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This is a Quantitative Study study.

October 18, 2025Open Access

Sketching approximations and LP approximations for finite CSPs are related

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This research demonstrates how approximations in CSPs link streaming algorithms and LP relaxations, suggesting new bounds.

The existence of an integrality gap in basic LPs implies a lower bound for sketching space of Ω(√n), enhancing understanding of CSPs.
All known linear space streaming lower bounds for Max-CSPs can be applied to instances with integrality gaps in basic LPs.
Combining recent distributed algorithms suggests sublinear space streaming algorithms could effectively implement basic LP across CSPs.
The findings suggest a dichotomy theorem relating LP roundability to linear and sublinear space streaming lower bounds.

Singer et al. (2025) studied this question.

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