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Minimum-Traveled-Distance Gathering of Oblivious Robots over Given Meeting Points

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Algorithms for Sensor Systems (ALGOSENSORS 2014)

Part of the book series: Lecture Notes in Computer Science ((LNCCN,volume 8847))

Abstract

The paper considers a new variant of the gathering problem of oblivious and asynchronous robots moving in the plane. Robots operate in standard Look-Compute-Move cycles. In one cycle, a robot perceives the current configuration in terms of robots distribution (Look), decides whether to move toward some direction (Compute), and in the positive case it moves (Move). Cycles are performed asynchronously for each robot. Robots are anonymous and execute the same distributed algorithm that must guarantee to move all robots to meet at some point among a predetermined set. During the Look phase robots perceive not only the relative positions of the other robots, but also the relative positions of a set of points referred to as meeting points where gathering must be finalized.

We are interested in designing a gathering algorithm that solves the problem by also minimizing the total distances covered by all robots. We characterize when this gathering problem can be optimally solved, and we provide a new distributed algorithm along with its correctness.

Work partially supported by the Italian Ministry of Education, University, and Research (MIUR) under national research projects: PRIN 2012C4E3KT “AMANDA – Algorithmics for MAssive and Networked DAta" and PRIN 2010N5K7EB “ARS TechnoMedia – Algoritmica per le Reti Sociali Tecno- mediate”.

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Notes

  1. 1.

    If points \(r\in U(R)\) and \(f\in F\), different from \(p\), are coincident, then points \(r,f\) will appear in this order in \(V^+(p)\).

  2. 2.

    Configurations in class \(\mathcal {S}_4\), that is all robots and all Weber points are collinear, have been already addressed.

  3. 3.

    As a consequence, there is a number odd of robots.

  4. 4.

    By Lemma 3, there cannot be more than two Weber points.

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Author information

Authors and Affiliations

  1. Dipartimento di Ingegneria e Scienze dell’Informazione e Matematica, Università degli Studi dell’Aquila, L’Aquila, Italy

    Serafino Cicerone & Gabriele Di Stefano

  2. Dipartimento di Matematica e Informatica, Università degli Studi di Perugia, Perugia, Italy

    Alfredo Navarra

Authors
  1. Serafino Cicerone
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  2. Gabriele Di Stefano
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  3. Alfredo Navarra
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Corresponding author

Correspondence to Alfredo Navarra .

Editor information

Editors and Affiliations

  1. Stony Brook University, Stonybrook, New York, USA

    Jie Gao

  2. University of Arizona, Tucson, Arizona, USA

    Alon Efrat

  3. TU Braunschweig, Braunschweig, Niedersachsen, Germany

    Sándor P. Fekete

  4. Rutgers University, New Brunswick, New Jersey, USA

    Yanyong Zhang

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Cicerone, S., Di Stefano, G., Navarra, A. (2015). Minimum-Traveled-Distance Gathering of Oblivious Robots over Given Meeting Points. In: Gao, J., Efrat, A., Fekete, S., Zhang, Y. (eds) Algorithms for Sensor Systems. ALGOSENSORS 2014. Lecture Notes in Computer Science(), vol 8847. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-46018-4_4

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  • DOI: https://doi.org/10.1007/978-3-662-46018-4_4

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  • Print ISBN: 978-3-662-46017-7

  • Online ISBN: 978-3-662-46018-4

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