The complexity of data aggregation in directed networks

Fabian Kuhn, Rotem Oshman

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

Abstract

We study problems of data aggregation, such as approximate counting and computing the minimum input value, in synchronous directed networks with bounded message bandwidth B = Ω(logn). In undirected networks of diameter D, many such problems can easily be solved in O(D) rounds, using O(logn)-size messages. We show that for directed networks this is not the case: when the bandwidth B is small, several classical data aggregation problems have a time complexity that depends polynomially on the size of the network, even when the diameter of the network is constant. We show that computing an ε-approximation to the size n of the network requires Ω(min{n, 1/ε2}/B) rounds, even in networks of diameter 2. We also show that computing a sensitive function (e.g., minimum and maximum) requires Ω(√n/B) rounds in networks of diameter 2, provided that the diameter is not known in advance to be o(√n/B). Our lower bounds are established by reduction from several well-known problems in communication complexity. On the positive side, we give a nearly optimal Õ(D+√n/B)-round algorithm for computing simple sensitive functions using messages of size B = Ω(logN), where N is a loose upper bound on the size of the network and D is the diameter.

Original languageEnglish
Title of host publicationDistributed Computing - 25th International Symposium, DISC 2011, Proceedings
Pages416-431
Number of pages16
DOIs
StatePublished - 2011
Externally publishedYes
Event25th International Symposium on Distributed Computing, DISC 2011 - Rome, Italy
Duration: 20 Sep 201122 Sep 2011

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume6950 LNCS
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349

Conference

Conference25th International Symposium on Distributed Computing, DISC 2011
Country/TerritoryItaly
CityRome
Period20/09/1122/09/11

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