Communication is bounded by root of rank [article]

Shachar Lovett
2013 arXiv   pre-print
We prove that any total boolean function of rank r can be computed by a deterministic communication protocol of complexity O(√(r)·(r)). Equivalently, any graph whose adjacency matrix has rank r has chromatic number at most 2^O(√(r)·(r)). This gives a nearly quadratic improvement in the dependence on the rank over previous results.
arXiv:1306.1877v2 fatcat:gjwhtfbefvc5bko63plkn2yqui