Document

**Published in:** LIPIcs, Volume 286, 27th International Conference on Principles of Distributed Systems (OPODIS 2023)

Research on distributed computing by a team of identical mobile computational entities, called robots, operating in a Euclidean space in Look-Compute-Move (LCM) cycles, has recently focused on better understanding how the computational power of robots depends on the interplay between their internal capabilities (i.e., persistent memory, communication), captured by the four standard computational models (OBLOT, LUMI, FSTA, and FCOM) and the conditions imposed by the external environment, controlling the activation of the robots and their synchronization of their activities, perceived and modeled as an adversarial scheduler.
We consider a set of adversarial asynchronous schedulers ranging from the classical semi-synchronous (Ssynch) and fully asynchronous (Asynch) settings, including schedulers (emerging when studying the atomicity of the combination of operations in the LCM cycles) whose adversarial power is in between those two. We ask the question: what is the computational relationship between a model M₁ under adversarial scheduler K₁ (M₁(K₁)) and a model M₂ under scheduler K₂ (M₂(K₂))? For example, are the robots in M₁(K₁) more powerful (i.e., they can solve more problems) than those in M₂(K₂)?
We answer all these questions by providing, through cross-model analysis, a complete characterization of the computational relationship between the power of the four models of robots under the considered asynchronous schedulers. In this process, we also provide qualified answers to several open questions, including the outstanding one on the proper dominance of Ssynch over Asynch in the case of unrestricted visibility.

Paola Flocchini, Nicola Santoro, Yuichi Sudo, and Koichi Wada. On Asynchrony, Memory, and Communication: Separations and Landscapes. In 27th International Conference on Principles of Distributed Systems (OPODIS 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 286, pp. 28:1-28:23, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{flocchini_et_al:LIPIcs.OPODIS.2023.28, author = {Flocchini, Paola and Santoro, Nicola and Sudo, Yuichi and Wada, Koichi}, title = {{On Asynchrony, Memory, and Communication: Separations and Landscapes}}, booktitle = {27th International Conference on Principles of Distributed Systems (OPODIS 2023)}, pages = {28:1--28:23}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-95977-308-9}, ISSN = {1868-8969}, year = {2024}, volume = {286}, editor = {Bessani, Alysson and D\'{e}fago, Xavier and Nakamura, Junya and Wada, Koichi and Yamauchi, Yukiko}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.OPODIS.2023.28}, URN = {urn:nbn:de:0030-drops-195188}, doi = {10.4230/LIPIcs.OPODIS.2023.28}, annote = {Keywords: Look-Compute-Move, Oblivious mobile robots, Robots with lights, Memory versus Communication, Moving and Computing, Asynchrony} }

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**Published in:** LIPIcs, Volume 257, 2nd Symposium on Algorithmic Foundations of Dynamic Networks (SAND 2023)

In this paper, we consider the partial gathering problem of mobile agents in synchronous dynamic tori. The partial gathering problem is a generalization of the (well-investigated) total gathering problem, which requires that all k agents distributed in the network terminate at a non-predetermined single node. The partial gathering problem requires, for a given positive integer g (< k), that agents terminate in a configuration such that either at least g agents or no agent exists at each node. So far, in almost cases, the partial gathering problem has been considered in static graphs. As only one exception, it is considered in a kind of dynamic rings called 1-interval connected rings, that is, one of the links in the ring may be missing at each time step. In this paper, we consider partial gathering in another dynamic topology. Concretely, we consider it in n× n dynamic tori such that each of row rings and column rings is represented as a 1-interval connected ring. In such networks, when k = O(gn), focusing on the relationship between the values of k, n, and g, we aim to characterize the solvability of the partial gathering problem and analyze the move complexity of the proposed algorithms when the problem can be solved. First, we show that agents cannot solve the problem when k = o(gn), which means that Ω (gn) agents are necessary to solve the problem. Second, we show that the problem can be solved with the total number of O(gn³) moves when 2gn+2n-1 ≤ k ≤ 2gn + 6n +16g -12. Finally, we show that the problem can be solved with the total number of O(gn²) moves when k ≥ 2gn + 6n +16g -11. From these results, we show that our algorithms can solve the partial gathering problem in dynamic tori with the asymptotically optimal number Θ (gn) of agents. In addition, we show that agents require a total number of Ω(gn²) moves to solve the partial gathering problem in dynamic tori when k = Θ(gn). Thus, when k ≥ 2gn+6n+16g -11, our algorithm can solve the problem with asymptotically optimal number O(gn²) of agent moves.

