Deterministic (1+)-approximate maximum matching with poly(1/) passes in the semi-streaming model and beyond
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Date
2022-09-06
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Language
en
Pages
13
248-260
248-260
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STOC 2022 - Proceedings of the 54th Annual ACM SIGACT Symposium on Theory of Computing
Abstract
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 (logn / loglogn) · (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. 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 a maximal matching and an algorithm for processing disjoint ( 1 / ϵ)-size connected components. Instantiating our framework in CONGEST yields a (logn, 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.Description
Funding Information: The second author of this work was supported by the Swiss NSF Grant under Grant No. P400P2_191122/1. Most of this work was done while the author was affiliated with MIT. The third author was supported in part by the Academy of Finland under Grant No. 334238. Publisher Copyright: © 2022 Owner/Author.
Keywords
algorithm, approximation, deterministic, matching, streaming
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Citation
Fischer, M, Mitrović, S & Uitto, J 2022, Deterministic (1+ )-approximate maximum matching with poly(1/ ) passes in the semi-streaming model and beyond . in S Leonardi & A Gupta (eds), STOC 2022 - Proceedings of the 54th Annual ACM SIGACT Symposium on Theory of Computing . ACM, pp. 248-260, ACM Symposium on Theory of Computing, Rome, Italy, 20/06/2022 . https://doi.org/10.1145/3519935.3520039
