Streaming and Sketching Complexity of CSPs: A survey

TL;DR

This survey reviews recent progress in understanding the complexity of approximately solving constraint satisfaction problems (CSPs) within streaming and sketching models, highlighting key results and proof techniques.

Contribution

It provides a comprehensive overview of the last decade's advances in CSP complexity in streaming and sketching contexts, including explanations of tight dichotomy results.

Findings

Existence of a tight dichotomy for sketching algorithms in subpolynomial space

Progress in understanding CSP approximation complexity in streaming models

Sketches of proof techniques for key complexity results

Abstract

In this survey we describe progress over the last decade or so in understanding the complexity of solving constraint satisfaction problems (CSPs) approximately in the streaming and sketching models of computation. After surveying some of the results we give some sketches of the proofs and in particular try to explain why there is a tight dichotomy result for sketching algorithms working in subpolynomial space regime.