Space-optimal rendezvous of mobile agents in asynchronous trees

  • Authors:

  • Daisuke Baba;Tomoko Izumi;Fukuhito Ooshita;Hirotsugu Kakugawa;Toshimitsu Masuzawa

  • Affiliations:

  • Graduate School of Information Science and Technology, Osaka University;College of Information Science and Engineering, Ritsumeikan University;Graduate School of Information Science and Technology, Osaka University;Graduate School of Information Science and Technology, Osaka University;Graduate School of Information Science and Technology, Osaka University

  • Venue:
  • SIROCCO'10 Proceedings of the 17th international conference on Structural Information and Communication Complexity
  • Year:
  • 2010

Quantified Score

Hi-index 0.00

Visualization

Abstract

We investigate the relation between the time complexity and the space complexity for the rendezvous problem with k agents in asynchronous tree networks. The rendezvous problem requires that all the agents in the system have to meet at a single node within finite time. First, we consider asymptotically time-optimal algorithms and investigate the minimum memory requirement per agent for asymptotically time-optimal algorithms. We show that there exists a tree with n nodes in which Ω(n) bits of memory per agent is required to solve the rendezvous problem in O(n) time (asymptotically time-optimal). Then, we present an asymptotically time-optimal rendezvous algorithm. This algorithm can be executed if each agent has O(n) bits of memory. From this lower/upper bound, this algorithm is asymptotically space-optimal on the condition that the time complexity is asymptotically optimal. Finally, we consider asymptotically space-optimal algorithms while allowing slowdown in time required to achieve rendezvous. We present an asymptotically space-optimal algorithm that each agent uses only O(logn) bits of memory. This algorithm terminates in O(Δn8) time where Δ is the maximum degree of the tree.