Randomized rendezvous of mobile agents in anonymous unidirectional ring networks

  • Authors:

  • Shinji Kawai;Fukuhito Ooshita;Hirotsugu Kakugawa;Toshimitsu Masuzawa

  • Affiliations:

  • Graduate School of Information Science and Technology, Osaka University, Japan;Graduate School of Information Science and Technology, Osaka University, Japan;Graduate School of Information Science and Technology, Osaka University, Japan;Graduate School of Information Science and Technology, Osaka University, Japan

  • Venue:
  • SIROCCO'12 Proceedings of the 19th international conference on Structural Information and Communication Complexity
  • Year:
  • 2012

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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(0p≤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(0p