A (1.999999)-approximation ratio for vertex cover problem

Majid Zohrehbandian

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arXiv · 2403.19680

A (1.999999)-approximation ratio for vertex cover problem

Majid Zohrehbandian

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Abstract

The vertex cover problem is a famous combinatorial problem, and its complexity has been heavily studied. While a 2-approximation can be trivially obtained for it, researchers have not been able to approximate it better than 2-\textit{o}(1). In this paper, by introducing a new semidefinite programming formulation that satisfies 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 correctness of the unique games conjecture.

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BibTeX RIS

Majid Zohrehbandian. 2024-02-22. A (1.999999)-approximation ratio for vertex cover problem. https://arxiv.org/abs/2403.19680

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