research-article

Towards a Complexity Theory for the Congested Clique

Authors:

Janne H. Korhonen,

Jukka SuomelaAuthors Info & Claims

SPAA '18: Proceedings of the 30th on Symposium on Parallelism in Algorithms and Architectures

Pages 163 - 172

https://doi.org/10.1145/3210377.3210391

Published: 11 July 2018 Publication History

Abstract

The congested clique model of distributed computing has been receiving attention as a model for densely connected distributed systems. While there has been significant progress on the side of upper bounds, we have very little in terms of lower bounds for the congested clique; indeed, it is now known that proving explicit congested clique lower bounds is as difficult as proving circuit lower bounds. In this work, we use various more traditional complexity theory tools to build a clearer picture of the complexity landscape of the congested clique: \beginitemize ıtem Nondeterminism and beyond: We introduce the nondeterministic congested clique model (analogous to NP) and show that there is a natural canonical problem family that captures all problems solvable in constant time with nondeterministic algorithms. We further generalise these notions by introducing the constant-round decision hierarchy (analogous to the polynomial hierarchy). ıtem Non-constructive lower bounds: We lift the prior non-uniform counting arguments to a general technique for proving non-constructive uniform lower bounds for the congested clique. In particular, we prove a time hierarchy theorem for the congested clique, showing that there are decision problems of essentially all complexities, both in the deterministic and nondeterministic settings. ıtem Fine-grained complexity: We map out relationships between various natural problems in the congested clique model, arguing that a reduction-based complexity theory currently gives us a fairly good picture of the complexity landscape of the congested clique. \enditemize

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Towards a Complexity Theory for the Congested Clique
1. Theory of computation

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cover image ACM Conferences

SPAA '18: Proceedings of the 30th on Symposium on Parallelism in Algorithms and Architectures

July 2018

437 pages

ISBN:9781450357999

DOI:10.1145/3210377

General Chair:
Christian Scheideler
University of Paderborn, Germany
,
Program Chair:
Jeremy Fineman
Georgetown University, USA

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Published: 11 July 2018

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SPAA '18: 30th ACM Symposium on Parallelism in Algorithms and Architectures

July 16 - 18, 2018

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SPAA '18 Paper Acceptance Rate 36 of 120 submissions, 30%;

Overall Acceptance Rate 447 of 1,461 submissions, 31%

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Cited By

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https://dl.acm.org/doi/10.1145/3662158.3662804
Ghaffari MWang BMohar BShinkar IO'Donnell R(2024)Lenzen’s Distributed Routing Generalized: A Full Characterization of Constant-Time RoutabilityProceedings of the 56th Annual ACM Symposium on Theory of Computing10.1145/3618260.3649627(1877-1888)Online publication date: 10-Jun-2024
https://dl.acm.org/doi/10.1145/3618260.3649627
Kerger PBernal Neira DGonzalez Izquierdo ZRieffel E(2023)Mind the O˜: Asymptotically Better, but Still Impractical, Quantum Distributed AlgorithmsAlgorithms10.3390/a1607033216:7(332)Online publication date: 11-Jul-2023
https://doi.org/10.3390/a16070332
Kumar M(2023)Fault-Tolerant Graph Realizations in the Congested Clique, RevisitedDistributed Computing and Intelligent Technology10.1007/978-3-031-24848-1_6(84-97)Online publication date: 8-Jan-2023
https://doi.org/10.1007/978-3-031-24848-1_6
Dory MParter M(2022)Exponentially Faster Shortest Paths in the Congested CliqueJournal of the ACM10.1145/352721369:4(1-42)Online publication date: 31-Aug-2022
https://dl.acm.org/doi/10.1145/3527213
Augustine JChoudhary KCohen APeleg DSivasubramaniam SSourav S(2022)Distributed Graph RealizationsIEEE Transactions on Parallel and Distributed Systems10.1109/TPDS.2021.310423933:6(1321-1337)Online publication date: 1-Jun-2022
https://doi.org/10.1109/TPDS.2021.3104239
Nanongkai DScquizzato M(2022)Equivalence classes and conditional hardness in massively parallel computationsDistributed Computing10.1007/s00446-021-00418-2Online publication date: 20-Jan-2022
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Kumar MMolla ASivasubramaniam S(2022)Fault-Tolerant Graph Realizations in the Congested CliqueAlgorithmics of Wireless Networks10.1007/978-3-031-22050-0_8(108-122)Online publication date: 13-Dec-2022
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Censor-Hillel KDory MKorhonen JLeitersdorf D(2021)Fast approximate shortest paths in the congested cliqueDistributed Computing10.1007/s00446-020-00380-534:6(463-487)Online publication date: 1-Dec-2021
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Dory MParter MEmek YCachin C(2020)Exponentially Faster Shortest Paths in the Congested CliqueProceedings of the 39th Symposium on Principles of Distributed Computing10.1145/3382734.3405711(59-68)Online publication date: 31-Jul-2020
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