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Algorithmica

, Volume 74, Issue 1, pp 117–155 | Cite as

Convergecast and Broadcast by Power-Aware Mobile Agents

  • Julian Anaya
  • Jérémie Chalopin
  • Jurek Czyzowicz
  • Arnaud LabourelEmail author
  • Andrzej Pelc
  • Yann Vaxès
Article
First Online:

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 \(\epsilon >0\).

Keywords

Convergecast Broadcast Mobile agent Power-aware Centralized algorithm Distributed algorithm Competitive ratio Graph 
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Copyright information

© European Union 2014

Authors and Affiliations

  • Julian Anaya
    • 1
  • Jérémie Chalopin
    • 2
  • Jurek Czyzowicz
    • 1
  • Arnaud Labourel
    • 2
    Email author
  • Andrzej Pelc
    • 1
  • Yann Vaxès
    • 2
  1. 1.Université du Québec en OutaouaisGatineauCanada
  2. 2.LIFCNRS & Aix-Marseille UniversityMarseilleFrance

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