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


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

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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)


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
  • Feedback Vertex Set
  • Branch and bound
  • Measure and conquer


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