Randomized rendezvous with limited memory

  • Authors:
  • Evangelos Kranakis;Danny Krizanc;Pat Morin

  • Affiliations:
  • Carleton University, Ottawa, ON, Canada;Wesleyan University, Middletown, CT;Carleton University, Ottawa, ON, Canada

  • Venue:
  • ACM Transactions on Algorithms (TALG)
  • Year:
  • 2011

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Abstract

We present a trade-off between the expected time for two identical agents to rendezvous on a synchronous, anonymous, oriented ring and the memory requirements of the agents. In particular, we show there exists a 2t state agent which can achieve rendezvous on an n-node ring in expected time O(n2/2t + 2t) and that any t/2 state agent requires expected time Ω(n2/2t). As a corollary we observe that Θ(log log n) bits of memory are necessary and sufficient to achieve rendezvous in linear time.