Near-quadratic lower bounds for two-pass graph streaming algorithms

Sepehr Assadi, Ran Raz

Research output: Chapter in Book/Report/Conference proceedingConference contribution

1 Scopus citations

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.

Original languageEnglish (US)
Title of host publicationProceedings - 2020 IEEE 61st Annual Symposium on Foundations of Computer Science, FOCS 2020
PublisherIEEE Computer Society
Pages342-353
Number of pages12
ISBN (Electronic)9781728196213
DOIs
StatePublished - Nov 2020
Event61st IEEE Annual Symposium on Foundations of Computer Science, FOCS 2020 - Virtual, Durham, United States
Duration: Nov 16 2020Nov 19 2020

Publication series

NameProceedings - Annual IEEE Symposium on Foundations of Computer Science, FOCS
Volume2020-November
ISSN (Print)0272-5428

Conference

Conference61st IEEE Annual Symposium on Foundations of Computer Science, FOCS 2020
Country/TerritoryUnited States
CityVirtual, Durham
Period11/16/2011/19/20

All Science Journal Classification (ASJC) codes

  • Computer Science(all)

Keywords

  • Graph streaming
  • communication complexity
  • multi pass streaming lower bounds
  • s-t reachability

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