Distributed uniformity testing

Orr Fischer, Uri Meir, Rotem Oshman

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

Abstract

In the uniformity testing problem, we are given access to samples from some unknown distribution on a fixed domain {1, .., n}, and our goal is to distinguish the case where is the uniform distribution from the case where is -far from uniform in L1 distance. Centralized uniformity testing has been extensively studied, and it is known that Θ(n/2) samples are necessary and sufficient. In this paper we study distributed uniformity testing: in a network of k nodes, each node i has access to si samples from the underlying distribution . Our goal is to test uniformity, while minimizing the number of samples per node, as well as the running time. We consider several distributed models: the LOCAL model, the CONGEST model, and a 0-round model where nodes cannot communicate with each other at all. We give upper bounds for each model, and a lower bound for the 0-round model. The key to our results is analyzing the centralized uniformity-testing problem in an unusual error regime, for which we give new upper and lower bounds.

Original languageEnglish
Title of host publicationPODC 2018 - Proceedings of the 2018 ACM Symposium on Principles of Distributed Computing
PublisherAssociation for Computing Machinery
Pages455-464
Number of pages10
ISBN (Print)9781450357951
StatePublished - 23 Jul 2018
Event37th ACM SIGACT-SIGOPS Symposium on Principles of Distributed Computing, PODC 2018 - Egham, United Kingdom
Duration: 23 Jul 201827 Jul 2018

Publication series

NameProceedings of the Annual ACM Symposium on Principles of Distributed Computing

Conference

Conference37th ACM SIGACT-SIGOPS Symposium on Principles of Distributed Computing, PODC 2018
Country/TerritoryUnited Kingdom
CityEgham
Period23/07/1827/07/18

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