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Near-optimal Distributed Triangle Enumeration via Expander Decompositions

Authors:

Thatchaphol Saranurak,

Hengjie ZhangAuthors Info & Claims

Journal of the ACM (JACM), Volume 68, Issue 3

Article No.: 21, Pages 1 - 36

https://doi.org/10.1145/3446330

Published: 13 May 2021 Publication History

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Abstract

We present improved distributed algorithms for variants of the triangle finding problem in the

model. We show that triangle detection, counting, and enumeration can be solved in

rounds using expander decompositions. This matches the triangle enumeration lower bound of

by Izumi and Le Gall [PODC’17] and Pandurangan, Robinson, and Scquizzato [SPAA’18], which holds even in the

model. The previous upper bounds for triangle detection and enumeration in

were

and

, respectively, due to Izumi and Le Gall [PODC’17].

An

-expander decomposition of a graph

is a clustering of the vertices

such that (i) each cluster

induces a subgraph with conductance at least

and (ii) the number of inter-cluster edges is at most

. We show that an

-expander decomposition with

can be constructed in

rounds for any

and positive integer

. For example, a

-expander decomposition only requires

rounds to compute, which is optimal up to subpolynomial factors, and a

-expander decomposition can be computed in

rounds, for any arbitrarily small constant

.

Our triangle finding algorithms are based on the following generic framework using expander decompositions, which is of independent interest. We first construct an expander decomposition. For each cluster, we simulate

algorithms with small overhead by applying the expander routing algorithm due to Ghaffari, Kuhn, and Su [PODC’17] Finally, we deal with inter-cluster edges using recursive calls.

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Hanauer KHenzinger MMünk RRäcke HVötsch MBaeza-Yates RBonchi F(2024)Expander Hierarchies for Normalized Cuts on GraphsProceedings of the 30th ACM SIGKDD Conference on Knowledge Discovery and Data Mining10.1145/3637528.3671978(1016-1027)Online publication date: 25-Aug-2024
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Index Terms

Near-optimal Distributed Triangle Enumeration via Expander Decompositions
1. Theory of computation
  1. Design and analysis of algorithms
    1. Distributed algorithms

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cover image Journal of the ACM

Journal of the ACM Volume 68, Issue 3

June 2021

244 pages

ISSN:0004-5411

EISSN:1557-735X

DOI:10.1145/3456663

Editor:
Éva Tardos
Cornell University, United States

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Publication History

Published: 13 May 2021

Accepted: 01 December 2020

Revised: 01 September 2020

Received: 01 November 2019

Published in JACM Volume 68, Issue 3

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https://dl.acm.org/doi/10.1145/3637528.3671978
Censor-Hillel KLeitersdorf DVulakh D(2024)Deterministic near-optimal distributed listing of cliquesDistributed Computing10.1007/s00446-024-00470-8Online publication date: 20-Jun-2024
https://doi.org/10.1007/s00446-024-00470-8
Abboud ALi JPanigrahi DSaranurak T(2023)All-Pairs Max-Flow is no Harder than Single-Pair Max-Flow: Gomory-Hu Trees in Almost-Linear Time2023 IEEE 64th Annual Symposium on Foundations of Computer Science (FOCS)10.1109/FOCS57990.2023.00137(2204-2212)Online publication date: 6-Nov-2023
https://doi.org/10.1109/FOCS57990.2023.00137
Liu Q(2023)A note on improved results for one round distributed clique listingInformation Processing Letters10.1016/j.ipl.2022.106355181:COnline publication date: 1-Mar-2023
https://dl.acm.org/doi/10.1016/j.ipl.2022.106355
Censor-Hillel KLeitersdorf DVulakh DMilani AWoelfel P(2022)Deterministic Near-Optimal Distributed Listing of CliquesProceedings of the 2022 ACM Symposium on Principles of Distributed Computing10.1145/3519270.3538434(271-280)Online publication date: 20-Jul-2022
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Gupta CHirvonen JKorhonen JStudený JSuomela JAgrawal KLee I(2022)Sparse Matrix Multiplication in the Low-Bandwidth ModelProceedings of the 34th ACM Symposium on Parallelism in Algorithms and Architectures10.1145/3490148.3538575(435-444)Online publication date: 11-Jul-2022
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