Article Source

• Almost Optimal Super-Constant-Pass Streaming Lower Bounds for Reachability

Almost Optimal Super-Constant-Pass Streaming Lower Bounds for Reachability

• Authors: Lijie Chen, Gillat Kol, Dmitry Paramonov, Raghuvansh R. Saxena, Zhao Song, Huacheng Yu
• Paper
• STOC 2021: Proceedings of the 53rd Annual ACM SIGACT Symposium on Theory of Computing, June 2021, Pages 570–583

Abstract

We give an almost quadratic lower bound on the space consumption of any -pass streaming algorithm solving the (directed) s-t reachability problem. This means that any such algorithm must essentially store the entire graph. As corollaries, we obtain almost quadratic space lower bounds for additional fundamental problems, including maximum matching, shortest path, matrix rank, and linear programming.

Our main technical contribution is the definition and construction of set hiding graphs, that may be of independent interest: we give a general way of encoding a set as a directed graph with vertices, such that deciding whether boils down to deciding if is reachable from , for a specific pair of vertices in the graph. Furthermore, we prove that our graph “hides” S, in the sense that no low-space streaming algorithm with a small number of passes can learn (almost) anything about S.