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

arXiv: https://arxiv.org/abs/2009.01161 · HTML: https://mlsanity.com/paper/2009.01161/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 2 Sep 2020.

## Built on by (most cited first, 3 of 3)

- [Bounded Memory Active Learning through Enriched Queries](https://mlsanity.com/paper/2102.05047/) (2021)
- [One Pass Streaming Algorithm for Super Long Token Attention Approximation in Sublinear Space](https://mlsanity.com/paper/2311.14652/) (2023)
- [Sketching Algorithms and Lower Bounds for Ridge Regression](https://mlsanity.com/paper/2204.06653/) (2022)

## Abstract (arXiv)

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 n2-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(n7/6) space algorithms, leaving open a large gap between (trivial) upper bounds and lower bounds.