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Filling Arbitrary Connected Areas by Silent Robots with Minimum Visibility Range

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Algorithms for Sensor Systems (ALGOSENSORS 2018)

Abstract

We study the uniform dispersal problem (also called the filling problem) in arbitrary connected areas. In the filling problem robots are injected one-by-one at \(k \ge 1\) Doors into an unknown area, subdivided into cells. The goal is to cover the area, i.e. each cell must be occupied by a robot. The robots are homogeneous, anonymous, autonomous, have limited visibility radius, limited persistent memory, and silent, i.e. do not use explicit communication. A fundamental question is how ‘weak’ those robots can be in terms of hardware requirements and still be able to solve the problem, which was initiated by Barrameda et al. [4]. In our previous paper [11] we presented an algorithm which solves the filling problem for orthogonal areas with O(1) bits of persistent memory, 1 hop visibility range and without explicit communication. The algorithm utilized the timing of movements and had O(n) runtime, where n is the number of cells in the area. In this paper, we generalize the problem for silent robots for an arbitrary connected area represented by a graph, while maintaining the 1 hop visibility range. The algorithm is collision-free, it terminates in \(O(k \cdot \varDelta \cdot n)\) rounds, and requires \(O(\varDelta \cdot \log k)\) bits of persistent memory, where \(\varDelta \) is the maximum degree of the graph.

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Acknowledgment

This work was partly performed in the frame of FIEK_16-1-2016-0007 project, implemented with the support provided from the National Research, Development and Innovation Fund of Hungary, financed under the FIEK_16 funding scheme.

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Correspondence to Attila Hideg .

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Hideg, A., Lukovszki, T., Forstner, B. (2019). Filling Arbitrary Connected Areas by Silent Robots with Minimum Visibility Range. In: Gilbert, S., Hughes, D., Krishnamachari, B. (eds) Algorithms for Sensor Systems. ALGOSENSORS 2018. Lecture Notes in Computer Science(), vol 11410. Springer, Cham. https://doi.org/10.1007/978-3-030-14094-6_13

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  • DOI: https://doi.org/10.1007/978-3-030-14094-6_13

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  • Publisher Name: Springer, Cham

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  • Online ISBN: 978-3-030-14094-6

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