Tight network topology dependent bounds on rounds of communication

Arkadev Chattopadhyay, Michael Langberg, Shi Li, Atri Rudra

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

Abstract

We prove tight network topology dependent bounds on the round complexity of computing well studied k-party functions such as set disjointness and element distinctness. Unlike the usual case in the CONGEST model in distributed computing, we x the function and then vary the underlying network topology. This complements the recent such results on total communication that have received some attention. We also present some applications to distributed graph computation problems. Our main contribution is a proof technique that allows us to reduce the problem on a general graph topology to a relevant two-party communication complexity problem. However, unlike many previous works that also used the same high level strategy, we do not reason about a two- party communication problem that is induced by a cut in the graph. To stitch' back the various lower bounds from the two party communication problems, we use the notion of timed graph that has seen prior use in network coding. Our reductions use some tools from Steiner tree packing and multi-commodity ow problems that have a delay constraint.

Original languageEnglish
Title of host publication28th Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 2017
EditorsPhilip N. Klein
PublisherAssociation for Computing Machinery
Pages2524-2539
Number of pages16
ISBN (Electronic)9781611974782
DOIs
StatePublished - 2017
Externally publishedYes
Event28th Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 2017 - Barcelona, Spain
Duration: 16 Jan 201719 Jan 2017

Publication series

NameProceedings of the Annual ACM-SIAM Symposium on Discrete Algorithms
Volume0

Conference

Conference28th Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 2017
Country/TerritorySpain
CityBarcelona
Period16/01/1719/01/17

Bibliographical note

Publisher Copyright:
Copyright © by SIAM.

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