Document Open Access Logo

Gathering and Election by Mobile Robots in a Continuous Cycle

Authors Paola Flocchini, Ryan Killick, Evangelos Kranakis, Nicola Santoro, Masafumi Yamashita

PDF
Thumbnail PDF

File

LIPIcs.ISAAC.2019.8.pdf
  • Filesize: 0.56 MB
  • 19 pages

Document Identifiers

Author Details

Paola Flocchini
  • School of Electrical Eng. and Comp. Sci., University of Ottawa, Ottawa, ON, K1N 6N5, Canada
Ryan Killick
  • School of Computer Science, Carleton University, Ottawa, ON, K1S 5B6, Canada
Evangelos Kranakis
  • School of Computer Science, Carleton University, Ottawa, ON, K1S 5B6, Canada
Nicola Santoro
  • School of Computer Science, Carleton University, Ottawa, ON, K1S 5B6, Canada
Masafumi Yamashita
  • Dept. of Comp. Sci. and Comm. Eng., Kyushu University, Motooka, Fukuoka, 819-0395, Japan

Funding

Paola Flocchini, Evangelos Kranakis, Nicola Santoro: Research supported in part by NSERC Discovery grant.
  • Flocchini, Paola: University Research Chair.
  • Killick, Ryan: Research supported by the NSERC Canada Graduate Scholarship.

Cite As Get BibTex

Paola Flocchini, Ryan Killick, Evangelos Kranakis, Nicola Santoro, and Masafumi Yamashita. Gathering and Election by Mobile Robots in a Continuous Cycle. In 30th International Symposium on Algorithms and Computation (ISAAC 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 149, pp. 8:1-8:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019) https://doi.org/10.4230/LIPIcs.ISAAC.2019.8

Abstract

Consider a set of n mobile computational entities, called robots, located and operating on a continuous cycle C (e.g., the perimeter of a closed region of R^2) of arbitrary length l. The robots are identical, can only see their current location, have no location awareness, and cannot communicate at a distance. In this weak setting, we study the classical problems of gathering (GATHER), requiring all robots to meet at a same location; and election (ELECT), requiring all robots to agree on a single one as the "leader". We investigate how to solve the problems depending on the amount of knowledge (exact, upper bound, none) the robots have about their number n and about the length of the cycle l. Cost of the algorithms is analyzed with respect to time and number of random bits. We establish a variety of new results specific to the continuous cycle - a geometric domain never explored before for GATHER and ELECT in a mobile robot setting; compare Monte Carlo and Las Vegas algorithms; and obtain several optimal bounds.

Subject Classification

ACM Subject Classification
  • Theory of computation → Distributed algorithms
Keywords
  • Cycle
  • Election
  • Gathering
  • Las Vegas
  • Monte Carlo
  • Randomized Algorithm

Metrics

  • Access Statistics
  • Total Accesses (updated on a weekly basis)
    0
    PDF Downloads
    0
    Metadata Views

