Polynomial pass lower bounds for graph streaming algorithms

Sepehr Assadi, Yu Chen, Sanjeev Khanna

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

20 Scopus citations

Abstract

We present new lower bounds that show that a polynomial number of passes are necessary for solving some fundamental graph problems in the streaming model of computation. For instance, we show that any streaming algorithm that finds a weighted minimum s-t cut in an n-vertex undirected graph requires n2−o(1) space unless it makes nΩ(1) passes over the stream. To prove our lower bounds, we introduce and analyze a new four-player communication problem that we refer to as the hidden-pointer chasing problem. This is a problem in spirit of the standard pointer chasing problem with the key difference that the pointers in this problem are hidden to players and finding each one of them requires solving another communication problem, namely the set intersection problem. Our lower bounds for graph problems are then obtained by reductions from the hidden-pointer chasing problem. Our hidden-pointer chasing problem appears flexible enough to find other applications and is therefore interesting in its own right. To showcase this, we further present an interesting application of this problem beyond streaming algorithms. Using a reduction from hidden-pointer chasing, we prove that any algorithm for submodular function minimization needs to make n2−o(1) value queries to the function unless it has a polynomial degree of adaptivity.

Original languageEnglish (US)
Title of host publicationSTOC 2019 - Proceedings of the 51st Annual ACM SIGACT Symposium on Theory of Computing
EditorsMoses Charikar, Edith Cohen
PublisherAssociation for Computing Machinery
Pages265-276
Number of pages12
ISBN (Electronic)9781450367059
DOIs
StatePublished - Jun 23 2019
Externally publishedYes
Event51st Annual ACM SIGACT Symposium on Theory of Computing, STOC 2019 - Phoenix, United States
Duration: Jun 23 2019Jun 26 2019

Publication series

NameProceedings of the Annual ACM Symposium on Theory of Computing
ISSN (Print)0737-8017

Conference

Conference51st Annual ACM SIGACT Symposium on Theory of Computing, STOC 2019
Country/TerritoryUnited States
CityPhoenix
Period6/23/196/26/19

All Science Journal Classification (ASJC) codes

  • Software

Keywords

  • Communication complexity
  • Graph streaming
  • Lower bounds

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