Rank Vertex Cover as a Natural Problem for Algebraic Compression
Data Structures and Algorithms
2017-05-11 v2
Abstract
The question of the existence of a polynomial kernelization of the Vertex Cover Above LP problem has been a longstanding, notorious open problem in Parameterized Complexity. Five years ago, the breakthrough work by Kratsch and Wahlstrom on representative sets has finally answered this question in the affirmative [FOCS 2012]. In this paper, we present an alternative, algebraic compression of the Vertex Cover Above LP problem into the Rank Vertex Cover problem. Here, the input consists of a graph G, a parameter k, and a bijection between V (G) and the set of columns of a representation of a matriod M, and the objective is to find a vertex cover whose rank is upper bounded by k.
Cite
@article{arxiv.1705.02822,
title = {Rank Vertex Cover as a Natural Problem for Algebraic Compression},
author = {Syed Mohammad Meesum and Fahad Panolan and Saket Saurabh and Meirav Zehavi},
journal= {arXiv preprint arXiv:1705.02822},
year = {2017}
}