Deterministic $(1+\varepsilon)$-Approximate Maximum Matching with $\mathsf{poly}(1/\varepsilon)$ Passes in the Semi-Streaming Model

We present a deterministic $(1+\varepsilon)$-approximate maximum matching algorithm in $\mathsf{poly}(1/\varepsilon)$ passes in the semi-streaming model, solving the long-standing open problem of breaking the exponential barrier in the dependence on $1/\varepsilon$. Our algorithm exponentially improves on the well-known randomized $(1/\varepsilon)^{O(1/\varepsilon)}$-pass algorithm from the seminal work by McGregor [APPROX05], the recent deterministic algorithm by Tirodkar with the same pass complexity [FSTTCS18], as well as the deterministic $\log n \cdot \mathsf{poly}(1/\varepsilon)$-pass algorithm by Ahn and Guha [ICALP11].