Speaker: Sanjeev Khanna
Affiliation: University of Pennsylvania

Title: Tight Bounds for Linear Sketches of Approximate Matchings

Abstract:
We consider the problem of approximating a maximum matching in dynamic graph streams where the stream may include both edge insertions and deletions. Our main result is a resolution of the space complexity of linear sketches for approximating the maximum matching in this model.

Specifically, we show that for any $\eps > 0$, there exists a single-pass streaming algorithm, which only maintains a linear sketch of size roughly $n^{2-3\eps}$ bits and recovers an $n^\epsilon$-approximate maximum matching in dynamic graph streams, where $n$ is the number of vertices in the graph. We complement this result with the following lower bound result: any linear sketch for approximating the maximum matching to within a factor of $n^\eps$ has to be of size at least $n^{2-3\eps -o(1)}$ bits.

This is based on joint work with Sepehr Assadi, Yang Li, and Grigory Yaroslavtsev.