research-article

Dispersion of Mobile Robots: A Study of Memory-Time Trade-offs

Authors:

John Augustine,

William K. Moses, Jr.Authors Info & Claims

ICDCN '18: Proceedings of the 19th International Conference on Distributed Computing and Networking

Article No.: 1, Pages 1 - 10

https://doi.org/10.1145/3154273.3154293

Published: 04 January 2018 Publication History

Abstract

We introduce a new problem in the domain of mobile robots, which we term dispersion. In this problem, n robots are placed in an n node graph arbitrarily and must coordinate with each other to reach a final configuration such that exactly one robot is at each node. We study this problem through the lenses of minimizing the memory required by each robot and of minimizing the number of rounds required to achieve dispersion.

Dispersion is of interest due to its relationship to the problems of scattering on a graph, exploration using mobile robots, and load balancing on a graph. Additionally, dispersion has an immediate real world application due to its relationship to the problem of recharging electric cars, as each car can be considered a robot and recharging stations and the roads connecting them nodes and edges of a graph respectively. Since recharging is a costly affair relative to traveling, we want to distribute these cars amongst the various available recharge points where communication should be limited to car-to-car interactions.

We provide lower bounds on both the memory required for robots to achieve dispersion and the minimum running time to achieve dispersion on any type of graph. We then analyze the trade-offs between time and memory for various types of graphs. We provide time optimal and memory optimal algorithms for several types of graphs and show the power of a little memory in terms of running time.

References

[1]

Ankush Agarwalla, John Augustine, William K. Moses Jr., Madhav Sankar K., and Arvind Krishna Sridhar. 2017. Deterministic Dispersion of Mobile Robots in Dynamic Rings. CoRR abs/1707.06391 (2017). https://arxiv.org/abs/1707.06391

Digital Library

[2]

Christoph Ambühl, Leszek Gasieniec, Andrzej Pelc, Tomasz Radzik, and Xiaohui Zhang. 2011. Tree exploration with logarithmic memory. ACM Transactions on Algorithms 7, 2 (2011), 17.

Digital Library

[3]

John Augustine and William K. Moses Jr. 2017. Dispersion of Mobile Robots: A Study of Memory-Time Trade-offs. CoRR abs/1707.05629 (2017). http://arxiv.org/abs/1707.05629

Digital Library

[4]

Lali Barriere, Paola Flocchini, Eduardo Mesa-Barrameda, and Nicola Santoro. 2011. Uniform scattering of autonomous mobile robots in a grid. International Journal of Foundations of Computer Science 22, 03 (2011), 679--697.

[5]

Petra Berenbrink, Colin Cooper, Tom Friedetzky, Tobias Friedrich, and Thomas Sauerwald. 2015. Randomized diffusion for indivisible loads. J. Comput. System Sci. 81, 1 (2015), 159--185.

Digital Library

[6]

Petra Berenbrink, Tom Friedetzky, and Zengjian Hu. 2009. A new analytical method for parallel, diffusion-type load balancing. J. Parallel and Distrib. Comput. 69, 1 (2009), 54--61.

Digital Library

[7]

Hans Leo Bodlaender and Jan van Leeuwen. 1986. Distribution of Records on a Ring of Processors. Department of Computer Science, University of Utrecht.

[8]

Peter Brass, Flavio Cabrera-Mora, Andrea Gasparri, and Jizhong Xiao. 2011. Multirobot tree and graph exploration. IEEE Transactions on Robotics 27, 4 (2011), 707--717.

Digital Library

[9]

Peter Brass, Ivo Vigan, and Ning Xu. 2014. Improved analysis of a multirobot graph exploration strategy. In Control Automation Robotics & Vision, 2014 13th International Conference on. IEEE, 1906--1910.

[10]

Reuven Cohen, Pierre Fraigniaud, David Ilcinkas, Amos Korman, and David Peleg. 2008. Label-guided graph exploration by a finite automaton. ACM Transactions on Algorithms 4, 4 (2008), 42.

Digital Library

[11]

George Cybenko. 1989. Dynamic load balancing for distributed memory multiprocessors. J. Parallel and Distrib. Comput. 7, 2 (1989), 279--301.

Digital Library

[12]

Dariusz Dereniowski, Yann Disser, Adrian Kosowski, Dominik Pająk, and Przemysław Uznański. 2015. Fast collaborative graph exploration. Information and Computation 243 (2015), 37--49.

Digital Library

[13]

Krzysztof Diks, Pierre Fraigniaud, Evangelos Kranakis, and Andrzej Pelc. 2002. Tree exploration with little memory. In Proceedings of the thirteenth annual ACM-SIAM symposium on Discrete algorithms. Society for Industrial and Applied Mathematics, 588--597.

Digital Library

[14]

Yann Disser, Frank Mousset, Andreas Noever, Nemanja Škorić, and Angelika Steger. 2016. A general lower bound for collaborative tree exploration. arXiv preprint arXiv:1610.01753 (2016).

