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| Main Author: | |
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| Format: | Preprint |
| Published: |
2023
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2305.05676 |
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Table of Contents:
- We provide a new approach for establishing hardness of approximation results, based on the theory recently introduced by the author. It allows one to directly show that approximating a problem beyond a certain threshold requires super-polynomial time. To exhibit the framework, we revisit two famous problems in this paper. The particular results we prove are: MAX-3-SAT$(1,\frac{7}{8}+ε)$ requires exponential time for any constant $ε$ satisfying $\frac{1}{8} \geq ε> 0$. In particular, the gap exponential time hypothesis (Gap-ETH) holds. MAX-3-LIN-2$(1-ε, \frac{1}{2}+ε)$ requires exponential time for any constant $ε$ satisfying $\frac{1}{4} \geq ε> 0$.