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**Published in:** LIPIcs, Volume 125, 22nd International Conference on Principles of Distributed Systems (OPODIS 2018)

A loosely-stabilizing leader election protocol with polylogarithmic convergence time in the population protocol model is presented in this paper. In the population protocol model, which is a common abstract model of mobile sensor networks, it is known to be impossible to design a self-stabilizing leader election protocol. Thus, in our prior work, we introduced the concept of loose-stabilization, which is weaker than self-stabilization but has similar advantage as self-stabilization in practice. Following this work, several loosely-stabilizing leader election protocols are presented. The loosely-stabilizing leader election guarantees that, starting from an arbitrary configuration, the system reaches a safe configuration with a single leader within a relatively short time, and keeps the unique leader for an sufficiently long time thereafter. The convergence times of all the existing loosely-stabilizing protocols, i.e., the expected time to reach a safe configuration, are polynomial in n where n is the number of nodes (while the holding times to keep the unique leader are exponential in n). In this paper, a loosely-stabilizing protocol with polylogarithmic convergence time is presented. Its holding time is not exponential, but arbitrarily large polynomial in n.

Yuichi Sudo, Fukuhito Ooshita, Hirotsugu Kakugawa, Toshimitsu Masuzawa, Ajoy K. Datta, and Lawrence L. Larmore. Loosely-Stabilizing Leader Election with Polylogarithmic Convergence Time. In 22nd International Conference on Principles of Distributed Systems (OPODIS 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 125, pp. 30:1-30:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019)

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@InProceedings{sudo_et_al:LIPIcs.OPODIS.2018.30, author = {Sudo, Yuichi and Ooshita, Fukuhito and Kakugawa, Hirotsugu and Masuzawa, Toshimitsu and Datta, Ajoy K. and Larmore, Lawrence L.}, title = {{Loosely-Stabilizing Leader Election with Polylogarithmic Convergence Time}}, booktitle = {22nd International Conference on Principles of Distributed Systems (OPODIS 2018)}, pages = {30:1--30:16}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-95977-098-9}, ISSN = {1868-8969}, year = {2019}, volume = {125}, editor = {Cao, Jiannong and Ellen, Faith and Rodrigues, Luis and Ferreira, Bernardo}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.OPODIS.2018.30}, URN = {urn:nbn:de:0030-drops-100901}, doi = {10.4230/LIPIcs.OPODIS.2018.30}, annote = {Keywords: Loose-stabilization, Population protocols, and Leader election} }

Document

**Published in:** LIPIcs, Volume 125, 22nd International Conference on Principles of Distributed Systems (OPODIS 2018)

Self-stabilizing and silent distributed algorithms for token distribution in rooted tree networks are given. Initially, each process of a graph holds at most l tokens. Our goal is to distribute the tokens in the whole network so that every process holds exactly k tokens. In the initial configuration, the total number of tokens in the network may not be equal to nk where n is the number of processes in the network. The root process is given the ability to create a new token or remove a token from the network. We aim to minimize the convergence time, the number of token moves, and the space complexity. A self-stabilizing token distribution algorithm that converges within O(n l) asynchronous rounds and needs Theta(nh epsilon) redundant (or unnecessary) token moves is given, where epsilon = min(k,l-k) and h is the height of the tree network. Two novel ideas to reduce the number of redundant token moves are presented. One reduces the number of redundant token moves to O(nh) without any additional costs while the other reduces the number of redundant token moves to O(n), but increases the convergence time to O(nh l). All algorithms given have constant memory at each process and each link register.

Yuichi Sudo, Ajoy K. Datta, Lawrence L. Larmore, and Toshimitsu Masuzawa. Self-Stabilizing Token Distribution with Constant-Space for Trees. In 22nd International Conference on Principles of Distributed Systems (OPODIS 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 125, pp. 31:1-31:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019)

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@InProceedings{sudo_et_al:LIPIcs.OPODIS.2018.31, author = {Sudo, Yuichi and Datta, Ajoy K. and Larmore, Lawrence L. and Masuzawa, Toshimitsu}, title = {{Self-Stabilizing Token Distribution with Constant-Space for Trees}}, booktitle = {22nd International Conference on Principles of Distributed Systems (OPODIS 2018)}, pages = {31:1--31:16}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-95977-098-9}, ISSN = {1868-8969}, year = {2019}, volume = {125}, editor = {Cao, Jiannong and Ellen, Faith and Rodrigues, Luis and Ferreira, Bernardo}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.OPODIS.2018.31}, URN = {urn:nbn:de:0030-drops-100918}, doi = {10.4230/LIPIcs.OPODIS.2018.31}, annote = {Keywords: token distribution, self-stabilization, constant-space algorithm} }

Document

**Published in:** LIPIcs, Volume 46, 19th International Conference on Principles of Distributed Systems (OPODIS 2015)

We give a silent self-stabilizing protocol for computing a maximum matching in an anonymous network with a tree topology. The round complexity of our protocol is O(diam), where diam is the diameter of the network, and the step complexity is O(n*diam), where n is the number of processes in the network. The working space complexity is O(1) per process, although the output necessarily takes O(log(delta)) space per process, where delta is the degree of that process. To implement parent pointers in constant space, regardless of degree, we use the cyclic Abelian group Z_7.

Ajoy K. Datta, Lawrence L. Larmore, and Toshimitsu Masuzawa. Maximum Matching for Anonymous Trees with Constant Space per Process. In 19th International Conference on Principles of Distributed Systems (OPODIS 2015). Leibniz International Proceedings in Informatics (LIPIcs), Volume 46, pp. 16:1-16:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2016)

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@InProceedings{datta_et_al:LIPIcs.OPODIS.2015.16, author = {Datta, Ajoy K. and Larmore, Lawrence L. and Masuzawa, Toshimitsu}, title = {{Maximum Matching for Anonymous Trees with Constant Space per Process}}, booktitle = {19th International Conference on Principles of Distributed Systems (OPODIS 2015)}, pages = {16:1--16:16}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-939897-98-9}, ISSN = {1868-8969}, year = {2016}, volume = {46}, editor = {Anceaume, Emmanuelle and Cachin, Christian and Potop-Butucaru, Maria}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.OPODIS.2015.16}, URN = {urn:nbn:de:0030-drops-66074}, doi = {10.4230/LIPIcs.OPODIS.2015.16}, annote = {Keywords: anonymous tree, maximum matching, self-stabilization, unfair daemon} }

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