research-article

Optimal distributed all pairs shortest paths and applications

Authors:

Stephan Holzer,

Roger WattenhoferAuthors Info & Claims

PODC '12: Proceedings of the 2012 ACM symposium on Principles of distributed computing

Pages 355 - 364

https://doi.org/10.1145/2332432.2332504

Published: 16 July 2012 Publication History

Abstract

We present an algorithm to compute All Pairs Shortest Paths (APSP) of a network in a distributed way. The model of distributed computation we consider is the message passing model: in each synchronous round, every node can transmit a different (but short) message to each of its neighbors. We provide an algorithm that computes APSP in O(n) communication rounds, where n denotes the number of nodes in the network. This implies a linear time algorithm for computing the diameter of a network. Due to a lower bound these two algorithms are optimal up to a logarithmic factor. Furthermore, we present a new lower bound for approximating the diameter D of a graph: Being allowed to answer D+1 or D can speed up the computation by at most a factor D. On the positive side, we provide an algorithm that achieves such a speedup of D and computes an (1+εepsilon) multiplicative approximation of the diameter. We extend these algorithms to compute or approximate other problems, such as girth, radius, center and peripheral vertices. At the heart of these approximation algorithms is the S-Shortest Paths problem which we solve in O(|S|+D) time.

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Index Terms

Optimal distributed all pairs shortest paths and applications
1. Theory of computation
  1. Computational complexity and cryptography
    1. Complexity classes
  2. Models of computation
    1. Concurrency
      1. Parallel computing models

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cover image ACM Conferences

PODC '12: Proceedings of the 2012 ACM symposium on Principles of distributed computing

July 2012

410 pages

ISBN:9781450314503

DOI:10.1145/2332432

General Chair:
Darek Kowalski
U. of Liverpool, UK and IMDEA Networks, Spain
,
Program Chair:
Alessandro Panconesi
Sapienza, University of Rome, Italy

Copyright © 2012 ACM.

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Published: 16 July 2012

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PODC '12: ACM Symposium on Principles of Distributed Computing

July 16 - 18, 2012

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Manoharan VRamachandran VKuznetsov PGelles ROlivetti D(2024)Computing Minimum Weight Cycle in the CONGEST ModelProceedings of the 43rd ACM Symposium on Principles of Distributed Computing10.1145/3662158.3662801(182-193)Online publication date: 17-Jun-2024
https://dl.acm.org/doi/10.1145/3662158.3662801
Chandra SChang YDory MGhaffari MLeitersdorf DAgrawal KPetrank E(2024)Fast Broadcast in Highly Connected NetworksProceedings of the 36th ACM Symposium on Parallelism in Algorithms and Architectures10.1145/3626183.3659959(331-343)Online publication date: 17-Jun-2024
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