyright information

© Springer Science+Business Media, LLC 2007

Authors and Affiliations

  • Fedor V. Fomin
    • 1
  • Serge Gaspers
    • 1
    Email author
  • Artem V. Pyatkin
    • 2
  • Igor Razgon
    • 3
  1. 1.Department of InformaticsUniversity of BergenBergenNorway
  2. 2.Sobolev Institute of MathematicsSB RASNovosibirskRussia
  3. 3.Computer Science DepartmentUniversity College CorkCorkIreland

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