Exploring and Triangulating a Region by a Swarm of Robots

  • Sándor P. Fekete
  • Tom Kamphans
  • Alexander Kröller
  • Joseph S. B. Mitchell
  • Christiane Schmidt
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6845)

Abstract

We consider online and offline problems related to exploring and surveying a region by a swarm of robots with limited communication range. The minimum relay triangulation problem (MRTP) asks for placing a minimum number of robots, such that their communication graph is a triangulated cover of the region. The maximum area triangulation problem (MATP) aims at finding a placement of n robots such that their communication graph contains a root and forms a triangulated cover of a maximum possible amount of area. Both problems are geometric versions of natural graph optimization problems.

The offline version of both problems share a decision problem, which we prove to be NP-hard. For the online version of the MRTP, we give a lower bound of 6/5 for the competitive ratio, and a strategy that achieves a ratio of 3; for different offline versions, we describe polynomial-time approximation schemes. For the MATP we show that no competitive ratio exists for the online problem, and give polynomial-time approximation schemes for offline versions.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2011

Authors and Affiliations

  • Sándor P. Fekete
    • 1
  • Tom Kamphans
    • 1
  • Alexander Kröller
    • 1
  • Joseph S. B. Mitchell
    • 2
  • Christiane Schmidt
    • 1
  1. 1.Algorithms GroupBraunschweig Institute of TechnologyGermany
  2. 2.Department of Applied Mathematics and StatisticsStony Brook UniversityUSA

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