Faster Exact and Parameterized Algorithm for Feedback Vertex Set in Bipartite Tournaments

A bipartite tournament is a directed graph T := (A ∪ B,E) such that every pair of vertices (a, b), a ∈ A, b ∈ B are connected by an arc, and no arc connects two vertices of A or two vertices of B. A feedback vertex set is a set S of vertices in T such that T − S is acyclic. In this article we consider the Feedback Vertex Set problem in bipartite tournaments. Here the input is a bipartite tournament T on n vertices together with an integer k, and the task is to determine whether T has a feedback vertex set of size at most k. We give a new algorithm for Feedback Vertex Set in Bipartite Tournaments. The running time of our algorithm is upper-bounded by O(1.6181 + nO(1)), improving over the previously best known algorithm with running time 2kkO(1) + nO(1) [Hsiao, ISAAC 2011]. As a by-product, we also obtain the fastest currently known exact exponential-time algorithm for the problem, with running time O(1.3820). 1998 ACM Subject Classification F.2.2 Nonnumerical Algorithms and Problems