Combinatorics and Graph Theory

    

New Insight Into Introducing a (2-ℇ)-Approximation Ratio for Minimum Vertex Cover Problem

Authors: Majid Zohrehbandian

Vertex cover problem is a famous combinatorial problem, which its complexity has been heavily studied over the years and it is known that there is not any mathematical programming formulation that approximates it better than 2-o(1), while a 2-approximation for it can be trivially obtained. In this paper, by a combination of a well-known semidefinite programming formulation and a randomized procedure, along with satisfying new properties, we introduce an approximation algorithm for the vertex cover problem with a performance ratio of 1.999999 on arbitrary graphs, en route to answering an open question about the unique games conjecture.

Comments: 9 Pages.

Download: PDF

Submission history

[v1] 2021-07-07 08:36:40
[v2] 2021-08-08 02:52:16
[v3] 2022-01-09 23:42:35
[v4] 2022-05-03 05:47:23
[v5] 2022-07-20 07:14:16

Unique-IP document downloads: 898 times

Vixra.org is a pre-print repository rather than a journal. Articles hosted may not yet have been verified by peer-review and should be treated as preliminary. In particular, anything that appears to include financial or legal advice or proposed medical treatments should be treated with due caution. Vixra.org will not be responsible for any consequences of actions that result from any form of use of any documents on this website.

Add your own feedback and questions here:
You are equally welcome to be positive or negative about any paper but please be polite. If you are being critical you must mention at least one specific error, otherwise your comment will be deleted as unhelpful.

comments powered by Disqus