Communication is bounded by root of rank

Shachar Lovett

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arXiv · 1306.1877

Communication is bounded by root of rank

Shachar Lovett

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Abstract

We prove that any total boolean function of rank $r$ can be computed by a deterministic communication protocol of complexity $O(\sqrt{r} \cdot \log(r))$. Equivalently, any graph whose adjacency matrix has rank $r$ has chromatic number at most $2^{O(\sqrt{r} \cdot \log(r))}$. This gives a nearly quadratic improvement in the dependence on the rank over previous results.

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Shachar Lovett. 2013-10-08. Communication is bounded by root of rank. https://arxiv.org/abs/1306.1877

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