An improved exact algorithm for undirected feedback vertex set

Mingyu Xiao () and Hiroshi Nagamochi ()
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Mingyu Xiao: University of Electronic Science and Technology of China
Hiroshi Nagamochi: Kyoto University

Journal of Combinatorial Optimization, 2015, vol. 30, issue 2, No 2, 214-241

Abstract: 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.

Keywords: Exact exponential algorithms; Feedback vertex set; Measure and conquer; Branch and bound (search for similar items in EconPapers)
Date: 2015
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DOI: 10.1007/s10878-014-9737-x

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