Distributed approximation of minimum k-edge-connected spanning subgraphs

Michal Dory

doi:10.1145/3212734.3212760

Distributed approximation of minimum k-edge-connected spanning subgraphs

Michal Dory

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

Abstract

In the minimum k-edge-connected spanning subgraph (k-ECSS) problem the goal is to find the minimum weight subgraph resistant to up to k − 1 edge failures. This is a central problem in network design, and a natural generalization of the minimum spanning tree (MST) problem. While the MST problem has been studied extensively by the distributed computing community, for k ≥ 2 less is known in the distributed setting. In this paper, we present fast randomized distributed approximation algorithms for k-ECSS in the Congest model. Our first contribution is an O(D + n)-round O(log n)-approximation for 2-ECSS, for a graph with n vertices and diameter D. The time complexity of our algorithm is almost tight and almost matches the time complexity of the MST problem. For larger constant values of k we give an O(n)-round O(log n)-approximation. Additionally, in the special case of unweighted 3-ECSS we show how to improve the time complexity to O(D log³ n) rounds. All our results significantly improve the time complexity of previous algorithms.

Original language	English
Title of host publication	PODC 2018 - Proceedings of the 2018 ACM Symposium on Principles of Distributed Computing
Publisher	Association for Computing Machinery
Pages	149-158
Number of pages	10
ISBN (Print)	9781450357951
DOIs	https://doi.org/10.1145/3212734.3212760
State	Published - 23 Jul 2018
Externally published	Yes
Event	37th ACM SIGACT-SIGOPS Symposium on Principles of Distributed Computing, PODC 2018 - Egham, United Kingdom Duration: 23 Jul 2018 → 27 Jul 2018

Publication series

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

Conference

Conference	37th ACM SIGACT-SIGOPS Symposium on Principles of Distributed Computing, PODC 2018
Country/Territory	United Kingdom
City	Egham
Period	23/07/18 → 27/07/18

Bibliographical note

Publisher Copyright:
© 2018 Association for Computing Machinery.

Keywords

Approximation algorithms
Distributed network design
K-edge-connectivity

ASJC Scopus subject areas

Software
Hardware and Architecture
Computer Networks and Communications

Access to Document

10.1145/3212734.3212760

Cite this

@inproceedings{074b3f76def64d298217d6d4b68b5c3c,

title = "Distributed approximation of minimum k-edge-connected spanning subgraphs",

abstract = "In the minimum k-edge-connected spanning subgraph (k-ECSS) problem the goal is to find the minimum weight subgraph resistant to up to k − 1 edge failures. This is a central problem in network design, and a natural generalization of the minimum spanning tree (MST) problem. While the MST problem has been studied extensively by the distributed computing community, for k ≥ 2 less is known in the distributed setting. In this paper, we present fast randomized distributed approximation algorithms for k-ECSS in the Congest model. Our first contribution is an O(D + n)-round O(log n)-approximation for 2-ECSS, for a graph with n vertices and diameter D. The time complexity of our algorithm is almost tight and almost matches the time complexity of the MST problem. For larger constant values of k we give an O(n)-round O(log n)-approximation. Additionally, in the special case of unweighted 3-ECSS we show how to improve the time complexity to O(D log3 n) rounds. All our results significantly improve the time complexity of previous algorithms.",

keywords = "Approximation algorithms, Distributed network design, K-edge-connectivity",

author = "Michal Dory",

note = "Publisher Copyright: {\textcopyright} 2018 Association for Computing Machinery.; 37th ACM SIGACT-SIGOPS Symposium on Principles of Distributed Computing, PODC 2018 ; Conference date: 23-07-2018 Through 27-07-2018",

year = "2018",

month = jul,

day = "23",

doi = "10.1145/3212734.3212760",

language = "English",

isbn = "9781450357951",

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

publisher = "Association for Computing Machinery",

pages = "149--158",

booktitle = "PODC 2018 - Proceedings of the 2018 ACM Symposium on Principles of Distributed Computing",

address = "United States",

}

Dory, M 2018, Distributed approximation of minimum k-edge-connected spanning subgraphs. in PODC 2018 - Proceedings of the 2018 ACM Symposium on Principles of Distributed Computing. Proceedings of the Annual ACM Symposium on Principles of Distributed Computing, Association for Computing Machinery, pp. 149-158, 37th ACM SIGACT-SIGOPS Symposium on Principles of Distributed Computing, PODC 2018, Egham, United Kingdom, 23/07/18. https://doi.org/10.1145/3212734.3212760

Distributed approximation of minimum k-edge-connected spanning subgraphs. / Dory, Michal.
PODC 2018 - Proceedings of the 2018 ACM Symposium on Principles of Distributed Computing. Association for Computing Machinery, 2018. p. 149-158 (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 - Distributed approximation of minimum k-edge-connected spanning subgraphs

AU - Dory, Michal

PY - 2018/7/23

Y1 - 2018/7/23

N2 - In the minimum k-edge-connected spanning subgraph (k-ECSS) problem the goal is to find the minimum weight subgraph resistant to up to k − 1 edge failures. This is a central problem in network design, and a natural generalization of the minimum spanning tree (MST) problem. While the MST problem has been studied extensively by the distributed computing community, for k ≥ 2 less is known in the distributed setting. In this paper, we present fast randomized distributed approximation algorithms for k-ECSS in the Congest model. Our first contribution is an O(D + n)-round O(log n)-approximation for 2-ECSS, for a graph with n vertices and diameter D. The time complexity of our algorithm is almost tight and almost matches the time complexity of the MST problem. For larger constant values of k we give an O(n)-round O(log n)-approximation. Additionally, in the special case of unweighted 3-ECSS we show how to improve the time complexity to O(D log3 n) rounds. All our results significantly improve the time complexity of previous algorithms.

AB - In the minimum k-edge-connected spanning subgraph (k-ECSS) problem the goal is to find the minimum weight subgraph resistant to up to k − 1 edge failures. This is a central problem in network design, and a natural generalization of the minimum spanning tree (MST) problem. While the MST problem has been studied extensively by the distributed computing community, for k ≥ 2 less is known in the distributed setting. In this paper, we present fast randomized distributed approximation algorithms for k-ECSS in the Congest model. Our first contribution is an O(D + n)-round O(log n)-approximation for 2-ECSS, for a graph with n vertices and diameter D. The time complexity of our algorithm is almost tight and almost matches the time complexity of the MST problem. For larger constant values of k we give an O(n)-round O(log n)-approximation. Additionally, in the special case of unweighted 3-ECSS we show how to improve the time complexity to O(D log3 n) rounds. All our results significantly improve the time complexity of previous algorithms.

KW - Approximation algorithms

KW - Distributed network design

KW - K-edge-connectivity

UR - https://www.scopus.com/pages/publications/85052447411

U2 - 10.1145/3212734.3212760

DO - 10.1145/3212734.3212760

M3 - Conference contribution

AN - SCOPUS:85052447411

SN - 9781450357951

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

SP - 149

EP - 158

BT - PODC 2018 - Proceedings of the 2018 ACM Symposium on Principles of Distributed Computing

PB - Association for Computing Machinery

T2 - 37th ACM SIGACT-SIGOPS Symposium on Principles of Distributed Computing, PODC 2018

Y2 - 23 July 2018 through 27 July 2018

ER -

Distributed approximation of minimum k-edge-connected spanning subgraphs

Abstract

Publication series

Conference

Bibliographical note

Keywords

ASJC Scopus subject areas

Access to Document

Other files and links

Fingerprint

Cite this