Abstract
An annulus is, informally, a ring-shaped region, often described by two concentric circles. The maximum-width empty annulus problem asks to find an annulus of a certain shape with the maximum possible width that avoids a given set of n points in the plane. This problem can also be interpreted as the problem of finding an optimal location of a ring-shaped obnoxious facility among the input points. In this paper, we study square and rectangular variants of the maximum-width empty anuulus problem, and present first nontrivial algorithms. Specifically, our algorithms run in \(O(n^3)\) and \(O(n^2 \log n)\) time for computing a maximum-width empty axis-parallel square and rectangular annulus, respectively. Both algorithms use only O(n) space.
S.W. Bae was supported by Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education (2018R1D1A1B07042755). P.R.S. Mahapatra was supported by Research Project through Department of Atomic Energy (NBHM), Government of India with Ref. No. 2/48(19)/2014/R&D-II/1045.
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Bae, S.W., Baral, A., Sinha Mahapatra, P.R. (2019). Maximum-Width Empty Square and Rectangular Annulus. In: Das, G., Mandal, P., Mukhopadhyaya, K., Nakano, Si. (eds) WALCOM: Algorithms and Computation. WALCOM 2019. Lecture Notes in Computer Science(), vol 11355. Springer, Cham. https://doi.org/10.1007/978-3-030-10564-8_6
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