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FPTAS for barrier covering problem with equal touching circles in 2D

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Abstract

In this paper, we consider a problem of optimal covering a barrier in the form of a line segment with equal circles distributed in a plane by moving their centers onto the segment or the line containing a segment. We require the neighboring circles in the cover to touch each other. The objective is to minimize the total traveled by circles Euclidian distance. The complexity status of the problem is not known. We propose an \(O(\frac{t_{AP}(n)}{\varepsilon ^2})\)–time FPTAS for the problem, where n is the number of circles and \(t_{AP}(n)\) is the time complexity of solving an assignment problem which is at most \(O(n^3)\).

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Acknowledgements

The research of A. Erzin is supported by Russian Science Foundation, project 19-71-10012 (contribution: Sects. 3, 4). The research of N. Lagutkina is supported by the Russian Foundation for Basic Research, projects 19-47-540007 (contribution: Sects. 1, 2).

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Authors and Affiliations

  1. Sobolev Institute of Mathematics, Novosibirsk, Russia

    Adil Erzin

  2. Novosibirsk State University, Novosibirsk, Russia

    Natalya Lagutkina

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  1. Adil Erzin
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  2. Natalya Lagutkina
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Correspondence to Adil Erzin.

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Erzin, A., Lagutkina, N. FPTAS for barrier covering problem with equal touching circles in 2D. Optim Lett 15, 1397–1406 (2021). https://doi.org/10.1007/s11590-020-01650-8

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