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An improved exact algorithm for undirected feedback vertex set

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Abstract

A feedback vertex set in an undirected graph is a subset of vertices removal of which leaves a graph with no cycles. Razgon (in: Proceedings of the 10th Scandinavian workshop on algorithm theory (SWAT 2006), pp. 160–171, 2006) gave a \(1.8899^n n^{O(1)}\)-time algorithm for finding a minimum feedback vertex set in an \(n\)-vertex undirected graph, which is the first exact algorithm for the problem that breaks the trivial barrier of \(2^n\). Later, Fomin et al. (Algorithmica 52:293–307, 2008) improved the result to \(1.7548^n n^{O(1)}\). In this paper, we further improve the result to \(1.7266^n n^{O(1)}\). Our algorithm is analyzed by the measure-and-conquer method. We get the improvement by designing new reductions based on biconnectivity of instances and introducing a new measure scheme on the structure of reduced graphs.

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Acknowledgments

Supported by NFSC of China under the Grant 61370071 and Fundamental Research Funds for the Central Universities under the Grant ZYGX2012J069

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Authors and Affiliations

  1. School of Computer Science and Engineering, University of Electronic Science and Technology of China, Chengdu, 611731, China

    Mingyu Xiao

  2. Department of Applied Mathematics and Physics, Graduate School of Informatics, Kyoto University, Yoshida Honmachi, Sakyo, Kyoto, 606-8501, Japan

    Hiroshi Nagamochi

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  1. Mingyu Xiao
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  2. Hiroshi Nagamochi
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Correspondence to Mingyu Xiao.

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Xiao, M., Nagamochi, H. An improved exact algorithm for undirected feedback vertex set. J Comb Optim 30, 214–241 (2015). https://doi.org/10.1007/s10878-014-9737-x

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  • DOI: https://doi.org/10.1007/s10878-014-9737-x

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