Improved Analysis of Highest-Degree Branching for Feedback Vertex Set

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.