A simple 7/3-approximation algorithm for feedback vertex set in tournaments
Manuel Aprile, Matthew Drescher, Samuel Fiorini, Tony Huynh
TL;DR
This paper presents a simplified and faster 7/3-approximation algorithm for the Feedback Vertex Set problem in tournaments, achieved by applying a single round of the Sherali-Adams hierarchy, matching the best known deterministic approximation.
Contribution
The authors introduce a novel, simplified approach that uses only one Sherali-Adams hierarchy round to achieve the optimal approximation ratio for FVST in tournaments.
Findings
Achieves a 7/3-approximation ratio for FVST in tournaments.
Simplifies previous algorithms, reducing runtime.
Matches the best deterministic approximation ratio.
Abstract
We show that performing just one round of the Sherali-Adams hierarchy gives an easy 7/3-approximation algorithm for the Feedback Vertex Set (FVST) problem in tournaments. This matches the best deterministic approximation algorithm for FVST due to Mnich, Williams, and V\'egh, and is a significant simplification and runtime improvement of their approach.
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Taxonomy
TopicsAdvanced Graph Theory Research · Game Theory and Voting Systems · Complexity and Algorithms in Graphs