Masahiro Shibata, Naoki Kitamura, Ryota Eguchi, Yuichi Sudo, Junya Nakamura, and Yonghwan Kim. Partial Gathering of Mobile Agents in Dynamic Tori. In 2nd Symposium on Algorithmic Foundations of Dynamic Networks (SAND 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 257, pp. 2:1-2:22, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)

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@InProceedings{shibata_et_al:LIPIcs.SAND.2023.2, author = {Shibata, Masahiro and Kitamura, Naoki and Eguchi, Ryota and Sudo, Yuichi and Nakamura, Junya and Kim, Yonghwan}, title = {{Partial Gathering of Mobile Agents in Dynamic Tori}}, booktitle = {2nd Symposium on Algorithmic Foundations of Dynamic Networks (SAND 2023)}, pages = {2:1--2:22}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-95977-275-4}, ISSN = {1868-8969}, year = {2023}, volume = {257}, editor = {Doty, David and Spirakis, Paul}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SAND.2023.2}, URN = {urn:nbn:de:0030-drops-179387}, doi = {10.4230/LIPIcs.SAND.2023.2}, annote = {Keywords: distributed system, mobile agents, partial gathering, dynamic tori} }

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**Published in:** LIPIcs, Volume 253, 26th International Conference on Principles of Distributed Systems (OPODIS 2022)

An autonomous mobile robot system consisting of many mobile computational entities (called robots) attracts much attention of researchers, and it is an emerging issue for a recent couple of decades to clarify the relation between the capabilities of robots and solvability of the problems.
Generally, each robot can observe all other robots as long as there are no restrictions on visibility range or obstructions, regardless of the number of robots. In this paper, we provide a new perspective on the observation by robots; a robot cannot necessarily observe all other robots regardless of distances to them. We call this new computational model the defected view model. Under this model, in this paper, we consider the gathering problem that requires all the robots to gather at the same non-predetermined point and propose two algorithms to solve the gathering problem in the adversarial (N,N-2)-defected model for N ≥ 5 (where each robot observes at most N-2 robots chosen adversarially) and the distance-based (4,2)-defected model (where each robot observes at most two robots closest to itself), respectively, where N is the number of robots. Moreover, we present an impossibility result showing that there is no (deterministic) gathering algorithm in the adversarial or distance-based (3,1)-defected model, and we also show an impossibility result for the gathering in a relaxed (N, N-2)-defected model.

Yonghwan Kim, Masahiro Shibata, Yuichi Sudo, Junya Nakamura, Yoshiaki Katayama, and Toshimitsu Masuzawa. Gathering of Mobile Robots with Defected Views. In 26th International Conference on Principles of Distributed Systems (OPODIS 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 253, pp. 14:1-14:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)

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@InProceedings{kim_et_al:LIPIcs.OPODIS.2022.14, author = {Kim, Yonghwan and Shibata, Masahiro and Sudo, Yuichi and Nakamura, Junya and Katayama, Yoshiaki and Masuzawa, Toshimitsu}, title = {{Gathering of Mobile Robots with Defected Views}}, booktitle = {26th International Conference on Principles of Distributed Systems (OPODIS 2022)}, pages = {14:1--14:18}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-95977-265-5}, ISSN = {1868-8969}, year = {2023}, volume = {253}, editor = {Hillel, Eshcar and Palmieri, Roberto and Rivi\`{e}re, Etienne}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.OPODIS.2022.14}, URN = {urn:nbn:de:0030-drops-176349}, doi = {10.4230/LIPIcs.OPODIS.2022.14}, annote = {Keywords: mobile robot, gathering, defected view model} }

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Brief Announcement

**Published in:** LIPIcs, Volume 246, 36th International Symposium on Distributed Computing (DISC 2022)

In this paper, we provide a new perspective on the observation by robots; a robot cannot necessarily observe all other robots regardless of distances to them. We introduce a new computational model with defected views called a (N,k)-defected model where k robots among N-1 other robots can be observed. We propose two gathering algorithms: one in the adversarial (N,N-2)-defected model for N ≥ 5 (where N is the number of robots) and the other in the distance-based (4,2)-defected model. Moreover, we present two impossibility results for a (3,1)-defected model and a relaxed (N, N-2)-defected model respectively. This announcement is short; the full paper is available at [Yonghwan Kim and others, 2022].

