Linear Programming Based Approximation Algorithms for Feedback Set Problems in Bipartite Tournaments

We consider the feedback vertex set and feedback arc set problems in 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 we can attain when using a certain linear program as the lower bound on the optimal value. For the feedback arc set problem in bipartite tournaments, we show that a recent 4-approximation algorithm proposed by Gupta [5, 6] is incorrect. We give an alternative 4-approximation algorithm based on an algorithm for feedback arc set in (regular) tournaments in [10, 11].