Improved Analysis of Highest-Degree Branching for Feedback Vertex Set

TL;DR

This paper proves that a high-degree branching algorithm for Feedback Vertex Set runs in $O(3.460^k n)$ time, improving the previous deterministic bound and confirming its empirical efficiency.

Contribution

It provides a rigorous theoretical analysis showing the algorithm's improved exponential runtime bound for Feedback Vertex Set.

Findings

The algorithm runs in $O(3.460^k n)$ time, improving previous bounds.

The analysis confirms the empirical efficiency of the highest-degree branching approach.

Provides a new theoretical foundation for the algorithm's performance.

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.