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Documents authored by Wada, Koichi

Document
Brief Announcement
DOI: 10.4230/LIPIcs.DISC.2024.48
Brief Announcement: Distinct Gathering Under Round Robin

Authors: Fabian Frei and Koichi Wada

Published in: LIPIcs, Volume 319, 38th International Symposium on Distributed Computing (DISC 2024)

Abstract
We resolve one of the longest-standing questions about autonomous mobile robots in a surprising way. Distinct Gathering is the fundamental cooperation task of letting robots, initially scattered across the plane in distinct locations, gather in an arbitrary single point. The scheduler Round Robin cyclically activates the robots one by one in a fixed order. When activated, a robot perceives all robot locations and moves wherever it wants based only on this information. For n = 2 robots, the task is trivial. What happens for n ≥ 3 has remained an open problem for decades by now. The established conjecture declares the task to be impossible in this case. We prove that it is indeed impossible for n = 3 but, to great surprise, possible again for any n ≥ 4. We go beyond the standard requirements by providing a very robust algorithm that does not require any consistency or self-consistency for the local Cartesian maps perceived by the robots and works even for non-rigid movement, that is, if robots may be unpredictably stopped and deactivated during a movement.
Cite as

Fabian Frei and Koichi Wada. Brief Announcement: Distinct Gathering Under Round Robin. In 38th International Symposium on Distributed Computing (DISC 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 319, pp. 48:1-48:8, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{frei_et_al:LIPIcs.DISC.2024.48,
  author =	{Frei, Fabian and Wada, Koichi},
  title =	{{Brief Announcement: Distinct Gathering Under Round Robin}},
  booktitle =	{38th International Symposium on Distributed Computing (DISC 2024)},
  pages =	{48:1--48:8},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-352-2},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{319},
  editor =	{Alistarh, Dan},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.DISC.2024.48},
  URN =		{urn:nbn:de:0030-drops-212768},
  doi =		{10.4230/LIPIcs.DISC.2024.48},
  annote =	{Keywords: Autonomous mobile robots, Distinct Gathering, Round Robin}
}
Document
Complete Volume
DOI: 10.4230/LIPIcs.OPODIS.2023
LIPIcs, Volume 286, OPODIS 2023, Complete Volume

Authors: Alysson Bessani, Xavier Défago, Junya Nakamura, Koichi Wada, and Yukiko Yamauchi

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

Abstract
LIPIcs, Volume 286, OPODIS 2023, Complete Volume
Cite as

27th International Conference on Principles of Distributed Systems (OPODIS 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 286, pp. 1-702, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@Proceedings{bessani_et_al:LIPIcs.OPODIS.2023,
  title =	{{LIPIcs, Volume 286, OPODIS 2023, Complete Volume}},
  booktitle =	{27th International Conference on Principles of Distributed Systems (OPODIS 2023)},
  pages =	{1--702},
  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},
  URN =		{urn:nbn:de:0030-drops-194896},
  doi =		{10.4230/LIPIcs.OPODIS.2023},
  annote =	{Keywords: LIPIcs, Volume 286, OPODIS 2023, Complete Volume}
}
Document
Front Matter
DOI: 10.4230/LIPIcs.OPODIS.2023.0
Front Matter, Table of Contents, Preface, Conference Organization

Authors: Alysson Bessani, Xavier Défago, Junya Nakamura, Koichi Wada, and Yukiko Yamauchi

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

Abstract
Front Matter, Table of Contents, Preface, Conference Organization
Cite as

27th International Conference on Principles of Distributed Systems (OPODIS 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 286, pp. 0:i-0:xvi, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{bessani_et_al:LIPIcs.OPODIS.2023.0,
  author =	{Bessani, Alysson and D\'{e}fago, Xavier and Nakamura, Junya and Wada, Koichi and Yamauchi, Yukiko},
  title =	{{Front Matter, Table of Contents, Preface, Conference Organization}},
  booktitle =	{27th International Conference on Principles of Distributed Systems (OPODIS 2023)},
  pages =	{0:i--0:xvi},
  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.2023.0},
  URN =		{urn:nbn:de:0030-drops-194903},
  doi =		{10.4230/LIPIcs.OPODIS.2023.0},
  annote =	{Keywords: Front Matter, Table of Contents, Preface, Conference Organization}
}
Document
DOI: 10.4230/LIPIcs.OPODIS.2023.28
On Asynchrony, Memory, and Communication: Separations and Landscapes

