Deterministic Symmetry Breaking in Ring Networks

Leszek Gasieniec, Tomasz Jurdzinski, Russell Martin, Grzegorz Stachowicz

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Abstract

We study a distributed coordination mechanism for uniform agents located on a circle. The agents perform their actions in synchronised rounds. At the beginning of each round an agent chooses the direction of its movement from clockwise, anticlockwise, or idle, and moves at unit speed during this round. Agents are not allowed to overpass, i.e., When an agent collides with another it instantly starts moving with the same speed in the opposite direction (without exchanging any information with the other agent). However, at the end of each round each agent has access to limited information regarding its trajectory of movement during this round. We assume that n mobile agents are initially located on a circle unit circumference at arbitrary but distinct positions unknown to other agents. The agents are equipped with unique identifiers from a fixed range. The location discovery task to be performed by each agent is to determine the initial position of every other agent. Our main result states that, if the only available information about movement in a round is limited to distance between the initial and the final position, then there is a superlinear lower bound on time needed to solve the location discovery problem. Interestingly, this result corresponds to a combinatorial symmetry breaking problem, which might be of independent interest. If, on the other hand, an agent has access to the distance to its first collision with another agent in a round, we design an asymptotically efficient and close to optimal solution for the location discovery problem.

Original languageEnglish (US)
Title of host publicationProceedings - 2015 IEEE 35th International Conference on Distributed Computing Systems, ICDCS 2015
PublisherInstitute of Electrical and Electronics Engineers Inc.
Pages517-526
Number of pages10
ISBN (Electronic)9781467372145
DOIs
StatePublished - Jul 22 2015
Externally publishedYes
Event35th IEEE International Conference on Distributed Computing Systems, ICDCS 2015 - Columbus, United States
Duration: Jun 29 2015Jul 2 2015

Publication series

NameProceedings - International Conference on Distributed Computing Systems
Volume2015-July

Conference

Conference35th IEEE International Conference on Distributed Computing Systems, ICDCS 2015
CountryUnited States
CityColumbus
Period6/29/157/2/15

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Keywords

  • bouncing
  • location discovery
  • mobile robots

ASJC Scopus subject areas

  • Software
  • Hardware and Architecture
  • Computer Networks and Communications

Cite this

Gasieniec, L., Jurdzinski, T., Martin, R., & Stachowicz, G. (2015). Deterministic Symmetry Breaking in Ring Networks. In Proceedings - 2015 IEEE 35th International Conference on Distributed Computing Systems, ICDCS 2015 (pp. 517-526). [7164937] (Proceedings - International Conference on Distributed Computing Systems; Vol. 2015-July). Institute of Electrical and Electronics Engineers Inc.. https://doi.org/10.1109/ICDCS.2015.59