Combinatorics and Graph Theory

    

A (1.999999)-Approximation Ratio for Vertex Cover Problem

Authors: Majid Zohrehbandian

The vertex cover problem is a famous combinatorial problem, and its complexity has been heavily studied. While a 2-approximation for it can be trivially obtained, researchers have not been able to approximate it better than 2-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.

Comments: 14 Pages.

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Submission history

[v1] 2024-03-11 20:22:56
[v2] 2024-05-05 07:03:26
[v3] 2024-10-14 02:49:43
[v4] 2024-12-25 01:21:50
[v5] 2025-03-10 21:17:57

Unique-IP document downloads: 732 times

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