Authors: Paola Flocchini, Nicola Santoro, Yuichi Sudo, and Koichi Wada

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

Abstract
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.
Cite as

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}
}
Document
DOI: 10.4230/LIPIcs.OPODIS.2021.9
Asynchronous Gathering in a Torus

Authors: Sayaka Kamei, Anissa Lamani, Fukuhito Ooshita, Sébastien Tixeuil, and Koichi Wada

Published in: LIPIcs, Volume 217, 25th International Conference on Principles of Distributed Systems (OPODIS 2021)

Abstract
We consider the gathering problem for asynchronous and oblivious robots that cannot communicate explicitly with each other but are endowed with visibility sensors that allow them to see the positions of the other robots. Most investigations on the gathering problem on the discrete universe are done on ring shaped networks due to the number of symmetric configurations. We extend in this paper the study of the gathering problem on torus shaped networks assuming robots endowed with local weak multiplicity detection. That is, robots cannot make the difference between nodes occupied by only one robot from those occupied by more than one robot unless it is their current node. Consequently, solutions based on creating a single multiplicity node as a landmark for the gathering cannot be used. We present in this paper a deterministic algorithm that solves the gathering problem starting from any rigid configuration on an asymmetric unoriented torus shaped network.
Cite as

Sayaka Kamei, Anissa Lamani, Fukuhito Ooshita, Sébastien Tixeuil, and Koichi Wada. Asynchronous Gathering in a Torus. In 25th International Conference on Principles of Distributed Systems (OPODIS 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 217, pp. 9:1-9:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)

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@InProceedings{kamei_et_al:LIPIcs.OPODIS.2021.9,
  author =	{Kamei, Sayaka and Lamani, Anissa and Ooshita, Fukuhito and Tixeuil, S\'{e}bastien and Wada, Koichi},
  title =	{{Asynchronous Gathering in a Torus}},
  booktitle =	{25th International Conference on Principles of Distributed Systems (OPODIS 2021)},
  pages =	{9:1--9:17},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-219-8},
  ISSN =	{1868-8969},
  year =	{2022},
  volume =	{217},
  editor =	{Bramas, Quentin and Gramoli, Vincent and Milani, Alessia},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.OPODIS.2021.9},
  URN =		{urn:nbn:de:0030-drops-157845},
  doi =		{10.4230/LIPIcs.OPODIS.2021.9},
  annote =	{Keywords: Autonomous distributed systems, Robots gathering, Torus}
}
Document
DOI: 10.4230/LIPIcs.OPODIS.2019.25
On Memory, Communication, and Synchronous Schedulers When Moving and Computing

Authors: Paola Flocchini, Nicola Santoro, and Koichi Wada

Published in: LIPIcs, Volume 153, 23rd International Conference on Principles of Distributed Systems (OPODIS 2019)

Abstract
We investigate the computational power of distributed systems whose autonomous computational entities, called robots, move and operate in the 2-dimensional Euclidean plane in synchronous Look-Compute-Move (LCM) cycles. Specifically, we focus on the power of persistent memory and that of explicit communication, and on their computational relationship. In the most common model, OBLOT, the robots are oblivious (no persistent memory) and silent (no explicit means of communication). In contrast, in the LUMI model, each robot is equipped with a constant-sized persistent memory (called light), visible to all the robots; hence, these luminous robots are capable in each cycle of both remembering and communicating. Since luminous robots are computationally more powerful than the standard oblivious one, immediate important questions are about the individual computational power of persistent memory and of explicit communication. In particular, which of the two capabilities, memory or communication, is more important? in other words, is it better to remember or to communicate ? In this paper we address these questions, focusing on two sub-models of LUMI: FSTA, where the robots have a constant-size persistent memory but are silent; and FCOM, where the robots can communicate a constant number of bits but are oblivious. We analyze the relationship among all these models and provide a complete exhaustive map of their computational relationship. Among other things, we prove that communication is more powerful than persistent memory under the fully synchronous scheduler Fsynch, while they are incomparable under the semi-synchronous scheduler Ssynch.
Cite as

Paola Flocchini, Nicola Santoro, and Koichi Wada. On Memory, Communication, and Synchronous Schedulers When Moving and Computing. In 23rd International Conference on Principles of Distributed Systems (OPODIS 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 153, pp. 25:1-25:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020)

