A 7/3-Approximation for Feedback Vertex Sets in Tournaments

Authors Matthias Mnich, Virginia Vassilevska Williams, László A. Végh

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Matthias Mnich
Virginia Vassilevska Williams
László A. Végh

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Matthias Mnich, Virginia Vassilevska Williams, and László A. Végh. A 7/3-Approximation for Feedback Vertex Sets in Tournaments. In 24th Annual European Symposium on Algorithms (ESA 2016). Leibniz International Proceedings in Informatics (LIPIcs), Volume 57, pp. 67:1-67:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2016)


We consider the minimum-weight feedback vertex set problem in tournaments: given a tournament with non-negative vertex weights, remove a minimum-weight set of vertices that intersects all cycles. This problem is NP-hard to solve exactly, and Unique Games-hard to approximate by a factor better than 2. We present the first 7/3 approximation algorithm for this problem, improving on the previously best known ratio 5/2 given by Cai et al. [FOCS 1998, SICOMP 2001].
  • Approximation algorithms
  • feedback vertex sets
  • tournaments


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