Yonghwan Kim, Masahiro Shibata, Yuichi Sudo, Junya Nakamura, Yoshiaki Katayama, and Toshimitsu Masuzawa. Brief Announcement: Gathering Despite Defected View. In 36th International Symposium on Distributed Computing (DISC 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 246, pp. 46:1-46:3, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)

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@InProceedings{kim_et_al:LIPIcs.DISC.2022.46, author = {Kim, Yonghwan and Shibata, Masahiro and Sudo, Yuichi and Nakamura, Junya and Katayama, Yoshiaki and Masuzawa, Toshimitsu}, title = {{Brief Announcement: Gathering Despite Defected View}}, booktitle = {36th International Symposium on Distributed Computing (DISC 2022)}, pages = {46:1--46:3}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-95977-255-6}, ISSN = {1868-8969}, year = {2022}, volume = {246}, editor = {Scheideler, Christian}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.DISC.2022.46}, URN = {urn:nbn:de:0030-drops-172377}, doi = {10.4230/LIPIcs.DISC.2022.46}, annote = {Keywords: mobile robot, gathering, defected view model} }

Document

**Published in:** LIPIcs, Volume 209, 35th International Symposium on Distributed Computing (DISC 2021)

In this work, we initiate the study of smoothed analysis of population protocols. We consider a population protocol model where an adaptive adversary dictates the interactions between agents, but with probability p every such interaction may change into an interaction between two agents chosen uniformly at random. That is, p-fraction of the interactions are random, while (1-p)-fraction are adversarial. The aim of our model is to bridge the gap between a uniformly random scheduler (which is too idealistic) and an adversarial scheduler (which is too strict).
We focus on the fundamental problem of leader election in population protocols. We show that, for a population of size n, the leader election problem can be solved in O(p^{-2}n log³ n) steps with high probability, using O((log² n) ⋅ (log (n/p))) states per agent, for all values of p ≤ 1. Although our result does not match the best known running time of O(n log n) for the uniformly random scheduler (p = 1), we are able to present a smooth transition between a running time of O(n polylog n) for p = 1 and an infinite running time for the adversarial scheduler (p = 0), where the problem cannot be solved. The key technical contribution of our work is a novel phase clock algorithm for our model. This is a key primitive for much-studied fundamental population protocol algorithms (leader election, majority), and we believe it is of independent interest.

Gregory Schwartzman and Yuichi Sudo. Smoothed Analysis of Population Protocols. In 35th International Symposium on Distributed Computing (DISC 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 209, pp. 34:1-34:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021)

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@InProceedings{schwartzman_et_al:LIPIcs.DISC.2021.34, author = {Schwartzman, Gregory and Sudo, Yuichi}, title = {{Smoothed Analysis of Population Protocols}}, booktitle = {35th International Symposium on Distributed Computing (DISC 2021)}, pages = {34:1--34:19}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-95977-210-5}, ISSN = {1868-8969}, year = {2021}, volume = {209}, editor = {Gilbert, Seth}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.DISC.2021.34}, URN = {urn:nbn:de:0030-drops-148362}, doi = {10.4230/LIPIcs.DISC.2021.34}, annote = {Keywords: Population protocols, Smoothed analysis, Leader election} }

Document

**Published in:** LIPIcs, Volume 209, 35th International Symposium on Distributed Computing (DISC 2021)

We consider the leader election problem in the population protocol model. In pragmatic settings of population protocols, self-stabilization is a highly desired feature owing to its fault resilience and the benefit of initialization freedom. However, the design of self-stabilizing leader election is possible only under a strong assumption (i.e., the knowledge of the exact size of a network) and rich computational resource (i.e., the number of states). Loose-stabilization is a promising relaxed concept of self-stabilization to address the aforementioned issue. Loose-stabilization guarantees that starting from any configuration, the network will reach a safe configuration where a single leader exists within a short time, and thereafter it will maintain the single leader for a long time, but not necessarily forever. The main contribution of this paper is giving a time-optimal loosely-stabilizing leader election protocol. The proposed protocol with design parameter τ ≥ 1 attains O(τ log n) parallel convergence time and Ω(n^τ) parallel holding time (i.e., the length of the period keeping the unique leader), both in expectation. This protocol is time-optimal in the sense of both the convergence and holding times in expectation because any loosely-stabilizing leader election protocol with the same length of the holding time is known to require Ω(τ log n) parallel time.

