Linear Kernelizations for Restricted 3-Hitting Set Problems

TL;DR

This paper investigates kernelization techniques for the 3-Hitting Set problem, equivalent to Vertex Cover on 3-uniform hypergraphs, demonstrating linear kernels for specific classes and establishing bounds on kernel sizes.

Contribution

The paper introduces linear kernelizations for Vertex Cover on 3-uniform hypergraphs in three classes and provides bounds on kernel sizes using parametric duality.

Findings

Existence of linear kernels in three classes of 3-uniform hypergraphs

Lower and upper bounds on kernel sizes established

Enhanced understanding of kernelization limits for these problems

Abstract

The 3-\textsc{Hitting Set} problem is also called the \textsc{Vertex Cover} problem on 3-uniform hypergraphs. In this paper, we address kernelizations of the \textsc{Vertex Cover} problem on 3-uniform hypergraphs. We show that this problem admits a linear kernel in three classes of 3-uniform hypergraphs. We also obtain lower and upper bounds on the kernel size for them by the parametric duality.