References

  1. Hagit Attiya and Yishay Mansour. Language complexity on the synchronous anonymous ring. Theoretical Computer Science, 53(2-3):169-185, 1987. Google Scholar
  2. Hagit Attiya, Marc Snir, and Manfred K. Warmuth. Computing on an Anonymous Ring. J. ACM, 35(4):845-875, 1988. Google Scholar
  3. Rena Bakhshi, Wan Fokkink, Jun Pang, and Jaco van de Pol. Leader Election in Anonymous Rings: Franklin Goes Probabilistic. In 5th IFIP International Conference On Theoretical Computer Science (TCS), pages 57-72, 2008. Google Scholar
  4. Francesco Bullo, Jorge Cortes, and Sonia Martinez. Distributed Control of Robotic Networks. Princeton University Press, 2009. Google Scholar
  5. Mark Cielibak, Paola Flocchini, Giuseppe Prencipe, and Nicola Santoro. Distributed computing by mobile robots: Gathering. SIAM Journal on Computing, 41(4):829-879, 2012. Google Scholar
  6. Reuven Cohen and David Peleg. Convergence Properties of the Gravitational Algorithm in Asynchronous Robot Systems. SIAM Journal on Computing, 34(6):1516-1528, 2005. Google Scholar
  7. Jurek Czyzowicz, Leszek Gasieniec, Adrian Kosowski, and Evangelos Kranakis. Boundary Patrolling by Mobile Agents with Distinct Maximal Speeds. In 19th Annual European Symposium on Algorithms, ESA, pages 701-712, 2011. Google Scholar
  8. Jurek Czyzowicz, Kostantinos Georgiou, and Evangelos Kranakis. Patrolling. In P. Flocchini, G. Prencipe, and N. Santoro, editors, Distributed Computing by Mobile Entities, chapter 15, pages 371-400. Springer, 2019. Google Scholar
  9. Jurek Czyzowicz, Evangelos Kranakis, Dominik Pajak, and Najmeh Taleb. Patrolling by Robots Equipped with Visibility. In 21st International Colloquium on Structural Information and Communication Complexity, SIROCCO, pages 224-234, 2014. Google Scholar
  10. Yoann Dieudonné, Franck Petit, and Vincent Franck. Leader election problem versus pattern formation problem. In 24th International Symposium on Distributed Computing (DISC), pages 267-281, 2010. Google Scholar
  11. Ofer Feinerman, Amos Korman, Shay Kutten, and Yoav Rodeh. Fast rendezvous on a cycle by agents with different speeds. In 5th International Conference on Distributed Computing and Networking, ICDCN, pages 1-13, 2014. Google Scholar
  12. Paola Flocchini, Evangelos Kranakis, Danny Krizanc, Flaminia L. Luccio, and Nicola Santoro. Sorting and election in anonymous asynchronous rings. Journal of Parallel and Distributed Computing, 64(2):254-265, 2004. Google Scholar
  13. Paola Flocchini, Giuseppe Prencipe, and Nicola Santoro. Self-deployment of mobile sensors on a ring. Theoretical Computer Science, 402(1):67-80, 2008. Google Scholar
  14. Paola Flocchini, Giuseppe Prencipe, and Nicola Santoro. Distributed Computing by Oblivious Mobile Robots. Morgan & Claypool, 2012. Google Scholar
  15. Paola Flocchini, Giuseppe Prencipe, and Nicola Santoro. Distributed Computing by Mobile Entities. Springer, 2019. Google Scholar
  16. Paola Flocchini, Giuseppe Prencipe, Nicola Santoro, and Peter Widmayer. Gathering of asynchronous mobile robots with limited visibility. Theoretical Computer Science, 337(1-3):147-168, 2006. Google Scholar
  17. Paola Flocchini, Giuseppe Prencipe, Nicola Santoro, and Peter Widmayer. Arbitrary pattern formation by asynchronous, anonymous, oblivious robots. Theoretical Computer Science, 407(1-3):412-447, 2008. Google Scholar
  18. Greg N. Frederickson and Nicola Santoro. Breaking Symmetry in Synchronous Networks. In 1st Aegean Workshop on Computing (now SPAA), pages 26-33, 1986. Google Scholar
  19. Nao Fujinaga, Yukiko Yamauchi, Shuji Kijima, and Masafumi Yamashita. Asynchronous pattern formation by anonymous oblivious mobile robots. SIAM Journal on Computing, 44(3):740-785, 2015. Google Scholar
  20. Noam Gordon, Israel A. Wagner, and Alfred M. Bruckstein. A randomized gathering algorithm for multiple robots with limited sensing capabilities. In International Workshop on Multi-Agent Robotic Systems, 2005. Google Scholar
  21. Rajiv Gupta, Scott A. Smolka, and Shaji Bhaskar. On Randomization in Sequential and Distributed Algorithms. ACM Comput. Surv., 26(1):7-86, 1994. Google Scholar
  22. Evan Huus and Evangelos Kranakis. Rendezvous of many agents with different speeds in a cycle. In 14th International Conference on Ad-Hoc Networks and Wireless, ADHOC-NOW, pages 195-209, 2015. Google Scholar
  23. Alon Itai and Michael Rodeh. Symmetry breaking in distributed networks. Information and Computation, 88(1):60-87, 1990. Google Scholar
  24. Taisuke Izumi, Tomoko Izumi, Sayaka Kamei, and Fukuhito Ooshita. Randomized gathering of mobile robots with local-multiplicity detection. In 11th International Symposium on Stabilizing, Safety, and Security of Distributed Systems, SSS, pages 384-398, 2009. Google Scholar
  25. Richard M. Karp. Probabilistic Recurrence Relations. J. ACM, 41(6):1136-1150, 1994. Google Scholar
  26. Evangelos Kranakis, Danny Krizanc, and Euripides Markou. The Mobile Agent Rendezvous Problem in the Ring. Morgan & Claypool, 2010. Google Scholar
  27. Ji Lin, A. Stephen Morse, and Brian D.O. Anderson. The Multi-Agent Rendezvous Problem. Parts 1 and 2. SIAM Journal on Control and Optimization, 46(6):2096-2147, 2007. Google Scholar
  28. Rajeev Motwani and Prabhakar Raghavan. Randomized Algorithms. Cambridge University Press, 1995. Google Scholar
  29. Fukuhito Ooshita, Shinji Kawai, Hirotsugu Kakugawa, and Toshimitsu Masuzawa. Randomized gathering of mobile agents in anonymous unidirectional ring networks. IEEE Transactions on Parallel and Distributed Systems, 25(5):1289-1296, 2014. Google Scholar
  30. Yukiko Yamauchi. Symmetry of Anonymous Robots. In P. Flocchini, G. Prencipe, and N. Santoro, editors, Distributed Computing by Mobile Entities, chapter 6, pages 109-133. Springer, 2019. Google Scholar
Questions / Remarks / Feedback
X

Feedback for Dagstuhl Publishing


Thanks for your feedback!

Feedback submitted

Could not send message

Please try again later or send an E-mail
© 2023-2024 Schloss Dagstuhl – LZI GmbH About DROPS Imprint Privacy Contact