Fast approximate shortest paths in the congested clique

Keren Censor-Hillel; Michal Dory; Janne H. Korhonen; Dean Leitersdorf

doi:10.1145/3293611.3331633

Fast approximate shortest paths in the congested clique

Keren Censor-Hillel, Michal Dory, Janne H. Korhonen, Dean Leitersdorf

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

Abstract

We design fast deterministic algorithms for distance computation in the CONGESTED CLIQUE model. Our key contributions include: A (2+)-approximation for all-pairs shortest paths problem in O(log²n / ) rounds on unweighted undirected graphs. With a small additional additive factor, this also applies for weighted graphs. This is the first sub-polynomial constant-factor approximation for APSP in this model. A (1+)-approximation for multi-source shortest paths problem from O(n) sources in O(log² n / ) rounds on weighted undirected graphs. This is the first sub-polynomial algorithm obtaining this approximation for a set of sources of polynomial size. Our main techniques are new distance tools that are obtained via improved algorithms for sparse matrix multiplication, which we leverage to construct efficient hopsets and shortest paths. Furthermore, our techniques extend to additional distance problems for which we improve upon the state-of-the-art, including diameter approximation, and an exact single-source shortest paths algorithm for weighted undirected graphs in (n_1/6) rounds.

Original language	English
Title of host publication	PODC 2019 - Proceedings of the 2019 ACM Symposium on Principles of Distributed Computing
Publisher	Association for Computing Machinery
Pages	74-83
Number of pages	10
ISBN (Electronic)	9781450362177
DOIs	https://doi.org/10.1145/3293611.3331633
State	Published - 16 Jul 2019
Externally published	Yes
Event	38th ACM Symposium on Principles of Distributed Computing, PODC 2019 - Toronto, Canada Duration: 29 Jul 2019 → 2 Aug 2019

Publication series

Name	Proceedings of the Annual ACM Symposium on Principles of Distributed Computing

Conference

Conference	38th ACM Symposium on Principles of Distributed Computing, PODC 2019
Country/Territory	Canada
City	Toronto
Period	29/07/19 → 2/08/19

Bibliographical note

Publisher Copyright:
© 2019 ACM.

Keywords

All-pairs shortest paths
Congested clique
Diameter
Distributed computing
Hopsets
Matrix multiplication
Single-source shortest paths
approximation algorithms

ASJC Scopus subject areas

Software
Hardware and Architecture
Computer Networks and Communications

Access to Document

10.1145/3293611.3331633

Cite this

Censor-Hillel, K., Dory, M., Korhonen, J. H., & Leitersdorf, D. (2019). Fast approximate shortest paths in the congested clique. In PODC 2019 - Proceedings of the 2019 ACM Symposium on Principles of Distributed Computing (pp. 74-83). (Proceedings of the Annual ACM Symposium on Principles of Distributed Computing). Association for Computing Machinery. https://doi.org/10.1145/3293611.3331633

@inproceedings{15e8290c7734403aafd39b65799c634f,

title = "Fast approximate shortest paths in the congested clique",

abstract = "We design fast deterministic algorithms for distance computation in the CONGESTED CLIQUE model. Our key contributions include: A (2+)-approximation for all-pairs shortest paths problem in O(log2n / ) rounds on unweighted undirected graphs. With a small additional additive factor, this also applies for weighted graphs. This is the first sub-polynomial constant-factor approximation for APSP in this model. A (1+)-approximation for multi-source shortest paths problem from O(n) sources in O(log2 n / ) rounds on weighted undirected graphs. This is the first sub-polynomial algorithm obtaining this approximation for a set of sources of polynomial size. Our main techniques are new distance tools that are obtained via improved algorithms for sparse matrix multiplication, which we leverage to construct efficient hopsets and shortest paths. Furthermore, our techniques extend to additional distance problems for which we improve upon the state-of-the-art, including diameter approximation, and an exact single-source shortest paths algorithm for weighted undirected graphs in (n1/6) rounds.",

keywords = "All-pairs shortest paths, Congested clique, Diameter, Distributed computing, Hopsets, Matrix multiplication, Single-source shortest paths, approximation algorithms",

author = "Keren Censor-Hillel and Michal Dory and Korhonen, {Janne H.} and Dean Leitersdorf",

note = "Publisher Copyright: {\textcopyright} 2019 ACM.; 38th ACM Symposium on Principles of Distributed Computing, PODC 2019 ; Conference date: 29-07-2019 Through 02-08-2019",

year = "2019",

month = jul,

day = "16",

doi = "10.1145/3293611.3331633",

language = "English",

series = "Proceedings of the Annual ACM Symposium on Principles of Distributed Computing",

publisher = "Association for Computing Machinery",

pages = "74--83",

booktitle = "PODC 2019 - Proceedings of the 2019 ACM Symposium on Principles of Distributed Computing",

