NearQuadratic Lower Bounds for TwoPass Graph Streaming Algorithms
Abstract
We prove that any twopass graph streaming algorithm for the $s$$t$ reachability problem in $n$vertex directed graphs requires nearquadratic space of $n^{2o(1)}$ bits. As a corollary, we also obtain nearquadratic 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 nontrivial streaming algorithm even when two passes over the input is allowed. Prior to our work, such impossibility results were only known for singlepass streaming algorithms, and the best twopass lower bounds only ruled out $o(n^{7/6})$ space algorithms, leaving open a large gap between (trivial) upper bounds and lower bounds.
 Publication:

arXiv eprints
 Pub Date:
 September 2020
 DOI:
 10.48550/arXiv.2009.01161
 arXiv:
 arXiv:2009.01161
 Bibcode:
 2020arXiv200901161A
 Keywords:

 Computer Science  Data Structures and Algorithms;
 Computer Science  Computational Complexity
 EPrint:
 61st IEEE Annual Symposium on Foundations of Computer Science, FOCS 2020