Deterministic Communication vs. Partition Number
We show that deterministic communication complexity can be super logarithmic 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 these results follow from a simple adaptation of a communication-to-query simulation theorem of Raz and McKenzie (Combinatorica 1999) together with lower bounds for the analogous query complexity questions.
Proceedings - Annual IEEE Symposium on Foundations of Computer Science, FOCS
Goos, M., Pitassi, T., & Watson, T. (2015). Deterministic Communication vs. Partition Number. Proceedings - Annual IEEE Symposium on Foundations of Computer Science, FOCS, 2015-December, 1077-1088. https://doi.org/10.1109/FOCS.2015.70