A polynomial kernel for Feedback Arc Set on Bipartite Tournaments
Chennai Mathematical Institute.
In the k-Feedback Arc/Vertex Set problem we are given a di- rected graph D and a positive integer k and the objective is to check whether it is possible to delete at most k arcs/vertices from D to make it acyclic. Dom et al.[CIAC, 2006 ] initiated a study of the Feedback Arc Set problem on bipartite tournaments (k-FASBT) in the realm of parameterized complexity. They showed that k-FASBT can be solved in time O(3:373^k n^6) on bipartite tournaments having n vertices. However, until now there was no known poly- nomial sized problem kernel for k-FASBT. In this paper we obtain a cubic vertex kernel for k-FASBT. This completes the kernelization picture for the Feedback Arc/Vertex Set problem on tournaments and bipartite tourna- ments, as for all other problems polynomial kernels were known before. We obtain our kernel using a non-trivial application of "independent modules" which could be of independent interest.