Search on a Line by Byzantine Robots

Authors Jurek Czyzowicz, Konstantinos Georgiou, Evangelos Kranakis, Danny Krizanc, Lata Narayanan, Jaroslav Opatrny, Sunil Shende

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Jurek Czyzowicz
Konstantinos Georgiou
Evangelos Kranakis
Danny Krizanc
Lata Narayanan
Jaroslav Opatrny
Sunil Shende

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Jurek Czyzowicz, Konstantinos Georgiou, Evangelos Kranakis, Danny Krizanc, Lata Narayanan, Jaroslav Opatrny, and Sunil Shende. Search on a Line by Byzantine Robots. In 27th International Symposium on Algorithms and Computation (ISAAC 2016). Leibniz International Proceedings in Informatics (LIPIcs), Volume 64, pp. 27:1-27:12, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2016)


We consider the problem of fault-tolerant parallel search on an infinite line by n robots. Starting from the origin, the robots are required to find a target at an unknown location. The robots can move with maximum speed 1 and can communicate in wireless mode among themselves. However, among the n robots, there are f robots that exhibit byzantine faults. A faulty robot can fail to report the target even after reaching it, or it can make malicious claims about having found the target when in fact it has not. Given the presence of such faulty robots, the search for the target can only be concluded when the non-faulty robots have sufficient verification that the target has been found. We aim to design algorithms that minimize the value of S_d (n, f), the time to find a target at a distance d from the origin by n robots among which f are faulty. We give several different algorithms whose running time depends on the ratio f/n, the density of faulty robots, and also prove lower bounds. Our algorithms are optimal for some densities of faulty robots.
  • Cow path problem
  • Parallel search
  • Mobile robots
  • Wireless communication
  • Byzantine faults


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