Combinatorics and Graph Theory

    

A Randomized 1.885903-Approximation Algorithm for the 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 we know that there is not any mathematical formulation that approximates it better than 2-o(1). In other words, it is known that it is hard to approximate to within any constant factor better than 2, 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 rounding procedure, along with satisfying new properties, we introduce an approximation algorithm for the vertex cover problem with a performance ratio of 1.885903 on arbitrary graphs, en route answering an open question about the unique games conjecture.

Comments: 7 Pages. Due to some comments, I preferred to add some explanations.

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Submission history

[v1] 2022-02-22 06:40:29
[v2] 2022-05-03 05:50:54

Unique-IP document downloads: 396 times

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