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Fast Distributed Algorithms for Connectivity and MST in Large Graphs

Authors:

Gopal Pandurangan,

Peter Robinson,

Michele ScquizzatoAuthors Info & Claims

ACM Transactions on Parallel Computing (TOPC), Volume 5, Issue 1

Article No.: 4, Pages 1 - 22

https://doi.org/10.1145/3209689

Published: 13 June 2018 Publication History

Abstract

Motivated by the increasing need to understand the algorithmic foundations of distributed large-scale graph computations, we study a number of fundamental graph problems in a message-passing model for distributed computing where k≥2 machines jointly perform computations on graphs with n nodes (typically, n>k). The input graph is assumed to be initially randomly partitioned among the k machines, a common implementation in many real-world systems. Communication is point-to-point, and the goal is to minimize the number of communication rounds of the computation.

Our main result is an (almost) optimal distributed randomized algorithm for graph connectivity. Our algorithm runs in Õ(n/k²) rounds (Õ notation hides a polylog(n) factor and an additive polylog(n) term). This improves over the best previously known bound of Õ(n/k) [Klauck et al., SODA 2015] and is optimal (up to a polylogarithmic factor) in light of an existing lower bound of Ω^˜(n/k²). Our improved algorithm uses a bunch of techniques, including linear graph sketching, that prove useful in the design of efficient distributed graph algorithms. Using the connectivity algorithm as a building block, we then present fast randomized algorithms for computing minimum spanning trees, (approximate) min-cuts, and for many graph verification problems. All these algorithms take Õ(n/k²) rounds and are optimal up to polylogarithmic factors. We also show an almost matching lower bound of Ω^˜(n/k²) rounds for many graph verification problems by leveraging lower bounds in random-partition communication complexity.

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Das RSoylu M(2023)A key review on graph data science: The power of graphs in scientific studiesChemometrics and Intelligent Laboratory Systems10.1016/j.chemolab.2023.104896240(104896)Online publication date: Sep-2023
https://doi.org/10.1016/j.chemolab.2023.104896
Nanongkai DScquizzato M(2022)Equivalence classes and conditional hardness in massively parallel computationsDistributed Computing10.1007/s00446-021-00418-235:2(165-183)Online publication date: 1-Apr-2022
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Index Terms

Fast Distributed Algorithms for Connectivity and MST in Large Graphs
1. Theory of computation
  1. Design and analysis of algorithms
    1. Distributed algorithms
    2. Parallel algorithms
      1. Massively parallel algorithms

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Published In

cover image ACM Transactions on Parallel Computing

ACM Transactions on Parallel Computing Volume 5, Issue 1

Special Issue on SPAA 2016

March 2018

140 pages

ISSN:2329-4949

EISSN:2329-4957

DOI:10.1145/3232649

Editor:
Phillip B. Gibbons
Carnegie Mellon University, Pittsburgh, USA

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Copyright © 2018 ACM.

Permission to make digital or hard copies of all or part of this work for personal or classroom use is granted without fee provided that copies are not made or distributed for profit or commercial advantage and that copies bear this notice and the full citation on the first page. Copyrights for components of this work owned by others than ACM must be honored. Abstracting with credit is permitted. To copy otherwise, or republish, to post on servers or to redistribute to lists, requires prior specific permission and/or a fee. Request permissions from [email protected]

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Publication History

Published: 13 June 2018

Accepted: 01 January 2018

Revised: 01 October 2017

Received: 01 November 2016

Published in TOPC Volume 5, Issue 1

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Cited By

Farouzi AZhou XBellatreche LMalki MOrdonez C(2024)Balanced parallel triangle enumeration with an adaptive algorithmDistributed and Parallel Databases10.1007/s10619-023-07437-x42:1(103-141)Online publication date: 1-Mar-2024
https://dl.acm.org/doi/10.1007/s10619-023-07437-x
Das RSoylu M(2023)A key review on graph data science: The power of graphs in scientific studiesChemometrics and Intelligent Laboratory Systems10.1016/j.chemolab.2023.104896240(104896)Online publication date: Sep-2023
https://doi.org/10.1016/j.chemolab.2023.104896
Nanongkai DScquizzato M(2022)Equivalence classes and conditional hardness in massively parallel computationsDistributed Computing10.1007/s00446-021-00418-235:2(165-183)Online publication date: 1-Apr-2022
https://dl.acm.org/doi/10.1007/s00446-021-00418-2
Pandurangan GRobinson PScquizzato M(2021)On the Distributed Complexity of Large-Scale Graph ComputationsACM Transactions on Parallel Computing10.1145/34609008:2(1-28)Online publication date: 15-Jul-2021
https://dl.acm.org/doi/10.1145/3460900
Augustine JKothapalli KPandurangan G(2021)Efficient Distributed Algorithms in the k-machine model via PRAM Simulations2021 IEEE International Parallel and Distributed Processing Symposium (IPDPS)10.1109/IPDPS49936.2021.00031(223-232)Online publication date: May-2021
https://doi.org/10.1109/IPDPS49936.2021.00031
Gilbert SLi Er Lu LScheideler CSpear M(2020)How Fast Can You Update Your MST?Proceedings of the 32nd ACM Symposium on Parallelism in Algorithms and Architectures10.1145/3350755.3400240(531-533)Online publication date: 6-Jul-2020
https://dl.acm.org/doi/10.1145/3350755.3400240
Zhang YAzad ABuluç A(2020)Parallel algorithms for finding connected components using linear algebraJournal of Parallel and Distributed Computing10.1016/j.jpdc.2020.04.009Online publication date: May-2020
https://doi.org/10.1016/j.jpdc.2020.04.009
Azad ABuluc A(2019)LACC: A Linear-Algebraic Algorithm for Finding Connected Components in Distributed Memory2019 IEEE International Parallel and Distributed Processing Symposium (IPDPS)10.1109/IPDPS.2019.00012(2-12)Online publication date: May-2019
https://doi.org/10.1109/IPDPS.2019.00012
Pandurangan GRobinson PScquizzato MScheideler CFineman J(2018)On the Distributed Complexity of Large-Scale Graph ComputationsProceedings of the 30th on Symposium on Parallelism in Algorithms and Architectures10.1145/3210377.3210409(405-414)Online publication date: 11-Jul-2018
https://dl.acm.org/doi/10.1145/3210377.3210409
Pandurangan GPeleg DScquizzato M(2018)Message lower bounds via efficient network synchronizationTheoretical Computer Science10.1016/j.tcs.2018.11.017Online publication date: Nov-2018
https://doi.org/10.1016/j.tcs.2018.11.017

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