Linear time and space gathering of anonymous 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, 1-5 Yamadaoka, Suita, Osaka 565-0871, Japan;College of Information Science and Engineering, Ritsumeikan University, 1-1-1 Noji higashi, Kusatsu, Shiga 525-8577, Japan;Graduate School of Information Science and Technology, Osaka University, 1-5 Yamadaoka, Suita, Osaka 565-0871, Japan;Graduate School of Information Science and Technology, Osaka University, 1-5 Yamadaoka, Suita, Osaka 565-0871, Japan;Graduate School of Information Science and Technology, Osaka University, 1-5 Yamadaoka, Suita, Osaka 565-0871, Japan

  • Venue:
  • Theoretical Computer Science
  • Year:
  • 2013

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Abstract

We investigate the relation between the (ideal) time and space complexities for the gathering problem with k anonymous agents in asynchronous anonymous tree networks. The gathering problem requires that all the agents in the network have to meet at a single node within a finite time. Although an asymptotically space-optimal algorithm is known, its time complexity is quite large. In this paper, we consider asymptotically (ideal-)time-optimal algorithms and investigate the minimum memory requirement per agent for asymptotically time-optimal algorithms. First, we show that there exists a tree with n nodes in which @W(n) bits of memory per agent is required to solve the gathering problem in O(n) time (asymptotically time-optimal). Then, we present an asymptotically time-optimal gathering 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.