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Move-Optimal Partial Gathering of Mobile Agents in Asynchronous Trees

  • Masahiro Shibata
  • Fukuhito Ooshita
  • Hirotsugu Kakugawa
  • Toshimitsu Masuzawa
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8576)

Abstract

In this paper, we consider the partial gathering problem of mobile agents in asynchronous tree networks. The partial gathering problem is a new generalization of the total gathering problem, which requires that all the agents meet at the same node. The partial gathering problem requires, for given input g, that each agent should move to a node and terminate so that at least g agents should meet at the same node. The requirement for the partial gathering problem is weaker than that for the (well-investigated) total gathering problem, and thus, we clarify the difference on the move complexity between them. We assume that n is the number of nodes and k is the number of agents. We propose two algorithms to solve the partial gathering problem. First, we consider the strong multiplicity detection and non-token model. In this model, we show that agents require Ω(kn) total moves to solve the partial gathering problem and we propose an algorithm to achieve the partial gathering in O (kn) total moves. Second, we consider the weak multiplicity detection and removable-token model. In this model, we propose an algorithm to achieve the partial gathering in O (gn) total moves. It is known that the partial gathering problem requires Ω(gn) total moves. Hence, the second algorithm is asymptotically optimal in terms of total moves.

Keywords

distributed system mobile agent gathering problem partial gathering problem 

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Copyright information

© Springer International Publishing Switzerland 2014

Authors and Affiliations

  • Masahiro Shibata
    • 1
  • Fukuhito Ooshita
    • 1
  • Hirotsugu Kakugawa
    • 1
  • Toshimitsu Masuzawa
    • 1
  1. 1.Graduate School of Information Science and TechnologyOsaka UniversityJapan

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