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Communication Complexity of Statistical Distance

Published:24 January 2018Publication History
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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 ±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).

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    • Published in

      cover image ACM Transactions on Computation Theory
      ACM Transactions on Computation Theory  Volume 10, Issue 1
      March 2018
      128 pages
      ISSN:1942-3454
      EISSN:1942-3462
      DOI:10.1145/3178548
      Issue’s Table of Contents

      Copyright © 2018 ACM

      Publisher

      Association for Computing Machinery

      New York, NY, United States

      Publication History

      • Published: 24 January 2018
      • Revised: 1 October 2017
      • Accepted: 1 October 2017
      • Received: 1 June 2017
      Published in toct Volume 10, Issue 1

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