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@InProceedings{flocchini_et_al:LIPIcs.OPODIS.2019.25,
  author =	{Flocchini, Paola and Santoro, Nicola and Wada, Koichi},
  title =	{{On Memory, Communication, and Synchronous Schedulers When Moving and Computing}},
  booktitle =	{23rd International Conference on Principles of Distributed Systems (OPODIS 2019)},
  pages =	{25:1--25:17},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-133-7},
  ISSN =	{1868-8969},
  year =	{2020},
  volume =	{153},
  editor =	{Felber, Pascal and Friedman, Roy and Gilbert, Seth and Miller, Avery},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.OPODIS.2019.25},
  URN =		{urn:nbn:de:0030-drops-118114},
  doi =		{10.4230/LIPIcs.OPODIS.2019.25},
  annote =	{Keywords: Look-Compute-Move, Oblivious mobile robots, Robots with lights, Memory versus Communication, Moving and Computing}
}
Document
DOI: 10.4230/LIPIcs.OPODIS.2019.27
Gathering on Rings for Myopic Asynchronous Robots With Lights

Authors: Sayaka Kamei, Anissa Lamani, Fukuhito Ooshita, Sébastien Tixeuil, and Koichi Wada

Published in: LIPIcs, Volume 153, 23rd International Conference on Principles of Distributed Systems (OPODIS 2019)

Abstract
We investigate gathering algorithms for asynchronous autonomous mobile robots moving in uniform ring-shaped networks. Different from most work using the Look-Compute-Move (LCM) model, we assume that robots have limited visibility and lights. That is, robots can observe nodes only within a certain fixed distance, and emit a color from a set of constant number of colors. We consider gathering algorithms depending on two parameters related to the initial configuration: M_{init}, which denotes the number of nodes between two border nodes, and O_{init}, which denotes the number of nodes hosting robots between two border nodes. In both cases, a border node is a node hosting one or more robots that cannot see other robots on at least one side. Our main contribution is to prove that, if M_{init} or O_{init} is odd, gathering is always feasible with three or four colors. The proposed algorithms do not require additional assumptions, such as knowledge of the number of robots, multiplicity detection capabilities, or the assumption of towerless initial configurations. These results demonstrate the power of lights to achieve gathering of robots with limited visibility.
Cite as

Sayaka Kamei, Anissa Lamani, Fukuhito Ooshita, Sébastien Tixeuil, and Koichi Wada. Gathering on Rings for Myopic Asynchronous Robots With Lights. In 23rd International Conference on Principles of Distributed Systems (OPODIS 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 153, pp. 27:1-27:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020)

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@InProceedings{kamei_et_al:LIPIcs.OPODIS.2019.27,
  author =	{Kamei, Sayaka and Lamani, Anissa and Ooshita, Fukuhito and Tixeuil, S\'{e}bastien and Wada, Koichi},
  title =	{{Gathering on Rings for Myopic Asynchronous Robots With Lights}},
  booktitle =	{23rd International Conference on Principles of Distributed Systems (OPODIS 2019)},
  pages =	{27:1--27:17},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-133-7},
  ISSN =	{1868-8969},
  year =	{2020},
  volume =	{153},
  editor =	{Felber, Pascal and Friedman, Roy and Gilbert, Seth and Miller, Avery},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.OPODIS.2019.27},
  URN =		{urn:nbn:de:0030-drops-118139},
  doi =		{10.4230/LIPIcs.OPODIS.2019.27},
  annote =	{Keywords: LCM robot system, ASYNC schedulers, myopic, luminous, ring networks}
}
Document
DOI: 10.4230/LIPIcs.ISAAC.2019.52
Efficient Circuit Simulation in MapReduce

Authors: Fabian Frei and Koichi Wada

Published in: LIPIcs, Volume 149, 30th International Symposium on Algorithms and Computation (ISAAC 2019)

