Single-pass streaming matching better than 0.5 in O(n) space

Determine whether there exists a single-pass streaming algorithm using O(n) space that computes a matching with approximation factor strictly greater than 0.5 on general graphs.

Background

The authors highlight a long-standing open question in streaming algorithms regarding maximum matching: current single-pass, O(n)-space algorithms achieve at most a 0.5-approximation, and surpassing this barrier remains unresolved.

This question is central due to the close relationship between one-way communication protocols and streaming algorithms, where communication lower bounds often imply space lower bounds.