Yuichi Sudo, Ryota Eguchi, Taisuke Izumi, and Toshimitsu Masuzawa. Time-Optimal Loosely-Stabilizing Leader Election in Population Protocols. In 35th International Symposium on Distributed Computing (DISC 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 209, pp. 40:1-40:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021)

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@InProceedings{sudo_et_al:LIPIcs.DISC.2021.40, author = {Sudo, Yuichi and Eguchi, Ryota and Izumi, Taisuke and Masuzawa, Toshimitsu}, title = {{Time-Optimal Loosely-Stabilizing Leader Election in Population Protocols}}, booktitle = {35th International Symposium on Distributed Computing (DISC 2021)}, pages = {40:1--40:17}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-95977-210-5}, ISSN = {1868-8969}, year = {2021}, volume = {209}, editor = {Gilbert, Seth}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.DISC.2021.40}, URN = {urn:nbn:de:0030-drops-148427}, doi = {10.4230/LIPIcs.DISC.2021.40}, annote = {Keywords: population protocols, leader election, loose-stabilization, self-stabilization} }

Document

**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.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.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} }

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Brief Announcement

**Published in:** LIPIcs, Volume 121, 32nd International Symposium on Distributed Computing (DISC 2018)

We present a fast loosely-stabilizing leader election protocol in the population protocol model. It elects a unique leader in a poly-logarithmic time and holds the leader for a polynomial time with arbitrarily large degree in terms of parallel time, i.e, the number of steps per the population size.

Yuichi Sudo, Fukuhito Ooshita, Hirotsugu Kakugawa, and Toshimitsu Masuzawa. Brief Announcement: Loosely-stabilizing Leader Election with Polylogarithmic Convergence Time. In 32nd International Symposium on Distributed Computing (DISC 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 121, pp. 52:1-52:3, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2018)

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@InProceedings{sudo_et_al:LIPIcs.DISC.2018.52, author = {Sudo, Yuichi and Ooshita, Fukuhito and Kakugawa, Hirotsugu and Masuzawa, Toshimitsu}, title = {{Brief Announcement: Loosely-stabilizing Leader Election with Polylogarithmic Convergence Time}}, booktitle = {32nd International Symposium on Distributed Computing (DISC 2018)}, pages = {52:1--52:3}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-95977-092-7}, ISSN = {1868-8969}, year = {2018}, volume = {121}, editor = {Schmid, Ulrich and Widder, Josef}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.DISC.2018.52}, URN = {urn:nbn:de:0030-drops-98410}, doi = {10.4230/LIPIcs.DISC.2018.52}, annote = {Keywords: Self-stabilization, Loose-stabilization, Population protocols} }

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

In the population protocol model Angluin et al. proposed in 2004, there exists no self-stabilizing leader election protocol for complete graphs, arbitrary graphs, trees, lines, degree-bounded graphs and so on unless the protocol knows the exact number of nodes. To circumvent the impossibility, we introduced the concept of loose-stabilization in 2009, which relaxes the closure requirement of self-stabilization. A loosely-stabilizing protocol guarantees that starting from any initial configuration a system reaches a safe configuration, and after that, the system keeps its specification (e.g. the unique leader) not forever, but for a sufficiently long time (e.g. exponentially large time with respect to the number of nodes). Our previous works presented two loosely-stabilizing leader election protocols for arbitrary graphs; One uses agent identifiers and the other uses random numbers to elect a unique leader. In this paper, we present a loosely-stabilizing protocol that solves leader election on arbitrary graphs without agent identifiers nor random numbers. By the combination of virus-propagation and token-circulation, the proposed protocol achieves polynomial convergence time and exponential holding time without such external entities. Specifically, given upper bounds N and Delta of the number of nodes n and the maximum degree of nodes delta respectively, it reaches a safe configuration within O(m*n^3*d + m*N*Delta^2*log(N)) expected steps, and keeps the unique leader for Omega(N*e^N) expected steps where m is the number of edges and d is the diameter of the graph. To measure the time complexity of the protocol, we assume the uniformly random scheduler which is widely used in the field of the population protocols.

Yuichi Sudo, Fukuhito Ooshita, Hirotsugu Kakugawa, and Toshimitsu Masuzawa. Loosely-Stabilizing Leader Election on Arbitrary Graphs in Population Protocols Without Identifiers nor Random Numbers. In 19th International Conference on Principles of Distributed Systems (OPODIS 2015). Leibniz International Proceedings in Informatics (LIPIcs), Volume 46, pp. 14:1-14:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2016)

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@InProceedings{sudo_et_al:LIPIcs.OPODIS.2015.14, author = {Sudo, Yuichi and Ooshita, Fukuhito and Kakugawa, Hirotsugu and Masuzawa, Toshimitsu}, title = {{Loosely-Stabilizing Leader Election on Arbitrary Graphs in Population Protocols Without Identifiers nor Random Numbers}}, booktitle = {19th International Conference on Principles of Distributed Systems (OPODIS 2015)}, pages = {14:1--14:16}, 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.dagstuhl.de/entities/document/10.4230/LIPIcs.OPODIS.2015.14}, URN = {urn:nbn:de:0030-drops-66054}, doi = {10.4230/LIPIcs.OPODIS.2015.14}, annote = {Keywords: Loose-stabilization, Population protocols, Leader election} }

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