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Convergecast and Broadcast by Power-Aware Mobile Agents

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Abstract

A set of identical, mobile agents is deployed in a weighted network. Each agent has a battery—a power source allowing it to move along network edges. An agent uses its battery proportionally to the distance traveled. We consider two tasks: convergecast, in which at the beginning, each agent has some initial piece of information, and information of all agents has to be collected by some agent; and broadcast in which information of one specified agent has to be made available to all other agents. In both tasks, the agents exchange the currently possessed information when they meet. The objective of this paper is to investigate what is the minimal value of power, initially available to all agents, so that convergecast or broadcast can be achieved. We study this question in the centralized and the distributed settings. In the centralized setting, there is a central monitor that schedules the moves of all agents. In the distributed setting every agent has to perform an algorithm being unaware of the network. In the centralized setting, we give a linear-time algorithm to compute the optimal battery power and the strategy using it, both for convergecast and for broadcast, when agents are on the line. We also show that finding the optimal battery power for convergecast or for broadcast is NP-hard for the class of trees. On the other hand, we give a polynomial algorithm that finds a 2-approximation for convergecast and a 4-approximation for broadcast, for arbitrary graphs.In the distributed setting, we give a 2-competitive algorithm for convergecast in trees and a 4-competitive algorithm for broadcast in trees. The competitive ratio of 2 is proved to be the best for the problem of convergecast, even if we only consider line networks. Indeed, we show that there is no (\(2-\epsilon \))-competitive algorithm for convergecast or for broadcast in the class of lines, for any \(\epsilon >0\).

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Authors and Affiliations

  1. Université du Québec en Outaouais, C.P. 1250, succ. Hull, Gatineau, J8X 3X7, QC, Canada

    Julian Anaya, Jurek Czyzowicz & Andrzej Pelc

  2. LIF, CNRS & Aix-Marseille University, 13288, Marseille, France

    Jérémie Chalopin, Arnaud Labourel & Yann Vaxès

Authors
  1. Julian Anaya
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  2. Jérémie Chalopin
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  3. Jurek Czyzowicz
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  4. Arnaud Labourel
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  5. Andrzej Pelc
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  6. Yann Vaxès
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Corresponding author

Correspondence to Arnaud Labourel.

Additional information

Jérémie Chalopin and Arnaud Labourel were partially supported by the ANR project MACARON (anr-13-js02-0002).

Andrzej Pelc was partially supported by NSERC discovery Grant and by the Research Chair in Distributed Computing at the Université du Québec en Outaouais.

A preliminary version of this paper appeared in Proc. 26th International Symposium of Distributed Computing (DISC 2012).

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Anaya, J., Chalopin, J., Czyzowicz, J. et al. Convergecast and Broadcast by Power-Aware Mobile Agents. Algorithmica 74, 117–155 (2016). https://doi.org/10.1007/s00453-014-9939-8

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  • DOI: https://doi.org/10.1007/s00453-014-9939-8

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