}

Censor-Hillel, K, Dory, M, Korhonen, JH & Leitersdorf, D 2019, Fast approximate shortest paths in the congested clique. in PODC 2019 - Proceedings of the 2019 ACM Symposium on Principles of Distributed Computing. Proceedings of the Annual ACM Symposium on Principles of Distributed Computing, Association for Computing Machinery, pp. 74-83, 38th ACM Symposium on Principles of Distributed Computing, PODC 2019, Toronto, Canada, 29/07/19. https://doi.org/10.1145/3293611.3331633

Fast approximate shortest paths in the congested clique. / Censor-Hillel, Keren; Dory, Michal; Korhonen, Janne H. et al.
PODC 2019 - Proceedings of the 2019 ACM Symposium on Principles of Distributed Computing. Association for Computing Machinery, 2019. p. 74-83 (Proceedings of the Annual ACM Symposium on Principles of Distributed Computing).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

TY - GEN

T1 - Fast approximate shortest paths in the congested clique

AU - Censor-Hillel, Keren

AU - Dory, Michal

AU - Korhonen, Janne H.

AU - Leitersdorf, Dean

PY - 2019/7/16

Y1 - 2019/7/16

N2 - We design fast deterministic algorithms for distance computation in the CONGESTED CLIQUE model. Our key contributions include: A (2+)-approximation for all-pairs shortest paths problem in O(log2n / ) rounds on unweighted undirected graphs. With a small additional additive factor, this also applies for weighted graphs. This is the first sub-polynomial constant-factor approximation for APSP in this model. A (1+)-approximation for multi-source shortest paths problem from O(n) sources in O(log2 n / ) rounds on weighted undirected graphs. This is the first sub-polynomial algorithm obtaining this approximation for a set of sources of polynomial size. Our main techniques are new distance tools that are obtained via improved algorithms for sparse matrix multiplication, which we leverage to construct efficient hopsets and shortest paths. Furthermore, our techniques extend to additional distance problems for which we improve upon the state-of-the-art, including diameter approximation, and an exact single-source shortest paths algorithm for weighted undirected graphs in (n1/6) rounds.

AB - We design fast deterministic algorithms for distance computation in the CONGESTED CLIQUE model. Our key contributions include: A (2+)-approximation for all-pairs shortest paths problem in O(log2n / ) rounds on unweighted undirected graphs. With a small additional additive factor, this also applies for weighted graphs. This is the first sub-polynomial constant-factor approximation for APSP in this model. A (1+)-approximation for multi-source shortest paths problem from O(n) sources in O(log2 n / ) rounds on weighted undirected graphs. This is the first sub-polynomial algorithm obtaining this approximation for a set of sources of polynomial size. Our main techniques are new distance tools that are obtained via improved algorithms for sparse matrix multiplication, which we leverage to construct efficient hopsets and shortest paths. Furthermore, our techniques extend to additional distance problems for which we improve upon the state-of-the-art, including diameter approximation, and an exact single-source shortest paths algorithm for weighted undirected graphs in (n1/6) rounds.

KW - All-pairs shortest paths

KW - Congested clique

KW - Diameter

KW - Distributed computing

KW - Hopsets

KW - Matrix multiplication

KW - Single-source shortest paths

KW - approximation algorithms

UR - http://www.scopus.com/inward/record.url?scp=85070984640&partnerID=8YFLogxK

U2 - 10.1145/3293611.3331633

DO - 10.1145/3293611.3331633

M3 - Conference contribution

AN - SCOPUS:85070984640

T3 - Proceedings of the Annual ACM Symposium on Principles of Distributed Computing

SP - 74

EP - 83

BT - PODC 2019 - Proceedings of the 2019 ACM Symposium on Principles of Distributed Computing

PB - Association for Computing Machinery

T2 - 38th ACM Symposium on Principles of Distributed Computing, PODC 2019

Y2 - 29 July 2019 through 2 August 2019

ER -

Fast approximate shortest paths in the congested clique

Abstract

Publication series

Conference

Bibliographical note

Keywords

ASJC Scopus subject areas

Access to Document

Other files and links

Fingerprint

Cite this