Communication complexity of statistical distance
Abstract
We prove nearly matching upper and lower bounds on the randomized communication complexity of the following problem: Alice and Bob are each given a probability distribution over n elements, and they wish to estimate within ±∈ the statistical (total variation) distance between their distributions. For some range of parameters, there is up to a logn factor gap between the upper and lower bounds, and we identify a barrier to using information complexity techniques to improve the lower bound in this case. We also prove a side result that we discovered along the way: the randomized communication complexity of n-bit Majority composed with n-bit Greater Than is O(n logn).
Publication Title
ACM Transactions on Computation Theory
Recommended Citation
Watson, T. (2018). Communication complexity of statistical distance. ACM Transactions on Computation Theory, 10 (1) https://doi.org/10.1145/3170708
