A (1.999999)-approximation ratio for vertex cover problem
Computational Complexity
2025-03-04 v6
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.
Cite
@article{arxiv.2403.19680,
title = {A (1.999999)-approximation ratio for vertex cover problem},
author = {Majid Zohrehbandian},
journal= {arXiv preprint arXiv:2403.19680},
year = {2025}
}