Abstract
A square or rectangular annulus is the closed region between a square or rectangle and its offset. In this paper, we address the problem of computing a minimum-width square or rectangular annulus that contains at least \(n-k\) points out of n given points in the plane. The k excluded points are considered as outliers of the n input points. We present several first algorithms to the problem.
This research was supported by Basic Science Research Program through the National Research Foundation of Koresa (NRF) funded by the Ministry of Education (2015R1D1A1A01057220).
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Abellanas, M., Hurtado, F., Icking, C., Ma, L., Palop, B., Ramos, P.: Best fitting rectangles. In: Proceedings of the European Workshop on Computational Geometry (EuroCG 2003) (2003)
Aggarwal, A., Imai, H., Katoh, N., Suri, S.: Finding \(k\) points with minimum diameter and related problems. J. Algorithms 12, 38–56 (1991)
Ahn, H.K., Bae, S.W., Demaine, E.D., Demaine, M.L., Kim, S.S., Korman, M., Reinbacher, I., Son, W.: Covering points by disjoint boxes with outliers. Comput. Geom. Theor. Appl. 44(3), 178–190 (2011)
Atanassov, R., Bose, P., Couture, M., Maheshwari, A., Morin, P., Paquette, M., Smid, M., Wuhrer, S.: Algorithms for optimal outlier removal. J. Discrete Alg. 7(2), 239–248 (2009)
Bae, S.W.: Computing a minimum-width square annulus in arbitrary orientation [extended abstract]. In: Proceedings of the 10th International Workshop on Algorithms and Computation (WALCOM 2016), vol. 9627, pp. 131–142 (2016)
de Berg, M., van Kreveld, M., Overmars, M., Schwarzkopf, O.: Computationsl Geometry: Alogorithms and Applications, 2nd edn. Springer, Heidelberg (2000)
Chan, T.M.: Geometric applications of a randomized optimization technique. Discrete Comput. Geom. 22(4), 547–567 (1999)
Chan, T.M.: Remarks on \(k\)-level algorithms in the plane (1999). Manuscript
Dey, T.K.: Improved bounds on planar \(k\)-sets and related problems. Discrete Comput. Geom. 19, 373–382 (1998)
Everett, H., Robert, J.M., van Kreveld, M.: An optimal algorithm for computing \((\le k)\)-levels, with applications. Int. J. Comput. Geom. Appl. 6(3), 247–261 (1996)
Gluchshenko, O.N., Hamacher, H.W., Tamir, A.: An optimal \(O(n \log n)\) algorithm for finding an enclosing planar rectilinear annulus of minimum width. Oper. Res. Lett. 37(3), 168–170 (2009)
Hershberger, J.: Finding the upper envelope of \(n\) line segments in \(O(n\log n)\) time. Inform. Proc. Lett. 33, 169–174 (1989)
Matoušek, J.: On geometric optimization with few violated constraints. Discrete Comput. Geom. 14, 365–384 (1995)
Mukherjee, J., Mahapatra, P., Karmakar, A., Das, S.: Minimum-width rectangular annulus. Theor. Comput. Sci. 508, 74–80 (2013)
Segal, M., Kedem, K.: Enclosing \(k\) points in the smallest axis parallel rectangle. Inform. Process. Lett. 65, 95–99 (1998)
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Bae, S.W. (2016). Computing a Minimum-Width Square or Rectangular Annulus with Outliers. In: Dinh, T., Thai, M. (eds) Computing and Combinatorics . COCOON 2016. Lecture Notes in Computer Science(), vol 9797. Springer, Cham. https://doi.org/10.1007/978-3-319-42634-1_36
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DOI: https://doi.org/10.1007/978-3-319-42634-1_36
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