Optimal Circle Search Despite the Presence of Faulty Robots

  • Konstantinos Georgiou
  • Evangelos Kranakis
  • Nikos Leonardos
  • Aris PagourtzisEmail author
  • Ioannis Papaioannou
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 11931)


We consider (nf)-search on a circle, a search problem of a hidden exit on a circle of unit radius for \(n > 1\) robots, f of which are faulty. All the robots start at the centre of the circle and can move anywhere with maximum speed 1. During the search, robots may communicate wirelessly. All messages transmitted by all robots are tagged with the robots’ unique identifiers which cannot be corrupted. The search is considered complete when the exit is found by a non-faulty robot (which must visit its location) and the remaining non-faulty robots know the correct location of the exit.

We study two models of faulty robots. First, crash-faulty robots may stop operating as instructed, and thereafter they remain nonfunctional. Second, Byzantine-faulty robots may transmit untrue messages at any time during the search so as to mislead the non-faulty robots, e.g., lie about the location of the exit.

When there are only crash fault robots, we provide optimal algorithms for the (nf)-search problem, with optimal worst-case search completion time \(1+\frac{(f+1)2\pi }{n}\). Our main technical contribution pertains to optimal algorithms for (n, 1)-search with a Byzantine-faulty robot, minimizing the worst-case search completion time, which equals \(1+\frac{4\pi }{n}\).


Adversary Byzantine Circle Exit Perimeter Robot Search Speed Wireless communication 


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Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  • Konstantinos Georgiou
    • 1
  • Evangelos Kranakis
    • 2
  • Nikos Leonardos
    • 3
  • Aris Pagourtzis
    • 4
    Email author
  • Ioannis Papaioannou
    • 4
  1. 1.Department of MathematicsRyerson UniversityTorontoCanada
  2. 2.School of Computer ScienceCarleton UniversityOttawaCanada
  3. 3.Department of Informatics and TelecommunicationsNational and Kapodistrian University of AthensIlissiaGreece
  4. 4.School of Electrical and Computer EngineeringNational Technical University of AthensZografouGreece

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