Deterministic communication vs. Partition number
We show that deterministic communication complexity can be superlogarithmic in the partition number of the associated communication matrix. We also obtain near-optimal deterministic lower bounds for the Clique vs. Independent Set problem, which in particular yields new lower bounds for the log-rank conjecture. All of these results follow from a simple adaptation of a communication-to-query simulation theorem of Raz and McKenzie [Combinatorica, 19 (1999), pp. 403-435] together with lower bounds for the analogous query complexity questions.
SIAM Journal on Computing
Göös, M., Pitassi, T., & Watson, T. (2018). Deterministic communication vs. Partition number. SIAM Journal on Computing, 47 (6), 2435-2450. https://doi.org/10.1137/16M1059369