Semidefinite programming and linear equations vs. homomorphism problems
Computational Complexity
2025-05-08 v3 Discrete Mathematics
Data Structures and Algorithms
Optimization and Control
Abstract
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.
Cite
@article{arxiv.2311.00882,
title = {Semidefinite programming and linear equations vs. homomorphism problems},
author = {Lorenzo Ciardo and Stanislav Živný},
journal= {arXiv preprint arXiv:2311.00882},
year = {2025}
}