Krzysztof Onak > Papers > Superlinear Lower Bounds for Multipass Graph Processing

Superlinear Lower Bounds for Multipass Graph Processing

Authors: Venkatesan Guruswami, Krzysztof Onak
Conference: The 28th IEEE Conference on Computational Complexity (CCC 2013).
Journal: Special issue of Algorithmica on Information Complexity and Applications, Algorithmica 76(3), 2016.

Abstract: We prove $n^{1+\Omega(1/p)}/p^{O(1)}$ lower bounds for the space complexity of $p$-pass streaming algorithms solving the following problems on $n$-vertex graphs:

Prior to our result, it was known that these problems require $\Omega(n^2)$ space in one pass, but no $n^{1+\Omega(1)}$ lower bound was known for any $p\ge 2$.

These streaming results follow from a communication complexity lower bound for a communication game in which the players hold two graphs on the same set of vertices. The task of the players is to find out whether the sets of vertices reachable from a specific vertex in exactly $p+1$ steps intersect. The game requires a significant amount of communication only if the players are forced to speak in a specific difficult order. This is reminiscent of lower bounds for communication problems such as indexing and pointer chasing. Among other things, our line of attack requires proving an information cost lower bound for a decision version of the classic pointer chasing problem and a direct sum type theorem for the disjunction of several instances of this problem.

Full paper: [PDF]
BibTeX: [DBLP]