Linear programming based approximation algorithms for feedback set problems in bipartite tournaments

We consider the feedback vertex set and feedback arc set problems on bipartite tournaments. We improve on recent results by giving a 2-approximation algorithm for the feedback vertex set problem. We show that this result is the best that we can attain when using optimal solutions to a certain linear program as a lower bound on the optimal value. For the feedback arc set problem on bipartite tournaments, we show that a recent 4-approximation algorithm proposed by Gupta (2008) [8], is incorrect. We give an alternative 4-approximation algorithm based on an algorithm for the feedback arc set on (non-bipartite) tournaments given by van Zuylen and Williamson (2009) [14].