Deterministic (1+ε)-approximate maximum matching with poly(1/ε) passes in the semi-streaming model and beyond

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]. Up to polynomial factors in 1/ε, our work matches the state-of-the-art deterministic (log n/ log log n) • (1/ε)-pass algorithm by Ahn and Guha [TOPC18], that is allowed a dependence on the number of nodes n. Our result also makes progress on the Open Problem 60 at sublinear.info 1 .

Moreover, we design a general framework that simulates our approach for the streaming setting in other models of computation. This framework requires access to an algorithm computing an O(1)approximate maximum matching and an algorithm for processing disjoint (poly 1/ε)-size connected components. Instantiating our framework in CONGEST yields a poly(log n, 1/ε) round algorithm for computing (1 + ε)-approximate maximum matching. In terms of the dependence on 1/ε, this result improves exponentially state-of-the-art result by Lotker, Patt-Shamir, and Pettie [LPSP15]. Our framework leads to the same quality of improvement in the context of the Massively Parallel Computation model as well.