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# Near-Quadratic Lower Bounds for Two-Pass Graph Streaming Algorithms

## Author(s): Assadi, Sepehr; Raz, Ran

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 Abstract: We prove that any two-pass graph streaming algorithm for the s-t reachability problem in n-vertex directed graphs requires near-quadratic space of n 2-o(1) bits. As a corollary, we also obtain near-quadratic space lower bounds for several other fundamental problems including maximum bipartite matching and (approximate) shortest path in undirected graphs. Our results collectively imply that a wide range of graph problems admit essentially no non-trivial streaming algorithm even when two passes over the input is allowed. Prior to our work, such impossibility results were only known for single-pass streaming algorithms, and the best two-pass lower bounds only ruled out o(n 7/6 ) space algorithms, leaving open a large gap between (trivial) upper bounds and lower bounds. Publication Date: 2020 Citation: Assadi, Sepehr, and Ran Raz. "Near-Quadratic Lower Bounds for Two-Pass Graph Streaming Algorithms." In IEEE 61st Annual Symposium on Foundations of Computer Science (FOCS) (2020): pp. 342-353. doi:10.1109/FOCS46700.2020.00040 DOI: 10.1109/FOCS46700.2020.00040 ISSN: 1523-8288 EISSN: 2575-8454 Pages: 342 - 353 Type of Material: Conference Article Journal/Proceeding Title: IEEE 61st Annual Symposium on Foundations of Computer Science (FOCS) Version: Author's manuscript

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