, Volume 101, Issue 9, pp 1241–1264 | Cite as

Optimal torus exploration by oblivious robots

  • Stéphane DevismesEmail author
  • Anissa Lamani
  • Franck Petit
  • Sébastien Tixeuil


We deal with a team of autonomous robots that are endowed with motion actuators and visibility sensors. Those robots are weak and evolve in a discrete environment. By weak, we mean that they are anonymous, uniform, unable to explicitly communicate, and oblivious. We first show that it is impossible to solve the terminating exploration of a simple torus of arbitrary size with less than 4 or 5 such robots, respectively depending on whether the algorithm is probabilistic or deterministic. Next, we propose in the SSYNC model a probabilistic solution for the terminating exploration of torus-shaped networks of size \(\ell \times L\), where \(7 \le \ell \le L\), by a team of 4 such weak robots. So, this algorithm is optimal w.r.t. the number of robots.


Robot Torus Exploration Obliviousness 

Mathematics Subject Classification



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Copyright information

© Springer-Verlag GmbH Austria, part of Springer Nature 2018

Authors and Affiliations

  • Stéphane Devismes
    • 1
    Email author
  • Anissa Lamani
    • 2
  • Franck Petit
    • 3
  • Sébastien Tixeuil
    • 3
  1. 1.VERIMAG, Université Grenoble AlpesGrenobleFrance
  2. 2.Kyushu UniversityFukuokaJapan
  3. 3.LIP6UPMC Sorbonne UniversitésParisFrance

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