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International Colloquium on Structural Information and Communication Complexity

SIROCCO 2014: Structural Information and Communication Complexity pp 327–342Cite as

Move-Optimal Partial Gathering of Mobile Agents in Asynchronous Trees

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Part of the book series: Lecture Notes in Computer Science ((LNTCS,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.

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Authors and Affiliations

  1. Graduate School of Information Science and Technology, Osaka University, Japan

    Masahiro Shibata, Fukuhito Ooshita, Hirotsugu Kakugawa & Toshimitsu Masuzawa

Authors
  1. Masahiro Shibata
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  2. Fukuhito Ooshita
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  3. Hirotsugu Kakugawa
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  4. Toshimitsu Masuzawa
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Editors and Affiliations

  1. School of Computer Science, Reykjavik University, Menntavegur 1, 101, Reykjavik, Iceland

    Magnús M. Halldórsson

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Shibata, M., Ooshita, F., Kakugawa, H., Masuzawa, T. (2014). Move-Optimal Partial Gathering of Mobile Agents in Asynchronous Trees. In: Halldórsson, M.M. (eds) Structural Information and Communication Complexity. SIROCCO 2014. Lecture Notes in Computer Science, vol 8576. Springer, Cham. https://doi.org/10.1007/978-3-319-09620-9_25

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  • DOI: https://doi.org/10.1007/978-3-319-09620-9_25

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-09619-3

  • Online ISBN: 978-3-319-09620-9

  • eBook Packages: Computer ScienceComputer Science (R0)

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