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

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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/10≈1.5926n minimal feedback vertex sets.

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Authors and Affiliations

  1. Department of Informatics, University of Bergen, 5020, Bergen, Norway

    Fedor V. Fomin & Serge Gaspers

  2. Sobolev Institute of Mathematics, SB RAS, 4 Acad. Koptyug avenue, 630090, Novosibirsk, Russia

    Artem V. Pyatkin

  3. Computer Science Department, University College Cork, Cork, Ireland

    Igor Razgon

Authors
  1. Fedor V. Fomin
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  2. Serge Gaspers
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  3. Artem V. Pyatkin
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  4. Igor Razgon
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Corresponding author

Correspondence to Serge Gaspers.

Additional information

Preliminary extended abstracts of this paper appeared in the proceedings of SWAT’06 [29] and IWPEC’06 [18].

Additional support of F.V. Fomin, S. Gaspers and A.V. Pyatkin by the Research Council of Norway.

The work of A.V. Pyatkin was partially supported by grants of the Russian Foundation for Basic Research (project code 05-01-00395), INTAS (project code 04–77–7173).

I. Razgon is supported by Science Foundation Ireland (Grant Number 05/IN/I886).

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Fomin, F.V., Gaspers, S., Pyatkin, A.V. et al. On the Minimum Feedback Vertex Set Problem: Exact and Enumeration Algorithms. Algorithmica 52, 293–307 (2008). https://doi.org/10.1007/s00453-007-9152-0

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  • DOI: https://doi.org/10.1007/s00453-007-9152-0

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