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Complete Visibility for Oblivious Robots in \(\mathcal{O}(N)\) Time

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Networked Systems (NETYS 2018)

Part of the book series: Lecture Notes in Computer Science ((LNCCN,volume 11028))

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Abstract

We consider the distributed setting of N autonomous mobile robots that operate in Look-Compute-Move cycles following the classic oblivious robots model. We study the fundamental problem where starting from an arbitrary initial configuration, N autonomous robots reposition themselves to a convex hull formation on the plane where each robot is visible to all others (the Complete Visibility problem). We assume obstructed visibility, where a robot cannot see another robot if a third robot is positioned between them on the straight line connecting them. We provide the first \(\mathcal{O}(N)\) time algorithm for this problem in the fully synchronous setting. Our contribution is a significant improvement over the runtime of the only previously known algorithm for this problem which has a lower bound of \(\varOmega (N^2)\) in the fully synchronous setting. The proposed algorithm is collision-free – robots do not share positions and their paths do not cross.

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Authors and Affiliations

  1. Department of Computer Science, Kent State University, Kent, OH, 44242, USA

    Gokarna Sharma

  2. School of Electrical Engineering and Computer Science, Louisiana State University, Baton Rouge, LA, 70803, USA

    Costas Busch & Supratik Mukhopadhyay

Authors
  1. Gokarna Sharma
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  2. Costas Busch
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  3. Supratik Mukhopadhyay
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Corresponding author

Correspondence to Gokarna Sharma .

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Editors and Affiliations

  1. Universität Freiburg, Freiburg, Germany

    Andreas Podelski

  2. University of Rennes 1, Rennes, France

    François Taïani

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Sharma, G., Busch, C., Mukhopadhyay, S. (2019). Complete Visibility for Oblivious Robots in \(\mathcal{O}(N)\) Time. In: Podelski, A., Taïani, F. (eds) Networked Systems. NETYS 2018. Lecture Notes in Computer Science(), vol 11028. Springer, Cham. https://doi.org/10.1007/978-3-030-05529-5_5

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  • DOI: https://doi.org/10.1007/978-3-030-05529-5_5

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-030-05528-8

  • Online ISBN: 978-3-030-05529-5

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