Best achievable approximation with o(n) space in single-pass streaming for Max-CSP

Determine, as a function of the predicate family F, the optimal approximation ratio achievable by any single-pass streaming algorithm for Max-CSP(F) when the available memory is o(n).

Background

The paper studies Max-CSP in the streaming setting, where constraints arrive in arbitrary order and the algorithm has limited memory. While O(n) space yields a trivial near-optimal solution by storing a linear number of constraints, the interesting regime is sublinear space. The authors note that understanding the best possible approximation in this regime has been a central focus.

They further explain that the answer depends strongly on the CSP family via the integrality gap of the BasicLP, and that a leading hypothesis formalizing this dependence is the Streaming Dichotomy Conjecture. This work proves the upper bound side of that conjecture, narrowing the open question largely to matching lower bounds.