Abstract
The MapReduce framework has firmly established itself as one of the most widely used parallel computing platforms for processing big data on tera- and peta-byte scale. Approaching it from a theoretical standpoint has proved to be notoriously difficult, however. In continuation of Goodrich et al.’s early efforts, explicitly espousing the goal of putting the MapReduce framework on footing equal to that of long-established models such as the PRAM, we investigate the obvious complexity question of how the computational power of MapReduce algorithms compares to that of combinational Boolean circuits commonly used for parallel computations. Relying on the standard MapReduce model introduced by Karloff et al. a decade ago, we develop an intricate simulation technique to show that any problem in NC (i.e., a problem solved by a logspace-uniform family of Boolean circuits of polynomial size and a depth polylogarithmic in the input size) can be solved by a MapReduce computation in O(T(n)/log n) rounds, where n is the input size and T(n) is the depth of the witnessing circuit family. Thus, we are able to closely relate the standard, uniform NC hierarchy modeling parallel computations to the deterministic MapReduce hierarchy DMRC by proving that NC^{i+1} subseteq DMRC^i for all i in N. Besides the theoretical significance, this result has important applied aspects as well. In particular, we show for all problems in NC^1 - many practically relevant ones, such as integer multiplication and division and the parity function, being among these - how to solve them in a constant number of deterministic MapReduce rounds.
Cite as

Fabian Frei and Koichi Wada. Efficient Circuit Simulation in MapReduce. In 30th International Symposium on Algorithms and Computation (ISAAC 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 149, pp. 52:1-52:21, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019)

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@InProceedings{frei_et_al:LIPIcs.ISAAC.2019.52,
  author =	{Frei, Fabian and Wada, Koichi},
  title =	{{Efficient Circuit Simulation in MapReduce}},
  booktitle =	{30th International Symposium on Algorithms and Computation (ISAAC 2019)},
  pages =	{52:1--52:21},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-130-6},
  ISSN =	{1868-8969},
  year =	{2019},
  volume =	{149},
  editor =	{Lu, Pinyan and Zhang, Guochuan},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ISAAC.2019.52},
  URN =		{urn:nbn:de:0030-drops-115487},
  doi =		{10.4230/LIPIcs.ISAAC.2019.52},
  annote =	{Keywords: MapReduce, Circuit Complexity, Parallel Algorithms, Nick’s Class NC}
}
Document
Brief Announcement
DOI: 10.4230/LIPIcs.DISC.2019.41
Brief Announcement: Model Checking Rendezvous Algorithms for Robots with Lights in Euclidean Space

Authors: Xavier Défago, Adam Heriban, Sébastien Tixeuil, and Koichi Wada

Published in: LIPIcs, Volume 146, 33rd International Symposium on Distributed Computing (DISC 2019)

Abstract
This announces the first successful attempt at using model-checking techniques to verify the correctness of self-stabilizing distributed algorithms for robots evolving in a continuous environment. The study focuses on the problem of rendezvous of two robots with lights and presents a generic verification model for the SPIN model checker. It will be presented in full at an upcoming venue.
Cite as

Xavier Défago, Adam Heriban, Sébastien Tixeuil, and Koichi Wada. Brief Announcement: Model Checking Rendezvous Algorithms for Robots with Lights in Euclidean Space. In 33rd International Symposium on Distributed Computing (DISC 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 146, pp. 41:1-41:3, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019)

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@InProceedings{defago_et_al:LIPIcs.DISC.2019.41,
  author =	{D\'{e}fago, Xavier and Heriban, Adam and Tixeuil, S\'{e}bastien and Wada, Koichi},
  title =	{{Brief Announcement: Model Checking Rendezvous Algorithms for Robots with Lights in Euclidean Space}},
  booktitle =	{33rd International Symposium on Distributed Computing (DISC 2019)},
  pages =	{41:1--41:3},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-126-9},
  ISSN =	{1868-8969},
  year =	{2019},
  volume =	{146},
  editor =	{Suomela, Jukka},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.DISC.2019.41},
  URN =		{urn:nbn:de:0030-drops-113487},
  doi =		{10.4230/LIPIcs.DISC.2019.41},
  annote =	{Keywords: Autonomous mobile robots, Rendezvous, Lights, Model Checking}
}
Document
Brief Announcement
DOI: 10.4230/LIPIcs.DISC.2019.43
Brief Announcement: Neighborhood Mutual Remainder and Its Self-Stabilizing Implementation of Look-Compute-Move Robots

Authors: Shlomi Dolev, Sayaka Kamei, Yoshiaki Katayama, Fukuhito Ooshita, and Koichi Wada

Published in: LIPIcs, Volume 146, 33rd International Symposium on Distributed Computing (DISC 2019)

