Affiliation:
1. University of California, San Diego, CA, USA
Abstract
We prove that any total boolean function of rank
r
can be computed by a deterministic communication protocol of complexity
O
(√ ċ log(
r
)). Equivalently, any graph whose adjacency matrix has rank
r
has chromatic number at most 2
O
(√
r
ċlog(
r
))
. This gives a nearly quadratic improvement in the dependence on the rank over previous results.
Funder
National Science Foundation CAREER
Publisher
Association for Computing Machinery (ACM)
Subject
Artificial Intelligence,Hardware and Architecture,Information Systems,Control and Systems Engineering,Software
Reference14 articles.
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