[15]

Miroslaw Dynia, J. Kutyłowski, F. Meyer auf der Heide, and Christian Schindelhauer. 2006. Smart robot teams exploring sparse trees. In International Symposium on Mathematical Foundations of Computer Science. Springer, 327--338.

Digital Library

[16]

Miroslaw Dynia, Jakub Łopusza&Nacute;ski, and Christian Schindelhauer. 2007. Why robots need maps. In International Colloquium on Structural Information and Communication Complexity. Springer, 41--50.

Digital Library

[17]

Yotam Elor and Alfred M Bruckstein. 2011. Uniform multi-agent deployment on a ring. Theoretical Computer Science 412, 8--10 (2011), 783--795.

Digital Library

[18]

Pierre Fraigniaud, Leszek Gasieniec, Dariusz R. Kowalski, and Andrzej Pelc. 2006. Collective tree exploration. Networks 48, 3 (2006), 166--177.

Digital Library

[19]

Yuya Higashikawa, Naoki Katoh, Stefan Langerman, and Shinichi Tanigawa. 2014. Online graph exploration algorithms for cycles and trees by multiple searchers. Journal of Combinatorial Optimization 28, 2 (2014), 480--495.

Digital Library

[20]

Artur Menc, Dominik Pajak, and Przemyslaw Uznanski. 2015. On the power of one bit: How to explore a graph when you cannot backtrack? arXiv preprint (2015).

[21]

S Muthukrishnan, Bhaskar Ghosh, and Martin H Schultz. 1998. First-and second-order diffusive methods for rapid, coarse, distributed load balancing. Theory of computing systems 31, 4 (1998), 331--354.

[22]

Christian Ortolf and Christian Schindelhauer. 2014. A Recursive Approach to Multi-robot Exploration of Trees. In International Colloquium on Structural Information and Communication Complexity. Springer, 343--354.

[23]

David Peleg and Allen Van Gelder. 1989. Packet distribution on a ring. J. Parallel and Distrib. Comput. 6, 3 (1989), 558--567.

Digital Library

[24]

Thomas Sauerwald and He Sun. 2012. Tight bounds for randomized load balancing on arbitrary network topologies. In Foundations of Computer Science, 2012 IEEE 53rd Annual Symposium on. IEEE, 341--350.

Digital Library

[25]

Masahiro Shibata, Toshiya Mega, Fukuhito Ooshita, Hirotsugu Kakugawa, and Toshimitsu Masuzawa. 2016. Uniform deployment of mobile agents in asynchronous rings. In Proceedings of the 2016 ACM Symposium on Principles of Distributed Computing. ACM, 415--424.

Digital Library

[26]

Raghu Subramanian and Isaac D Scherson. 1994. An analysis of diffusive load-balancing. In Proceedings of the sixth annual ACM symposium on Parallel algorithms and architectures. ACM, 220--225.

Digital Library

[27]

Yuichi Sudo, Daisuke Baba, Junya Nakamura, Fukuhito Ooshita, Hirotsugu Kakugawa, and Toshimitsu Masuzawa. 2015. A single agent exploration in unknown undirected graphs with whiteboards. IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences 98, 10 (2015), 2117--2128.

[28]

Cheng-Zhong Xu and Francis C. M. Lau. 1992. Analysis of the generalized dimension exchange method for dynamic load balancing. J. Parallel and Distrib. Comput. 16, 4 (1992), 385--393.

Cited By

Kaur TSaxena AMandal PMondal K(2025)Black Hole Search in Dynamic GraphsProceedings of the 26th International Conference on Distributed Computing and Networking10.1145/3700838.3700869(221-230)Online publication date: 4-Jan-2025
https://dl.acm.org/doi/10.1145/3700838.3700869
Saxena AKaur TMondal K(2025)Dispersion on Time Varying GraphsProceedings of the 26th International Conference on Distributed Computing and Networking10.1145/3700838.3700845(269-273)Online publication date: 4-Jan-2025
https://dl.acm.org/doi/10.1145/3700838.3700845
Mondal BGoswami PSau B(2025)Time Optimal Distance-k-Dispersion on Dynamic RingProceedings of the 26th International Conference on Distributed Computing and Networking10.1145/3700838.3700843(259-263)Online publication date: 4-Jan-2025
https://dl.acm.org/doi/10.1145/3700838.3700843
Show More Cited By

Index Terms

Dispersion of Mobile Robots: A Study of Memory-Time Trade-offs
1. Theory of computation
  1. Design and analysis of algorithms

Recommendations

Efficient dispersion of mobile robots on graphs
ICDCN '19: Proceedings of the 20th International Conference on Distributed Computing and Networking

The dispersion problem on graphs requires k robots placed arbitrarily at the n nodes of an anonymous graph, where k ≤ n, to coordinate with each other to reach a final configuration in which each robot is at a distinct node of the graph. The dispersion ...
Dispersion of Mobile Robots in the Global Communication Model
ICDCN '20: Proceedings of the 21st International Conference on Distributed Computing and Networking

The dispersion problem on graphs asks k ≤ n robots placed initially arbitrarily on the nodes of an n-node anonymous graph to reposition autonomously to reach a configuration in which each robot is on a distinct node of the graph. This problem is of ...
Dispersion of Mobile Robots Tolerating Faults
ICDCN '21: Adjunct Proceedings of the 2021 International Conference on Distributed Computing and Networking

The dispersion problem on graphs asks k ≤ n robots initially placed arbitrarily on the nodes of an n-node anonymous graph to reposition autonomously to reach a configuration with each robot on a distinct node. This problem is of interest due to its ...

