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- W4308669594 abstract "We give an $widetilde{O}(sqrt{n})$-space single-pass $0.483$-approximation streaming algorithm for estimating the maximum directed cut size (Max-DICUT) in a directed graph on $n$ vertices. This improves over an $O(log n)$-space $4/9 < 0.45$ approximation algorithm due to Chou, Golovnev, and Velusamy (FOCS 2020), which was known to be optimal for $o(sqrt{n})$-space algorithms. Max-DICUT is a special case of a constraint satisfaction problem (CSP). In this broader context, we give the first CSP for which algorithms with $widetilde{O}(sqrt{n})$ space can provably outperform $o(sqrt{n})$-space algorithms. The key technical contribution of our work is development of the notions of a first-order snapshot of a (directed) graph and of estimates of such snapshots. These snapshots can be used to simulate certain (non-streaming) Max-DICUT algorithms, including the oblivious algorithms introduced by Feige and Jozeph (Algorithmica, 2015), who showed that one such algorithm achieves a 0.483-approximation. Previous work of the authors (SODA 2023) studied the restricted case of bounded-degree graphs, and observed that in this setting, it is straightforward to estimate the snapshot with $ell_1$ errors and this suffices to simulate oblivious algorithms. But for unbounded-degree graphs, even defining an achievable and sufficient notion of estimation is subtle. We describe a new notion of snapshot estimation and prove its sufficiency using careful smoothing techniques, and then develop an algorithm which sketches such an estimate via a delicate process of intertwined vertex- and edge-subsampling. Prior to our work, the only streaming algorithms for any CSP on general instances were based on generalizations of the $O(log n)$-space algorithm for Max-DICUT, and thus our work opens the possibility of a new class of algorithms for approximating CSPs." @default.
- W4308669594 created "2022-11-14" @default.
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- W4308669594 date "2022-11-07" @default.
- W4308669594 modified "2023-09-25" @default.
- W4308669594 title "Improved Streaming Algorithms for Maximum Directed Cut via Smoothed Snapshots" @default.
- W4308669594 doi "https://doi.org/10.48550/arxiv.2211.03916" @default.
- W4308669594 hasPublicationYear "2022" @default.
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