Single-pass streaming estimation of maximum matching size beyond 0.5

Ascertain whether a single-pass streaming algorithm using O(n) space can estimate the size of the maximum matching within a factor strictly greater than 0.5 on general graphs.

Background

Beyond constructing approximate matchings, even estimating the maximum matching size better than the 0.5 threshold is unresolved in the single-pass, linear-space streaming model.

Resolving this would inform both matching algorithms and related dual problems such as vertex cover.

References

Even estimating the size of the maximum matching (the dual of minimum vertex cover) within a factor greater than 0.5 remains unresolved in this setting.

— One-way Communication Complexity of Minimum Vertex Cover in General Graphs (2505.00164 - Derakhshan et al., 30 Apr 2025) in Introduction, Relation to streaming algorithms