Comments

Information & Contributors

Information

Published In

cover image ACM Other conferences

ICDCN '18: Proceedings of the 19th International Conference on Distributed Computing and Networking

January 2018

494 pages

ISBN:9781450363723

DOI:10.1145/3154273

Copyright © 2018 ACM.

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

Publisher

Association for Computing Machinery

New York, NY, United States

Publication History

Published: 04 January 2018

Permissions

Request permissions for this article.

Request Permissions

Check for updates

Author Tags

Qualifiers

Research-article
Research
Refereed limited

Funding Sources

Science and Engineering Research Board, Department of Science and Technology, Government of India

Conference

ICDCN '18

ICDCN '18: 19th International Conference on Distributed Computing and Networking

January 4 - 7, 2018

Varanasi, India

Contributors

Other Metrics

View Article Metrics

Bibliometrics & Citations

Bibliometrics

Article Metrics

46
Total Citations
View Citations
247
Total Downloads

Downloads (Last 12 months)33
Downloads (Last 6 weeks)3

Reflects downloads up to 05 Mar 2025

Other Metrics

View Author Metrics

Citations

Cited By

Kaur TSaxena AMandal PMondal K(2025)Black Hole Search in Dynamic GraphsProceedings of the 26th International Conference on Distributed Computing and Networking10.1145/3700838.3700869(221-230)Online publication date: 4-Jan-2025
https://dl.acm.org/doi/10.1145/3700838.3700869
Saxena AKaur TMondal K(2025)Dispersion on Time Varying GraphsProceedings of the 26th International Conference on Distributed Computing and Networking10.1145/3700838.3700845(269-273)Online publication date: 4-Jan-2025
https://dl.acm.org/doi/10.1145/3700838.3700845
Mondal BGoswami PSau B(2025)Time Optimal Distance-k-Dispersion on Dynamic RingProceedings of the 26th International Conference on Distributed Computing and Networking10.1145/3700838.3700843(259-263)Online publication date: 4-Jan-2025
https://dl.acm.org/doi/10.1145/3700838.3700843
Banerjee RKumar MMolla A(2025)Optimal Fault-Tolerant Dispersion on Oriented GridsProceedings of the 26th International Conference on Distributed Computing and Networking10.1145/3700838.3700842(254-258)Online publication date: 4-Jan-2025
https://dl.acm.org/doi/10.1145/3700838.3700842
Kaur TMondal K(2025)Memory optimal distance-2-dispersion with terminationInternational Journal of Parallel, Emergent and Distributed Systems10.1080/17445760.2025.2469514(1-22)Online publication date: 2-Mar-2025
https://doi.org/10.1080/17445760.2025.2469514
Goswami PSharma AGhosh SSau B(2025)Time optimal gathering of myopic robots on an infinite triangular gridTheoretical Computer Science10.1016/j.tcs.2024.1149301023:COnline publication date: 1-Jan-2025
https://dl.acm.org/doi/10.1016/j.tcs.2024.114930
Gupta AKulkarni S(2024)Tolerance to Asynchrony of an Algorithm for Gathering Myopic Robots on an Infinite Triangular Grid2024 19th European Dependable Computing Conference (EDCC)10.1109/EDCC61798.2024.00023(61-68)Online publication date: 8-Apr-2024
https://doi.org/10.1109/EDCC61798.2024.00023
Gorain BMandal PMondal KPandit S(2024)Collaborative Dispersion by Silent RobotsJournal of Parallel and Distributed Computing10.1016/j.jpdc.2024.104852(104852)Online publication date: Feb-2024
https://doi.org/10.1016/j.jpdc.2024.104852
Kshemkalyani AKumar MMolla ASharma G(2024)Faster Leader Election and Its Applications for Mobile Agents with Parameter AdviceDistributed Computing and Intelligent Technology10.1007/978-3-031-81404-4_9(108-123)Online publication date: 31-Dec-2024
https://doi.org/10.1007/978-3-031-81404-4_9
Himani Pandit S(2024)Optimal Dispersion in Triangular Grids: Achieving Efficiency Without Prior KnowledgeDistributed Computing and Intelligent Technology10.1007/978-3-031-81404-4_7(75-91)Online publication date: 31-Dec-2024
https://doi.org/10.1007/978-3-031-81404-4_7
Show More Cited By

View Options

Login options

Check if you have access through your login credentials or your institution to get full access on this article.

Full Access

Get this Publication

View options

PDF

View or Download as a PDF file.

eReader

View online with eReader.

Figures

Tables

Media

View Table of Conten