Volume 6 (2010) Article 6 pp. 113-134

Rounds vs. Queries Tradeoff in Noisy Computation

by Navin Goyal and Michael Saks

Received: January 26, 2010
Published: September 2, 2010

We show that a noisy parallel decision tree making $O(n)$ queries needs $\Omega(\log^{*}n)$ rounds to compute OR of $n$ bits. This answers a question of Newman [IEEE Conference on Computational Complexity, 2004, 113--124]. We prove more general tradeoffs between the number of queries and rounds. We also settle a similar question for computing MAX in the noisy comparison tree model; these results bring out interesting differences among the noise models.

DOI: 10.4086/toc.2010.v006a006

© 2010 Navin Goyal and Michael Saks
Licensed under a Creative Commons Attribution License (CC-BY)