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An improved exact algorithm for undirected feedback vertex set

Author

Listed:
  • Mingyu Xiao

    (University of Electronic Science and Technology of China)

  • Hiroshi Nagamochi

    (Kyoto University)

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 $$1.8899^n n^{O(1)}$$ 1 . 8899 n n O ( 1 ) -time algorithm for finding a minimum feedback vertex set in an $$n$$ n -vertex undirected graph, which is the first exact algorithm for the problem that breaks the trivial barrier of $$2^n$$ 2 n . Later, Fomin et al. (Algorithmica 52:293–307, 2008) improved the result to $$1.7548^n n^{O(1)}$$ 1 . 7548 n n O ( 1 ) . In this paper, we further improve the result to $$1.7266^n n^{O(1)}$$ 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.

Suggested Citation

  • Mingyu Xiao & Hiroshi Nagamochi, 2015. "An improved exact algorithm for undirected feedback vertex set," Journal of Combinatorial Optimization, Springer, vol. 30(2), pages 214-241, August.
    • Handle: RePEc:spr:jcomop:v:30:y:2015:i:2:d:10.1007_s10878-014-9737-x
    DOI: 10.1007/s10878-014-9737-x
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