Abstract
In this paper, we define a new concept neighborhood mutual remainder (NMR). An NMR distributed algorithms should satisfy global fairness, l-exclusion and repeated local rendezvous requirements. We give a simple self-stabilizing algorithm to demonstrate the design paradigm to achieve NMR, and also present applications of NMR to a Look-Compute-Move robot system.
Cite as

Shlomi Dolev, Sayaka Kamei, Yoshiaki Katayama, Fukuhito Ooshita, and Koichi Wada. Brief Announcement: Neighborhood Mutual Remainder and Its Self-Stabilizing Implementation of Look-Compute-Move Robots. In 33rd International Symposium on Distributed Computing (DISC 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 146, pp. 43:1-43:3, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019)

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@InProceedings{dolev_et_al:LIPIcs.DISC.2019.43,
  author =	{Dolev, Shlomi and Kamei, Sayaka and Katayama, Yoshiaki and Ooshita, Fukuhito and Wada, Koichi},
  title =	{{Brief Announcement: Neighborhood Mutual Remainder and Its Self-Stabilizing Implementation of Look-Compute-Move Robots}},
  booktitle =	{33rd International Symposium on Distributed Computing (DISC 2019)},
  pages =	{43:1--43:3},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-126-9},
  ISSN =	{1868-8969},
  year =	{2019},
  volume =	{146},
  editor =	{Suomela, Jukka},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.DISC.2019.43},
  URN =		{urn:nbn:de:0030-drops-113504},
  doi =		{10.4230/LIPIcs.DISC.2019.43},
  annote =	{Keywords: neighborhood mutual remainder, self-stabilization, LCM robot}
}
Document
DOI: 10.4230/LIPIcs.OPODIS.2018.24
Optimal Rendezvous L-Algorithms for Asynchronous Mobile Robots with External-Lights

Authors: Takashi Okumura, Koichi Wada, and Xavier Défago

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

Abstract
We study the Rendezvous problem for two autonomous mobile robots in asynchronous settings with persistent memory called light. It is well known that Rendezvous is impossible in a basic model when robots have no lights, even if the system is semi-synchronous. On the other hand, Rendezvous is possible if robots have lights of various types with a constant number of colors. If robots can observe not only their own lights but also other robots' lights, their lights are called full-light. If robots can only observe the state of other robots' lights, the lights are called external-light. This paper focuses on robots with external-lights in asynchronous settings and a particular class of algorithms called L-algorithms, where an L-algorithm computes a destination based only on the current colors of observable lights. When considering L-algorithms, Rendezvous can be solved by robots with full-lights and three colors in general asynchronous settings (called ASYNC) and the number of colors is optimal under these assumptions. In contrast, there exist no L-algorithms in ASYNC with external-lights regardless of the number of colors. In this paper, extending the impossibility result, we show that there exist no L-algorithms in so-called LC-1-Bounded ASYNC with external-lights regardless of the number of colors, where LC-1-Bounded ASYNC is a proper subset of ASYNC and other robots can execute at most one Look operation between the Look operation of a robot and its subsequent Compute operation. We also show that LC-1-Bounded ASYNC is the minimal subclass in which no L-algorithms with external-lights exist. That is, Rendezvous can be solved by L-algorithms using external-lights with a finite number of colors in LC-0-Bounded ASYNC (equivalently LC-atomic ASYNC). Furthermore, we show that the algorithms are optimal in the number of colors they use.
Cite as

Takashi Okumura, Koichi Wada, and Xavier Défago. Optimal Rendezvous L-Algorithms for Asynchronous Mobile Robots with External-Lights. In 22nd International Conference on Principles of Distributed Systems (OPODIS 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 125, pp. 24:1-24:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019)

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@InProceedings{okumura_et_al:LIPIcs.OPODIS.2018.24,
  author =	{Okumura, Takashi and Wada, Koichi and D\'{e}fago, Xavier},
  title =	{{Optimal Rendezvous L-Algorithms for Asynchronous Mobile Robots with External-Lights}},
  booktitle =	{22nd International Conference on Principles of Distributed Systems (OPODIS 2018)},
  pages =	{24:1--24:16},
  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.2018.24},
  URN =		{urn:nbn:de:0030-drops-100843},
  doi =		{10.4230/LIPIcs.OPODIS.2018.24},
  annote =	{Keywords: Autonomous mobile robots, Rendezvous, Lights, L-algorithms}
}
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