Weizmann Logo
Electronic Colloquium on Computational Complexity

Under the auspices of the Computational Complexity Foundation (CCF)

Login | Register | Classic Style



TR16-148 | 23rd September 2016 03:54

Communication Complexity with Small Advantage


Authors: Thomas Watson
Publication: 23rd September 2016 09:15
Downloads: 661


We study problems in randomized communication complexity when the protocol is only required to attain some small advantage over purely random guessing, i.e., it produces the correct output with probability at least $\epsilon$ greater than one over the codomain size of the function. Previously, Braverman and Moitra (STOC 2013) showed that the set-intersection function requires $\Theta(\epsilon n)$ communication to achieve advantage $\epsilon$. Building on this, we prove the same bound for several variants of set-intersection: (1) the classic "tribes" function obtained by composing with And (provided $1/\epsilon$ is at most the width of the And), and (2) the variant where the sets are uniquely intersecting and the goal is to determine partial information about (say, certain bits of the index of) the intersecting coordinate.

ISSN 1433-8092 | Imprint