Near-optimal distributed maximum flow

Mohsen Ghaffari; Andreas Karrenbauer; Fabian Kuhn; Christoph Lenzen; Boaz Patt-Shamir

doi:10.1145/2767386.2767440

Near-optimal distributed maximum flow

Mohsen Ghaffari, Andreas Karrenbauer, Fabian Kuhn, Christoph Lenzen, Boaz Patt-Shamir

School of Electrical Engineering

Tel Aviv University

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

Abstract

We present a near-optimal distributed algorithm for (1 + o(1))-approximation of single-commodity maximum flow in undirected weighted networks that runs in (D + √n) • no(1) communication rounds in the CONGEST model. Here, n and D denote the number of nodes and the network diameter, respectively. This is the first improvement over the trivial O(m) time bound, and it nearly matches the ω(D + √ n) round complexity lower bound. The algorithm contains two sub-algorithms of indepenadent interest, both with running time (D + √n) • no(1): Distributed construction of a spanning tree of average stretch no(1). Distributed construction of an no(1)-congestion approxaimator consisting of the cuts induced by O(log n) viratual trees. The distributed representation of the cut approximator allows for evaluation in (D + √n) • no(1) rounds. All our algorithms make use of randomization and succeed with high probability.

Original language	English
Title of host publication	PODC 2015 - Proceedings of the 2015 ACM Symposium on Principles of Distributed Computing
Publisher	Association for Computing Machinery
Pages	81-90
Number of pages	10
ISBN (Electronic)	9781450336178
DOIs	https://doi.org/10.1145/2767386.2767440
State	Published - 21 Jul 2015
Event	ACM Symposium on Principles of Distributed Computing, PODC 2015 - Donostia-San Sebastian, Spain Duration: 21 Jul 2015 → 23 Jul 2015

Publication series

Name	Proceedings of the Annual ACM Symposium on Principles of Distributed Computing
Volume	2015-July

Conference

Conference	ACM Symposium on Principles of Distributed Computing, PODC 2015
Country/Territory	Spain
City	Donostia-San Sebastian
Period	21/07/15 → 23/07/15

All Science Journal Classification (ASJC) codes

Software
Hardware and Architecture
Computer Networks and Communications

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10.1145/2767386.2767440

Cite this

Ghaffari, M., Karrenbauer, A., Kuhn, F., Lenzen, C., & Patt-Shamir, B. (2015). Near-optimal distributed maximum flow. In PODC 2015 - Proceedings of the 2015 ACM Symposium on Principles of Distributed Computing (pp. 81-90). (Proceedings of the Annual ACM Symposium on Principles of Distributed Computing; Vol. 2015-July). Association for Computing Machinery. https://doi.org/10.1145/2767386.2767440

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abstract = "We present a near-optimal distributed algorithm for (1 + o(1))-approximation of single-commodity maximum flow in undirected weighted networks that runs in (D + √n) • no(1) communication rounds in the CONGEST model. Here, n and D denote the number of nodes and the network diameter, respectively. This is the first improvement over the trivial O(m) time bound, and it nearly matches the ω(D + √ n) round complexity lower bound. The algorithm contains two sub-algorithms of indepenadent interest, both with running time (D + √n) • no(1): Distributed construction of a spanning tree of average stretch no(1). Distributed construction of an no(1)-congestion approxaimator consisting of the cuts induced by O(log n) viratual trees. The distributed representation of the cut approximator allows for evaluation in (D + √n) • no(1) rounds. All our algorithms make use of randomization and succeed with high probability.",

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Ghaffari, M, Karrenbauer, A, Kuhn, F, Lenzen, C & Patt-Shamir, B 2015, Near-optimal distributed maximum flow. in PODC 2015 - Proceedings of the 2015 ACM Symposium on Principles of Distributed Computing. Proceedings of the Annual ACM Symposium on Principles of Distributed Computing, vol. 2015-July, Association for Computing Machinery, pp. 81-90, ACM Symposium on Principles of Distributed Computing, PODC 2015, Donostia-San Sebastian, Spain, 21/07/15. https://doi.org/10.1145/2767386.2767440

Near-optimal distributed maximum flow. / Ghaffari, Mohsen; Karrenbauer, Andreas; Kuhn, Fabian et al.
PODC 2015 - Proceedings of the 2015 ACM Symposium on Principles of Distributed Computing. Association for Computing Machinery, 2015. p. 81-90 (Proceedings of the Annual ACM Symposium on Principles of Distributed Computing; Vol. 2015-July).

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

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Near-optimal distributed maximum flow

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