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Improved Analysis of Highest-Degree Branching for Feedback Vertex Set
Algorithmica ( IF 0.9 ) Pub Date : 2021-03-15 , DOI: 10.1007/s00453-021-00815-w
Yoichi Iwata , Yusuke Kobayashi

Recent empirical evaluations of exact algorithms for Feedback Vertex Set have demonstrated the efficiency of a highest-degree branching algorithm with a degree-based pruning. In this paper, we prove that this empirically fast algorithm runs in \(O(3.460^k n)\) time, where k is the solution size. This improves the previous best \(O(3.619^k n)\)-time deterministic algorithm obtained by Kociumaka and Pilipczuk (Inf Process Lett 114:556–560, 2014. https://doi.org/10.1016/j.ipl.2014.05.001).



中文翻译:

反馈顶点集最高度分支的改进分析

反馈顶点集的精确算法的最新经验评估表明,最高程度的分支算法与基于程度的修剪是有效的。在本文中,我们证明了这种基于经验的快速算法可以在\(O(3.460 ^ kn)\)时间内运行,其中k是解的大小。这改善了Kociumaka和Pilipczuk(Inf Process Lett 114:556-560,2014. https://doi.org/10.1016/j.ipl。)所获得的先前最佳\(O(3.619 ^ kn)\)时间确定性算法。 2014.05.001)。

更新日期:2021-03-15
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