Saved in:
| Main Author: | |
|---|---|
| Format: | Preprint |
| Published: |
2023
|
| Subjects: | |
| Online Access: | https://arxiv.org/abs/2305.05676 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866914688793575424 |
|---|---|
| author | Çivril, Ali |
| author_facet | Çivril, Ali |
| 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 $\frac{1}{4} \geq ε> 0$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2305_05676 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Scheme-Theoretic Approach to Computational Complexity. IV. A New Perspective on Hardness of Approximation Çivril, Ali Computational Complexity 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 $\frac{1}{4} \geq ε> 0$. |
| title | Scheme-Theoretic Approach to Computational Complexity. IV. A New Perspective on Hardness of Approximation |
| topic | Computational Complexity |
| url | https://arxiv.org/abs/2305.05676 |