Clique Is Hard on Average for Sherali-Adams with Bounded Coefficients
Fuente:
arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866910423345790976 |
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| author | de Rezende, Susanna F. Potechin, Aaron Risse, Kilian |
| author_facet | de Rezende, Susanna F. Potechin, Aaron Risse, Kilian |
| contents | We prove that Sherali-Adams with polynomially bounded coefficients requires proofs of size $n^{Ω(d)}$ to rule out the existence of an $n^{Θ(1)}$-clique in Erdős-Rényi random graphs whose maximum clique is of size $d\leq 2\log n$. This lower bound is tight up to the multiplicative constant in the exponent. We obtain this result by introducing a technique inspired by pseudo-calibration which may be of independent interest. The technique involves defining a measure on monomials that precisely captures the contribution of a monomial to a refutation. This measure intuitively captures progress and should have further applications in proof complexity. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2404_16722 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Clique Is Hard on Average for Sherali-Adams with Bounded Coefficients de Rezende, Susanna F. Potechin, Aaron Risse, Kilian Computational Complexity F.2.2; F.1.3; I.2.3; F.4.1 We prove that Sherali-Adams with polynomially bounded coefficients requires proofs of size $n^{Ω(d)}$ to rule out the existence of an $n^{Θ(1)}$-clique in Erdős-Rényi random graphs whose maximum clique is of size $d\leq 2\log n$. This lower bound is tight up to the multiplicative constant in the exponent. We obtain this result by introducing a technique inspired by pseudo-calibration which may be of independent interest. The technique involves defining a measure on monomials that precisely captures the contribution of a monomial to a refutation. This measure intuitively captures progress and should have further applications in proof complexity. |
| title | Clique Is Hard on Average for Sherali-Adams with Bounded Coefficients |
| topic | Computational Complexity F.2.2; F.1.3; I.2.3; F.4.1 |
| url | https://arxiv.org/abs/2404.16722 |