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Asynchronous Filling by Myopic Luminous Robots

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Algorithms for Sensor Systems (ALGOSENSORS 2020)

Part of the book series: Lecture Notes in Computer Science ((LNCCN,volume 12503))

Abstract

We consider the problem of filling an unknown area represented by an arbitrary connected graph of n vertices by mobile luminous robots. In this problem, the robots enter the graph one-by-one through a specific vertex, called the Door, and they eventually have to cover all vertices of the graph while avoiding collisions. The robots are anonymous and make decisions driven by the same local rule of behavior. They have limited persistent memory and limited visibility range. We investigate the Filling problem in the asynchronous model.

We assume that the robots know an upper bound \(\varDelta \) on the maximum degree of the graph before entering. We present an algorithm solving the asynchronous Filling problem with robots having 1 hop visibility range, \(O(\log \varDelta )\) bits of persistent storage, and \(\varDelta +4\) colors, including the color when the light is off. We analyze the algorithm in terms of asynchronous rounds, where a round means the smallest time interval in which each robot, which has not yet finished the algorithm, has been activated at least once. We show that this algorithm needs \(O(n^2)\) asynchronous rounds. Our analysis provides the first asymptotic upper bound on the running time in terms of asynchronous rounds.

Then we show how the number of colors can be reduced to O(1) at the cost of the running time. The algorithm with 1 hop visibility range, \(O(\log \varDelta )\) bits of persistent memory, and O(1) colors needs \(O(n^2\log \varDelta )\) rounds. We show how the running time can be improved by robots with a visibility range of 2 hops, \(O(\log \varDelta )\) bits of persistent memory, and \(\varDelta + 4\) colors (including the color when the light is off). We show that the algorithm needs O(n) asynchronous rounds. Finally, we show how to extend our solution to the k-Door case, \(k\ge 2\), by using \(\varDelta + k + 4\) colors, including the color when the light is off.

The research has been partially supported by the European Union, co-financed by the European Social Fund (EFOP-3.6.3-VEKOP-16-2017-00002).

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Notes

  1. 1.

    In  [6] it is assumed that the robot sees all eight sourrounding cells and able to communicate with robots at that eight cells. Assuming orthogonal movements, a cell sharing only one corner with the current cell of the robot are reachable in two hops.

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Authors and Affiliations

  1. Department of Automation and Applied Informatics, Budapest University of Technology and Economics, Budapest, Hungary

    Attila Hideg

  2. Faculty of Informatics, Eötvös Loránd University, Budapest, Hungary

    Tamás Lukovszki

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  1. Attila Hideg
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  2. Tamás Lukovszki
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Correspondence to Tamás Lukovszki .

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Editors and Affiliations

  1. Mathematics and Computer Science, University of Perugia, Perugia, Italy

    Cristina M. Pinotti

  2. Mathematics and Computer Science, University of Perugia, Perugia, Italy

    Alfredo Navarra

  3. Computer Science and Engineering, Indian Institute of Technology Delhi, New Delhi, India

    Amitabha Bagchi

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Hideg, A., Lukovszki, T. (2020). Asynchronous Filling by Myopic Luminous Robots. In: Pinotti, C.M., Navarra, A., Bagchi, A. (eds) Algorithms for Sensor Systems. ALGOSENSORS 2020. Lecture Notes in Computer Science(), vol 12503. Springer, Cham. https://doi.org/10.1007/978-3-030-62401-9_8

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  • DOI: https://doi.org/10.1007/978-3-030-62401-9_8

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