The Sherali-Adams Hierarchy for Promise CSPs through Tensors

Lorenzo Ciardo; Stanislav Živný

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arXiv · 2203.02478

The Sherali-Adams Hierarchy for Promise CSPs through Tensors

Lorenzo Ciardo·Stanislav Živný

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Abstract

We study the Sherali-Adams linear programming hierarchy in the context of promise constraint satisfaction problems (PCSPs). We characterise when a level of the hierarchy accepts an instance in terms of a homomorphism problem for an appropriate multilinear structure obtained through a tensor power of the constraint language. The geometry of this structure, which consists in a space of tensors satisfying certain symmetries, allows then to establish non-solvability of the approximate graph colouring problem via constantly many levels of Sherali-Adams. Besides this primary application, our tensorisation construction introduces a new tool to the study of hierarchies of algorithmic relaxations for computational problems within (and, possibly, beyond) the context of constraint satisfaction. In particular, we see it as a key step towards the algebraic characterisation of the power of Sherali-Adams for PCSPs.

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BibTeX RIS

Lorenzo Ciardo, Stanislav Živný. 2022-03-04. The Sherali-Adams Hierarchy for Promise CSPs through Tensors. https://arxiv.org/abs/2203.02478

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