Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Communication is bounded by root of rank   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.

33
The categories of this paper are: plasm-ph
20
The categories of this paper are: acc-phys
10
The categories of this paper are: q-bio
32
The categories of this paper are: atom-ph
34
The categories of this paper are: chem-ph
0
The categories of this paper are: hep-ph
28
The categories of this paper are: alg-geom
27
The categories of this paper are: comp-gas
17
The categories of this paper are: q-fin
18
The categories of this paper are: econ
14
The categories of this paper are: math-ph
29
The categories of this paper are: funct-an
26
The categories of this paper are: bayes-an
19
The categories of this paper are: eess
37
The categories of this paper are: supr-con
21
The categories of this paper are: adap-org