Maximum Matching Size for Bounded Arboricity Graphs in the Dynamic Graph Stream Model using $\tilde{O}(n^{2/3})$ space

Abstract

The paper presents a one-pass algorithm in the insert-delete graph stream model that returns a $(1+\varepsilon)(\alpha+2)$-approximation for the size of the maximum matching in a graph of arboricity at most $\alpha$. The algorithm uses $O(\varepsilon^{-4/3}\alpha^{4/3}n^{2/3} \text{polylog} n)$ space. For constant $\alpha$ and $\varepsilon$, this improves the best known previous space bound from $O(n^{4/5} \text{polylog} n)$ to $O(n^{2/3} \text{polylog} n)$. The algorithm is a linear sketch and requires no bounds on the number of deletions or on the arboricity of intermediate graphs.