A Polynomial Kernel for Funnel Arc Deletion Set
Abstract
In Directed Feeback 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 $\mathcal{C}$Arc Deletion Set ($\mathcal{C}$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 $\mathcal{C}$. In this work, we choose $\mathcal{C}$ to be the class of funnels. FunnelArc Deletion Set is NPhard even if the input is a DAG, but is fixedparameter tractable with respect to $k$. So far no polynomial kernels for this problem were known. Our main result is a kernel for FunnelArc Deletion Set with $\mathcal{O}(k^6)$ many vertices and $\mathcal{O}(k^7)$ many arcs, computable in linear time.
 Publication:

arXiv eprints
 Pub Date:
 November 2019
 arXiv:
 arXiv:1911.05520
 Bibcode:
 2019arXiv191105520G
 Keywords:

 Computer Science  Data Structures and Algorithms
 EPrint:
 Submitted to STACS 2020