Semidefinite programming and linear equations vs. homomorphism problems
Fuente:
arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2023
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| _version_ | 1866909603144400896 |
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| author | Ciardo, Lorenzo Živný, Stanislav |
| author_facet | Ciardo, Lorenzo Živný, Stanislav |
| contents | We introduce a relaxation for homomorphism problems that combines semidefinite programming with linear Diophantine equations, and propose a framework for the analysis of its power based on the spectral theory of association schemes. We use this framework to establish an unconditional lower bound against the semidefinite programming + linear equations model, by showing that the relaxation does not solve the approximate graph homomorphism problem and thus, in particular, the approximate graph colouring problem. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2311_00882 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Semidefinite programming and linear equations vs. homomorphism problems Ciardo, Lorenzo Živný, Stanislav Computational Complexity Discrete Mathematics Data Structures and Algorithms Optimization and Control We introduce a relaxation for homomorphism problems that combines semidefinite programming with linear Diophantine equations, and propose a framework for the analysis of its power based on the spectral theory of association schemes. We use this framework to establish an unconditional lower bound against the semidefinite programming + linear equations model, by showing that the relaxation does not solve the approximate graph homomorphism problem and thus, in particular, the approximate graph colouring problem. |
| title | Semidefinite programming and linear equations vs. homomorphism problems |
| topic | Computational Complexity Discrete Mathematics Data Structures and Algorithms Optimization and Control |
| url | https://arxiv.org/abs/2311.00882 |