An improved exact algorithm for undirected feedback vertex set

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 feedba...

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Bibliographic Details
Published in:Journal of combinatorial optimization Vol. 30; no. 2; pp. 214 - 241
Main Authors: Xiao, Mingyu, Nagamochi, Hiroshi
Format: Journal Article
Language:English
Published: New York Springer US 01.08.2015
Subjects:
Combinatorics
Convex and Discrete Geometry
Mathematical Modeling and Industrial Mathematics
Mathematics
Mathematics and Statistics
Operations Research/Decision Theory
Optimization
Theory of Computation
Measure and conquer
Exact exponential algorithms
Feedback vertex set
Branch and bound
ISSN:1382-6905, 1573-2886
Online Access:Get full text
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Summary: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.
ISSN:1382-6905
1573-2886
DOI:10.1007/s10878-014-9737-x