A 13k-kernel for Planar Feedback Vertex Set via Region Decomposition

TL;DR

This paper presents a polynomial-time kernelization algorithm that reduces planar Feedback Vertex Set instances to at most 13k vertices, using novel reduction rules and the region decomposition technique, with tight analysis.

Contribution

It introduces a new kernel size bound of 13k vertices for planar Feedback Vertex Set using region decomposition, improving previous results.

Findings

Kernel size of at most 13k vertices for planar Feedback Vertex Set

Introduction of new reduction rules for kernelization

Application and tight analysis of region decomposition technique

Abstract

We show a kernel of at most $13k$ vertices for the Planar Feedback Vertex Set problem restricted to planar graphs, i.e., a polynomial-time algorithm that transforms an input instance $(G,k)$ to an equivalent instance with at most $13k$ vertices. To this end we introduce a few new reduction rules. However, our main contribution is an application of the region decomposition technique in the analysis of the kernel size. We show that our analysis is tight, up to a constant additive term.