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Scheme-Theoretic Approach to Computational Complexity. IV. A New Perspective on Hardness of Approximation

2023/05/09 by Ali Çivril, Çivril, Ali
Computer Science · #Algorithms and Data Compression #Complexity and Algorithms in Graphs #Machine Learning and Algorithms #cs.CC

paper · pdf · doi:10.48550/arxiv.2305.05676

openalex publication_date 2023/05/09 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

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,(7)/(8)+ε) requires exponential time for any constant ε satisfying (1)/(8) ≥ ε> 0. In particular, the gap exponential time hypothesis (Gap-ETH) holds. MAX-3-LIN-2(1-ε, (1)/(2)+ε) requires exponential time for any constant ε satisfying (1)/(4) ≥ ε> 0.

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