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Gathering and Election by Mobile Robots in a Continuous Cycle

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

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Subject Classification

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

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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.

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

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.

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