[go: up one dir, main page]
More Web Proxy on the site http://driver.im/ skip to main content
10.1145/3007748.3007772acmotherconferencesArticle/Chapter ViewAbstractPublication PagesicdcnConference Proceedingsconference-collections
research-article

A Self-Stabilizing Minimal k-Grouping Algorithm

Published: 05 January 2017 Publication History

Abstract

We consider the minimal k-grouping problem: given a graph G = (V, E) and a constant k, partition G into subgraphs of diameter no greater than k, such that the union of any two subgraphs has diameter greater than k. We give a silent self-stabilizing asynchronous distributed algorithm for this problem in the composite atomicity model of computation, assuming the network has unique process identifiers. Our algorithm works under the weakly-fair daemon. The time complexity (i.e. the number of rounds to reach a legitimate configuration) of our algorithm is O (nD/k) where n is the number of processes in the network and D is the diameter of the network. The space complexity of each process is O((n + nfalse) log n) where nfalse is the number of false identifiers, i.e., identifiers that do not match the identifier of any process, but which are stored in the local memory of at least one process at the initial configuration. Our algorithm guarantees that the number of groups is at most 2n/k + 1 after convergence. We also give a novel composition technique to concatenate a silent algorithm repeatedly, which we call loop composition.

References

[1]
A. D Amis, R. Prakash, T. HP. Vuong, and D. T. Huynh. Max-min d-cluster formation in wireless ad hoc networks. In Proc. of INFOCOM 2000, volume 1, pages 32--41, 2000.
[2]
A. K. Datta, S. Gurumurthy, F. Petit, and V. Villain. Self-stabilizing network orientation algorithms in arbitrary rooted networks. In Proc. of ICDCS 2000, pages 576--583, 2000.
[3]
A. K. Datta, L. L. Larmore, S. Devismes, K. Heurtefeux, and Y. Rivierre. Competitive self-stabilizing k-clustering. In Proc. of ICDCS 2012, pages 476--485, 2012.
[4]
A. K. Datta, L. L. Larmore, S. Devismes, K. Heurtefeux, and Y. Rivierre. Self-stabilizing small k-dominating sets. International Journal of Networking and Computing, 3(1):116--136, 2013.
[5]
A. K Datta, L. L Larmore, and P.l Vemula. An O(n)-time self-stabilizing leader election algorithm. Journal of Parallel and Distributed Computing, 71(11):1532--1544, 2011.
[6]
J. S. Deogun, D. Kratsch, and G. Steiner. An approximation algorithm for clustering graphs with dominating diametral path. IPL, 61(3):121--127, 1997.
[7]
EW Dijkstra. Self stabilizing systems in spite of distributed control. Communications of the ACM, 17:643--644, 1974.
[8]
S. Dolev. Self-stabilization. MIT press, 2000.
[9]
S. Dolev and T. Herman. Parallel composition of stabilizing algorithms. In Proc. of WSS 1999, pages 25--32, 1999.
[10]
B. Ducourthial, S. Khalfallah, and F. Petit. Best-effort group service in dynamic networks. In Proc. of SPAA 2010, pages 233--242, 2010.
[11]
Y. Fernandess and D. Malkhi. K-clustering in wireless ad hoc networks. In Proceedings of the second ACM international workshop on Principles of mobile computing, pages 31--37, 2002.
[12]
T. R. Herman. Adaptivity through distributed convergence. PhD thesis, University of Texas at Austin, 1992.
[13]
Y. Yamauchi, S. Kamei, F. Ooshita, Y. Katayama, H. Kakugawa, and T. Masuzawa. Hierarchical composition of self-stabilizing protocols preserving the fault-containment property. IEICE transactions on information and systems, 92(3):451--459, 2009.
[14]
Y. Yamauchi, S. Kamei, F. Ooshita, Y. Katayama, H. Kakugawa, and T. Masuzawa. Timer-based composition of fault-containing self-stabilizing protocols. Information Sciences, 180(10):1802--1816, 2010.

Cited By

View all
  • (2023)A self-stabilizing distributed algorithm for the 1-MIS problem under the distance-3 model2023 Eleventh International Symposium on Computing and Networking Workshops (CANDARW)10.1109/CANDARW60564.2023.00025(100-106)Online publication date: 27-Nov-2023
  • (2023)Self-stabilizing 2-minimal dominating set algorithms based on loop compositionTheoretical Computer Science10.1016/j.tcs.2023.114314(114314)Online publication date: Nov-2023
  • (2022)A self-stabilizing 2-minimal dominating set algorithm based on loop composition in networks of girth at least 72022 IEEE International Parallel and Distributed Processing Symposium (IPDPS)10.1109/IPDPS53621.2022.00114(1140-1150)Online publication date: May-2022
  • Show More Cited By

Recommendations

Comments

Please enable JavaScript to view thecomments powered by Disqus.

Information & Contributors

Information

Published In

cover image ACM Other conferences
ICDCN '17: Proceedings of the 18th International Conference on Distributed Computing and Networking
January 2017
367 pages
ISBN:9781450348393
DOI:10.1145/3007748
Permission to make digital or hard copies of all or part of this work for personal or classroom use is granted without fee provided that copies are not made or distributed for profit or commercial advantage and that copies bear this notice and the full citation on the first page. Copyrights for components of this work owned by others than the author(s) must be honored. Abstracting with credit is permitted. To copy otherwise, or republish, to post on servers or to redistribute to lists, requires prior specific permission and/or a fee. Request permissions from [email protected].

In-Cooperation

  • IDRBT: IDRBT

Publisher

Association for Computing Machinery

New York, NY, United States

Publication History

Published: 05 January 2017

Permissions

Request permissions for this article.

Check for updates

Qualifiers

  • Research-article
  • Research
  • Refereed limited

Conference

ICDCN '17

Contributors

Other Metrics

Bibliometrics & Citations

Bibliometrics

Article Metrics

  • Downloads (Last 12 months)0
  • Downloads (Last 6 weeks)0
Reflects downloads up to 20 Dec 2024

Other Metrics

Citations

Cited By

View all
  • (2023)A self-stabilizing distributed algorithm for the 1-MIS problem under the distance-3 model2023 Eleventh International Symposium on Computing and Networking Workshops (CANDARW)10.1109/CANDARW60564.2023.00025(100-106)Online publication date: 27-Nov-2023
  • (2023)Self-stabilizing 2-minimal dominating set algorithms based on loop compositionTheoretical Computer Science10.1016/j.tcs.2023.114314(114314)Online publication date: Nov-2023
  • (2022)A self-stabilizing 2-minimal dominating set algorithm based on loop composition in networks of girth at least 72022 IEEE International Parallel and Distributed Processing Symposium (IPDPS)10.1109/IPDPS53621.2022.00114(1140-1150)Online publication date: May-2022
  • (2019)A Self-stabilizing 1-Maximal Independent Set AlgorithmStabilization, Safety, and Security of Distributed Systems10.1007/978-3-030-34992-9_27(338-353)Online publication date: 14-Nov-2019
  • (2018)Constant-Space Self-stabilizing Token Distribution in TreesStructural Information and Communication Complexity10.1007/978-3-030-01325-7_4(25-29)Online publication date: 31-Oct-2018

View Options

Login options

View options

PDF

View or Download as a PDF file.

PDF

eReader

View online with eReader.

eReader

Media

Figures

Other

Tables

Share

Share

Share this Publication link

Share on social media