What is known about Vertex Cover Kernelization?

11/23/2018
by   Michael R. Fellows, et al.
0

We are pleased to dedicate this survey on kernelization of the Vertex Cover problem, to Professor Juraj Hromkovič on the occasion of his 60th birthday. The Vertex Cover problem is often referred to as the Drosophila of parameterized complexity. It enjoys a long history. New and worthy perspectives will always be demonstrated first with concrete results here. This survey discusses several research directions in Vertex Cover kernelization. The Barrier Degree of Vertex Cover kernelization is discussed. We have reduction rules that kernelize vertices of small degree, including in this paper new results that reduce graphs almost to minimum degree five. Can this process go on forever? What is the minimum vertex-degree barrier for polynomial-time kernelization? Assuming the Exponential-Time Hypothesis, there is a minimum degree barrier. The idea of automated kernelization is discussed. We here report the first experimental results of an AI-guided branching algorithm for Vertex Cover whose logic seems amenable for application in finding reduction rules to kernelize small-degree vertices. The survey highlights a central open problem in parameterized complexity. Happy Birthday, Juraj!

READ FULL TEXT

page 1

page 2

page 3

page 4

research
10/30/2018

Weighted vertex cover on graphs with maximum degree 3

We give a parameterized algorithm for weighted vertex cover on graphs wi...
research
03/14/2019

An Exact Algorithm for Minimum Weight Vertex Cover Problem in Large Graphs

This paper proposes a novel branch-and-bound(BMWVC) algorithm to exactly...
research
03/16/2020

On the parameterized complexity of 2-partitions

We give an FPT algorithm for deciding whether the vertex set a digraph D...
research
11/08/2019

Reconfiguring k-path vertex covers

A vertex subset I of a graph G is called a k-path vertex cover if every ...
research
05/07/2020

Neighbourhood Evaluation Criteria for Vertex Cover Problem

Neighbourhood Evaluation Criteria is a heuristical approximate algorithm...
research
08/01/2022

Reduction Rules and ILP Are All You Need: Minimal Directed Feedback Vertex Set

This note describes the development of an exact solver for Minimal Direc...
research
05/11/2023

Backdoor to the Hidden Ground State: Planted Vertex Cover Example

We introduce a planted vertex cover problem on regular random graphs and...

Please sign up or login with your details

Forgot password? Click here to reset