Abstract
We consider the rendezvous problem of multiple (mobile) agents in anonymous unidirectional ring networks under the constraint that each agent knows neither the number of nodes nor the number of agents. First, we prove for any (small) constant p(0 < p ≤ 1) that there exists no randomized algorithm that solves, with probability p, the rendezvous problem with (terminal) detection. For this reason, we consider the relaxed rendezvous problem, called the rendezvous problem without detection that does not require termination detection. We prove that there exists no randomized algorithm that solves, with probability 1, the rendezvous problem without detection. For the remaining cases, we show the possibility, that is, we propose a randomized algorithm that solves, with any given constant probability p(0 < p < 1), the rendezvous problem without detection.
This work is supported in part by Grant-in-Aid for Scientific Research ((B)2030012, (B)22300009, (B)23700056, (C)24500039) of JSPS.
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Kawai, S., Ooshita, F., Kakugawa, H., Masuzawa, T. (2012). Randomized Rendezvous of Mobile Agents in Anonymous Unidirectional Ring Networks. In: Even, G., Halldórsson, M.M. (eds) Structural Information and Communication Complexity. SIROCCO 2012. Lecture Notes in Computer Science, vol 7355. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-31104-8_26
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DOI: https://doi.org/10.1007/978-3-642-31104-8_26
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