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arXiv · 1705.02822

Rank Vertex Cover as a Natural Problem for Algebraic Compression

Syed Mohammad Meesum·Fahad Panolan·Saket Saurabh·Meirav Zehavi
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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.

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Syed Mohammad Meesum, Fahad Panolan, Saket Saurabh, Meirav Zehavi. 2017-05-08. Rank Vertex Cover as a Natural Problem for Algebraic Compression. https://arxiv.org/abs/1705.02822

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