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International Symposium on Distributed Computing

DISC 2016: Distributed Computing pp 85–98Cite as

Asynchronous Embedded Pattern Formation Without Orientation

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Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 9888))

Abstract

We consider the Embedded Pattern Formation (epf) problem introduced in [Fujinaga et al., SIAM J. on Comput., 44(3), 2015]. Given a set F of distinct points in the Euclidean plane (called here fixed-points) and a set R of robots such that \(|R|=|F|\), the problem asks for a distributed algorithm that moves robots so as to occupy all points in F. Initially, each robot occupies a distinct position.

Robots operate in standard Look-Compute-Move cycles. In one cycle, a robot perceives the current configuration in terms of the robots’ positions and the fixed-points (Look) according to its own coordinate system, decides whether to move (Compute), and in the positive case it moves (Move). Cycles are performed asynchronously for each robot. Robots are oblivious, anonymous and execute the same algorithm.

In the mentioned paper, the problem has been investigated by assuming chirality, that is robots share a common left-right orientation. The obtained solution has been used as a sub-procedure to solve the Pattern Formation problem, without fixed-points but still with chirality.

Here we investigate the other branch, that is, we are interested in solving epf without chirality. We fully characterize when the epf problem can be accomplished and we design a deterministic distributed algorithm that solves the problem for all configurations but those identified as unsolvable. Our approach is also characterized by the use of logical predicates in order to formally describe our algorithm as well as its correctness.

The work has been partially supported by the European project “Geospatial based Environment for Optimisation Systems Addressing Fire Emergencies” (GEO-SAFE), contract no. H2020-691161 and by the Italian projects: PRIN 2012C4E3KT “AMANDA – Algorithmics for MAssive and Networked DAta”; “RISE: un nuovo framework distribuito per data collection, monitoraggio e comunicazioni in contesti di emergency response”, Fondazione Cassa Risparmio Perugia, code 2016.0104.021.

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Notes

  1. 1.

    The existence of such robots is guaranteed by the fact that the initial configuration was solvable, and hence by Lemma 3 there were no axes with only fixed-points. Moreover, the moves performed from the initial configuration until the current step guarantee to not create such kind of axes.

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Authors and Affiliations

  1. Dipartimento di Ingegneria e Scienze dell’Informazione e Matematica, Università degli Studi dell’Aquila, Via Vetoio, Coppito, 67100, L’aquila, Italy

    Serafino Cicerone & Gabriele Di Stefano

  2. Dipartimento di Matematica e Informatica, Università degli Studi di Perugia, Via Vanvitelli 1, 06123, 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. LABRI, Univ of Bordeaux LABRI, Talence Cedex, France

    Cyril Gavoille

  2. CNRS, Universite Bordeaux 1 CNRS, Talence Cedex, France

    David Ilcinkas

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© 2016 Springer-Verlag Berlin Heidelberg

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Cicerone, S., Di Stefano, G., Navarra, A. (2016). Asynchronous Embedded Pattern Formation Without Orientation. In: Gavoille, C., Ilcinkas, D. (eds) Distributed Computing. DISC 2016. Lecture Notes in Computer Science(), vol 9888. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-53426-7_7

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  • DOI: https://doi.org/10.1007/978-3-662-53426-7_7

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-662-53425-0

  • Online ISBN: 978-3-662-53426-7

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