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Collective Tree Exploration

  • Pierre Fraigniaud
  • Leszek Gasieniec
  • Dariusz R. Kowalski
  • Andrzej Pelc
Part of the Lecture Notes in Computer Science book series (LNCS, volume 2976)

Abstract

An n-node tree has to be explored by k mobile agents (robots), starting in its root. Every edge of the tree must be traversed by at least one robot, and exploration must be completed as fast as possible. Even when the tree is known in advance, scheduling optimal collective exploration turns out to be NP-hard. We investigate the problem of distributed collective exploration of unknown trees. Not surprisingly, communication between robots influences the time of exploration. Our main communication scenario is the following: robots can communicate by writing at the currently visited node previously acquired information, and reading information available at this node. We construct an exploration algorithm whose running time for any tree is only O(k/log k) larger than optimal exploration time with full knowledge of the tree. (We say that the algorithm has overheadO(k/log k)). On the other hand we show that, in order to get overhead sublinear in the number of robots, some communication is necessary. Indeed, we prove that if robots cannot communicate at all, then every distributed exploration algorithm works in time Ω (k) larger than optimal exploration time with full knowledge, for some trees.

Keywords

Mobile Agent Competitive Ratio Port Number Unknown Environment Communication Scenario 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2004

Authors and Affiliations

  • Pierre Fraigniaud
    • 1
  • Leszek Gasieniec
    • 2
  • Dariusz R. Kowalski
    • 3
    • 4
  • Andrzej Pelc
    • 5
  1. 1.CNRS-LRI, Université Paris-SudOrsayFrance
  2. 2.Department of Computer ScienceThe University of LiverpoolLiverpoolUK
  3. 3.Max-Planck-Institut für InformatikSaarbrückenGermany
  4. 4.Instytut InformatykiUniwersytet WarszawskiWarszawaPoland
  5. 5.Département d’informatiqueUniversité du Québec en OutaouaisHullCanada

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