Deterministic (1+ε)-Approximate Maximum Matching with 𝗉𝗈𝗅𝗒(1/ε) Passes in the Semi-Streaming Model

06/08/2021

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by   Manuela Fischer, et al.

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We present a deterministic (1+ε)-approximate maximum matching algorithm in 𝗉𝗈𝗅𝗒(1/ε) passes in the semi-streaming model, solving the long-standing open problem of breaking the exponential barrier in the dependence on 1/ε. Our algorithm exponentially improves on the well-known randomized (1/ε)^O(1/ε)-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 ·𝗉𝗈𝗅𝗒(1/ε)-pass algorithm by Ahn and Guha [ICALP11].