Faster deterministic Feedback Vertex Set

TL;DR

This paper introduces two improved deterministic algorithms for the Feedback Vertex Set problem, achieving faster running times through novel reduction and branching rules, surpassing previous deterministic methods.

Contribution

The paper presents a new reduction rule and a simplified branching approach that improve the deterministic algorithms' running time for Feedback Vertex Set.

Findings

First algorithm runs in O*((2 + φ)^k) time, surpassing previous best.

Second algorithm achieves O*(3.592^k) running time with more branching rules.

Simpler analysis and fewer rules make the algorithms more practical.

Abstract

We present two new deterministic algorithms for the Feedback Vertex Set problem parameterized by the solution size. We begin with a simple algorithm, which runs in O*((2 + \phi)^k) time, where \phi < 1.619 is the golden ratio. It already surpasses the previously fastest O*((1+2sqrt(2))^k)-time deterministic algorithm due to Cao et al. [SWAT 2010]. In our developments we follow the approach of Cao et al., however, thanks to a new reduction rule, we obtain not only better dependency on the parameter in the running time, but also a solution with simple analysis and only a single branching rule. Then, we present a modification of the algorithm which, using a more involved set of branching rules, achieves O*(3.592^k) running time.