@inproceedings{eab8fd53feb942d4abd3cda7ce522285,

title = "Polynomial pass lower bounds for graph streaming algorithms",

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.",

keywords = "Communication complexity, Graph streaming, Lower bounds",

author = "Sepehr Assadi and Yu Chen and Sanjeev Khanna",

note = "Publisher Copyright: {\textcopyright} 2019 Copyright held by the owner/author(s). Publication rights licensed to ACM.; 51st Annual ACM SIGACT Symposium on Theory of Computing, STOC 2019 ; Conference date: 23-06-2019 Through 26-06-2019",

year = "2019",

month = jun,

day = "23",

doi = "10.1145/3313276.3316361",

language = "English (US)",

series = "Proceedings of the Annual ACM Symposium on Theory of Computing",

publisher = "Association for Computing Machinery",

pages = "265--276",

editor = "Moses Charikar and Edith Cohen",

booktitle = "STOC 2019 - Proceedings of the 51st Annual ACM SIGACT Symposium on Theory of Computing",

}