A quadratic vertex kernel for feedback arc set in bipartite tournaments

Abstract

The k-feedback arc set problem is to determine whether there is a set F of at most k arcs in a directed graph G such that the removal of F makes G acyclic. The k-feedback arc set problems in tournaments and bipartite tournaments (k-FAST and k-FASBT) have applications in ranking aggregation and have been extensively studied from the viewpoint of parameterized complexity. Recently, Misra et al. provide a problem kernel with O(k 3) vertices for k-FASBT. Answering an open question by Misra et al., we improve the kernel bound to O(k 2) vertices by introducing a new concept called "bimodule." © 2012 Springer-Verlag.