An Almost Singularly Optimal Asynchronous Distributed MST Algorithm

Fabien Dufoulon, Shay Kutten, William K. Moses, Gopal Pandurangan, David Peleg

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

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Abstract

A singularly (near) optimal distributed algorithm is one that is (near) optimal in two criteria, namely, its time and message complexities. For synchronous CONGEST networks, such algorithms are known for fundamental distributed computing problems such as leader election [Kutten et al., JACM 2015] and Minimum Spanning Tree (MST) construction [Pandurangan et al., STOC 2017, Elkin, PODC 2017]. However, it is open whether a singularly (near) optimal bound can be obtained for the MST construction problem in general asynchronous CONGEST networks. In this paper, we present a randomized distributed MST algorithm that, with high probability, computes an MST in asynchronous CONGEST networks and takes Õ(D1+ε + √n) time and Õ(m) messages1, where n is the number of nodes, m the number of edges, D is the diameter of the network, and ε > 0 is an arbitrarily small constant (both time and message bounds hold with high probability). Since (Equation presented)(D + √n) and Ω(m) are respective time and message lower bounds for distributed MST construction in the standard KT0 model, our algorithm is message optimal (up to a polylog(n) factor) and almost time optimal (except for a Dε factor). Our result answers an open question raised in Mashregi and King [DISC 2019] by giving the first known asynchronous MST algorithm that has sublinear time (for all D = O(n1-ε)) and uses Õ(m) messages. Using a result of Mashregi and King [DISC 2019], this also yields the first asynchronous MST algorithm that is sublinear in both time and messages in the KT1 CONGEST model. A key tool in our algorithm is the construction of a low diameter rooted spanning tree in asynchronous CONGEST that has depth Õ(D1+ε) (for an arbitrarily small constant ε > 0) in Õ(D1+ε) time and Õ(m) messages. To the best of our knowledge, this is the first such construction that is almost singularly optimal in the asynchronous setting. This tree construction may be of independent interest as it can also be used for efficiently performing basic tasks such as verified broadcast and convergecast in asynchronous networks.

Original languageEnglish
Title of host publication36th International Symposium on Distributed Computing, DISC 2022
EditorsChristian Scheideler
PublisherSchloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing
ISBN (Electronic)9783959772556
DOIs
StatePublished - 1 Oct 2022
Externally publishedYes
Event36th International Symposium on Distributed Computing, DISC 2022 - Augusta, United States
Duration: 25 Oct 202227 Oct 2022

Publication series

NameLeibniz International Proceedings in Informatics, LIPIcs
Volume246
ISSN (Print)1868-8969

Conference

Conference36th International Symposium on Distributed Computing, DISC 2022
Country/TerritoryUnited States
CityAugusta
Period25/10/2227/10/22

Bibliographical note

Publisher Copyright:
© Fabien Dufoulon, Shay Kutten, William K. Moses Jr., Gopal Pandurangan, and David Peleg.

Funding

Funding Fabien Dufoulon: This work was supported in part by NSF grants CCF-1717075, CCF-1540512, IIS-1633720, and BSF grant 2016419. Shay Kutten: This work was supported in part by the Bi-national Science Foundation (BSF) grant 2016419 and supported in part by ISF grant 1346/22. William K. Moses Jr.: This work was supported in part by NSF grants CCF1540512, IIS-1633720, CCF-1717075, and BSF grant 2016419. Gopal Pandurangan: This work was supported in part by NSF grants CCF-1717075, CCF-1540512, IIS-1633720, and BSF grant 2016419. David Peleg: This work was supported in part by the US-Israel Binational Science Foundation grant 2018043.

FundersFunder number
National Science Foundation2016419, CCF-1540512, IIS-1633720, CCF-1717075
Iowa Science Foundation1346/22
United States-Israel Binational Science Foundation2018043

    Keywords

    • Asynchronous networks
    • Distributed Algorithm
    • Minimum Spanning Tree
    • Singularly Optimal

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