Nine lower bound conjectures on streaming approximation algorithms for CSPs
Noah G. Singer
TL;DR
This paper surveys the landscape of streaming algorithms for Max-CSPs and introduces nine frontier conjectures that aim to delineate unconditional lower bounds in various streaming regimes. It analyzes both single-pass and multi-pass models, highlighting how results for Max-Cut and Max-DiCut differ with respect to input order and space usage, and it frames a general sketching dichotomy (CGSV24) that governs what can be achieved with polylogarithmic space versus sublinear superpolylogarithmic space. By connecting classical communication complexity reductions to streaming lower bounds, the work clarifies where nontrivial streaming approximations are possible and where they are provably hard, while outlining key conjectures that would unify and extend current bounds across CSPs like Max-Cut, Max-DiCut, Max-3-And, and monarchy-inspired predicates. The joint aim is to map the limits of streaming CSP approximations, inform future algorithm design, and guide the search for tight, space-accuracy tradeoffs with broad implications for sublinear-memory computation. The findings have significant implications for understanding information-theoretic constraints on compression of CSP instances and for guiding practical streaming algorithms in graph- and predicate-based optimization problems.
Abstract
In this column, we overview recent progress by many authors on understanding the approximability of constraint satisfaction problems (CSPs) in low-space streaming models. Inspired by this recent progress, we collate nine conjectural lower bounds against streaming algorithms for CSPs, some of which appear here for the first time.