A 7/3-approximation algorithm for feedback vertex set in tournaments via Sherali–Adams

Abstract

We study the feedback vertex set problem in tournaments from the polyhedral point of view, and in particular we show that performing just one round of the Sherali–Adams hierarchy gives a relaxation with integrality gap 7/3. This allows us to derive a 7/3-approximation algorithm for the feedback vertex set problem in tournaments that matches the best deterministic approximation guarantee due to Mnich, Williams, and Végh, and is a simplification and runtime improvement of their approach.