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On approximating maximum covering cycles in undirected graphs

  • Dirk Briskorn
Short Communication
  • 36 Downloads

Abstract

We consider the problem to find a cycle in an undirected graph such that a maximum number of nodes is in the cycle or adjacent to a node in the cycle. The problem is known to be NP-hard and we strengthen this result by showing that there is no constant factor approximation algorithm unless \(P=NP\).

Keywords

Undirected graphs Maximum covering cycle Approximation 

References

  1. 1.
    Álvarez-Miranda, E., Sinnl, M.: A branch-and-cut algorithm for the maximum covering cycle problem. Ann. Oper. Res.  https://doi.org/10.1007/s10479-018-2856-5
  2. 2.
    Grosso, A., Salassa, F., Vancroonenburg, W.: Searching for a cycle with maximum coverage in undirected graphs. Optim. Lett. 10, 1493–1504 (2016)MathSciNetCrossRefMATHGoogle Scholar
  3. 3.
    Karger, D., Motwani, R., Ramkumar, G.D.S.: On approximating the longest path in a graph. Algorithmica 18, 82–98 (1997)MathSciNetCrossRefMATHGoogle Scholar

Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Lehrstuhl für BWL, insbesondere Produktion und LogistikBergische Universität WuppertalWuppertalGermany

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