A Polynomial Kernel for Funnel Arc Deletion Set

Abstract

In Directed Feedback Arc Set (DFAS) we search for a set of at most k arcs which intersect every cycle in the input digraph. It is a wellknown open problem in parameterized complexity to decide if DFAS admits a kernel of polynomial size. We consider C-Arc Deletion Set (C-ADS), a variant of DFAS where we want to remove at most k arcs from the input digraph in order to turn it into a digraph of a class C. In this work, we choose C to be the class of funnels. Funnel-ADS is NP-hard even if the input is a DAG, but is fixed-parameter tractable with respect to k. So far no polynomial kernels for this problem were known. Our main result is a kernel for Funnel-ADS with O(k 6 ) many vertices and O(k 7 ) many arcs, computable in linear time.