Publication details
Towards a Polynomial Kernel for Directed Feedback Vertex Set
| Authors | |
|---|---|
| Year of publication | 2017 |
| Type | Article in Proceedings |
| Conference | 42nd International Symposium on Mathematical Foundations of Computer Science, {MFCS} 2017, August 21-25, 2017 - Aalborg, Denmark |
| MU Faculty or unit | |
| Citation | |
| Web | http://drops.dagstuhl.de/opus/volltexte/2017/8112/ |
| Doi | http://dx.doi.org/10.4230/LIPIcs.MFCS.2017.36 |
| Keywords | parameterized algorithms; kernelization; (directed) feedback vertex set |
| Description | In the Directed Feedback Vertex Set (DFVS) problem, the input is a directed graph D and an integer k. The objective is to determine whether there exists a set of at most k vertices intersecting every directed cycle of D. DFVS was shown to be fixed-parameter tractable when parameterized by solution size by Chen, Liu, Lu, O'Sullivan and Razgon [JACM 2008]; since then, the existence of a polynomial kernel for this problem has become one of the largest open problems in the area of parameterized algorithmics. In this paper, we study DFVS parameterized by the feedback vertex set number of the underlying undirected graph. We provide two main contributions: a polynomial kernel for this problem on general instances, and a linear kernel for the case where the input digraph is embeddable on a surface of bounded genus. |