Communication Complexity of Statistical Distance

By Thomas Watson. 2018

9 citations recorded by the source corpus.

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 ±ε the statistical (total variation) distance between their distributions. For some range of parameters, there is up to a log n 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 Θ (n log n).

Subfields: Computational Theory and Mathematics, Electrical and Electronic Engineering

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