research-article

Optimal deterministic routing and sorting on the congested clique

Author:

Christoph LenzenAuthors Info & Claims

PODC '13: Proceedings of the 2013 ACM symposium on Principles of distributed computing

Pages 42 - 50

https://doi.org/10.1145/2484239.2501983

Published: 22 July 2013 Publication History

Abstract

Consider a clique of n nodes, where in each synchronous round each pair of nodes can exchange O(log n) bits. We provide deterministic constant-time solutions for two problems in this model. The first is a routing problem where each node is source and destination of n messages of size O(log n). The second is a sorting problem where each node i is given n keys of size O(log n) and needs to receive the i^th batch of n keys according to the global order of the keys. The latter result also implies deterministic constant-round solutions for related problems such as selection or determining modes.

References

[1]

R. Cole, K. Ost, and S. Schirra. Edge-Coloring Bipartite Multigraphs in O(|E| log Δ) Time. Combinatorica, 21:5--12, 2001.

[2]

D. Dolev, C. Lenzen, and S. Peled. "Tri, Tri again": Finding Triangles and Small Subgraphs in a Distributed Setting. In Proc. 26th Symposium on Distributed Computing (DISC), pages 195--209, 2012.

Digital Library

[3]

M. Elkin. An Unconditional Lower Bound on the Time-Approximation Tradeoff for the Minimum Spanning Tree Problem. SIAM Journal on Computing, 36(2):463--501, 2006.

Digital Library

[4]

S. Frischknecht, S. Holzer, and R. Wattenhofer. Networks Cannot Compute Their Diameter in Sublinear Time. In Proc. 23rd Symposium on Discrete Algorithms (SODA), pages 1150--1162, 2012.

Digital Library

[5]

M. T. Goodrich. Communication-Efficient Parallel Sorting. SIAM Journal on Computing, 29(2):416--432, Oct. 1999.

Digital Library

[6]

F. Kuhn, T. Moscibroda, and R. Wattenhofer. Local Computation: Lower and Upper Bounds. Computing Research Repository, abs/1011.5470, 2010.

[7]

C. Lenzen and R. Wattenhofer. Tight Bounds for Parallel Randomized Load Balancing. In Proc. 43rd Symposium on Theory of Computing (STOC), pages 11--20, 2011.

Digital Library

[8]

N. Linial. Locality in Distributed Graph Algorithms. SIAM Journal on Computing, 21(1):193--201, 1992.

Digital Library

[9]

Z. Lotker, B. Patt-Shamir, and D. Peleg. Distributed MST for Constant Diameter Graphs. Distributed Computing, 18(6):453--460, 2006.

Digital Library

[10]

L. Lovász and M. D. Plummer. Matching Theory. American Mathematical Society, 2009. Reprint with corrections.

[11]

M. Naor. A Lower Bound on Probabilistic Algorithms for Distributive Ring Coloring. SIAM Journal on Discrete Mathematics, 4(3):409--412, 1991.

[12]

B. Patt-Shamir and M. Teplitsky. The Round Complexity of Distributed Sorting: Extended Abstract. In Proc. 30th Symposium on Principles of Distributed Computing (PODC), pages 249--256, 2011.

Digital Library

[13]

D. Peleg. Distributed Computing: A Locality-Sensitive Approach. Society for Industrial and Applied Mathematics, 2000.

Digital Library

[14]

D. Peleg and V. Rubinovich. Near-tight Lower Bound on the Time Complexity of Distributed MST Construction. SIAM Journal on Computing, 30:1427--1442, 2000.

Digital Library

[15]

A. D. Sarma, S. Holzer, L. Kor, A. Korman, D. Nanongkai, G. Pandurangan, D. Peleg, and R. Wattenhofer. Distributed Verification and Hardness of Distributed Approximation. SIAM Journal on Computation, 41(5):1235--1265, 2012.

Cited By

Bui HChandra SChang YDory MLeitersdorf DKuznetsov PGelles ROlivetti D(2024)Improved All-Pairs Approximate Shortest Paths in Congested CliqueProceedings of the 43rd ACM Symposium on Principles of Distributed Computing10.1145/3662158.3662804(391-400)Online publication date: 17-Jun-2024
https://dl.acm.org/doi/10.1145/3662158.3662804
Haeupler BPatel SRoeyskoe AStein CZuzic GMohar BShinkar IO'Donnell R(2024)Polylog-Competitive Deterministic Local Routing and SchedulingProceedings of the 56th Annual ACM Symposium on Theory of Computing10.1145/3618260.3649678(812-822)Online publication date: 10-Jun-2024
https://dl.acm.org/doi/10.1145/3618260.3649678
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
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Optimal deterministic routing and sorting on the congested clique

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cover image ACM Conferences

PODC '13: Proceedings of the 2013 ACM symposium on Principles of distributed computing

July 2013

422 pages

ISBN:9781450320658

DOI:10.1145/2484239

General Chair:
Panagiota Fatourou
FORTH ICS & University of Crete, Greece
,
Program Chair:
Gadi Taubenfeld
IDC, Israel

Copyright © 2013 ACM.

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Published: 22 July 2013

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PODC '13: ACM Symposium on Principles of Distributed Computing

July 22 - 24, 2013

Québec, Montréal, Canada

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PODC '13 Paper Acceptance Rate 37 of 145 submissions, 26%;

Overall Acceptance Rate 740 of 2,477 submissions, 30%

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Cited By

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https://dl.acm.org/doi/10.1145/3662158.3662804
Haeupler BPatel SRoeyskoe AStein CZuzic GMohar BShinkar IO'Donnell R(2024)Polylog-Competitive Deterministic Local Routing and SchedulingProceedings of the 56th Annual ACM Symposium on Theory of Computing10.1145/3618260.3649678(812-822)Online publication date: 10-Jun-2024
https://dl.acm.org/doi/10.1145/3618260.3649678
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
Saikia P(2024)An O(1)-rounds Deterministic Distributed Approximation Algorithm for the Traveling Salesman Problem in Congested Clique2024 20th International Conference on Distributed Computing in Smart Systems and the Internet of Things (DCOSS-IoT)10.1109/DCOSS-IoT61029.2024.00034(179-186)Online publication date: 29-Apr-2024
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Behnezhad SHajiaghayi MHarris D(2023)Exponentially Faster Massively Parallel Maximal MatchingJournal of the ACM10.1145/361736070:5(1-18)Online publication date: 11-Oct-2023
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Forster Sde Vos TOshman RNolin AHalldorsson MBalliu A(2023)Brief Announcement: The Laplacian Paradigm in Deterministic Congested CliqueProceedings of the 2023 ACM Symposium on Principles of Distributed Computing10.1145/3583668.3594577(75-78)Online publication date: 19-Jun-2023
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