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Improved Analysis of Highest-Degree Branching for Feedback Vertex Set

Authors Yoichi Iwata, Yusuke Kobayashi

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Author Details

Yoichi Iwata
  • National Institute of Informatics, Tokyo, Japan
Yusuke Kobayashi
  • Kyoto University, Kyoto, Japan

Funding

  • Iwata, Yoichi: Supported by JSPS KAKENHI Grant Number JP17K12643.
  • Kobayashi, Yusuke: Supported by JSPS KAKENHI Grants Number JP16K16010, 17K19960, and 18H05291.

Acknowledgements

We would like to thank Yixin Cao for valuable discussions and thank organizers of PACE challenge 2016 for motivating us to study FVS.

Cite AsGet BibTex

Yoichi Iwata and Yusuke Kobayashi. Improved Analysis of Highest-Degree Branching for Feedback Vertex Set. In 14th International Symposium on Parameterized and Exact Computation (IPEC 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 148, pp. 22:1-22:11, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019)
https://doi.org/10.4230/LIPIcs.IPEC.2019.22

Abstract

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 heuristic. 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., 2014).

Subject Classification

ACM Subject Classification
  • Theory of computation → Fixed parameter tractability
Keywords
  • Feedback Vertex Set
  • Branch and bound
  • Measure and conquer

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