Randomized Rendezvous of Mobile Agents in Anonymous Unidirectional Ring Networks
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.
KeywordsMobile Agent Single Node Correct Number Identical Node Impossibility Result
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- 6.Dieudonné, Y., Pelc, A.: Deterministic gathering of anonymous agents in arbitrary networks. Arxiv preprint arXiv:1111.0321 (2011)Google Scholar
- 7.Gasieniec, L., Pelc, A., Radzik, T., Zhang, X.: Tree exploration with logarithmic memory. In: Proc. of SODA, pp. 585–594 (2007)Google Scholar
- 10.Kranakis, E., Krizanc, D., Markou, E.: The mobile agent rendezvous problem in the ring. Synthesis Lectures on Distributed Computing Theory, Lecture # 1. Morgan & Claypool Publishers (2010)Google Scholar
- 12.Sudo, Y., Baba, D., Nakamura, J., Ooshita, F., Kakugawa, H., Masuzawa, T.: An agent exploration in unknown undirected graphs with whiteboards. In: Proc. of WRAS, p. 8 (2010)Google Scholar