Minimum-Width Double-Strip and Parallelogram Annulus
In this paper, we study the problem of computing a minimum-width double-strip or parallelogram annulus that encloses a given set of n points in the plane. A double-strip is a closed region in the plane whose boundary consists of four parallel lines and a parallelogram annulus is a closed region between two edge-parallel parallelograms. We present several first algorithms for these problems. Among them are O(n^2) and O(n^3 log n)-time algorithms that compute a minimum-width double-strip and parallelogram annulus, respectively, when their orientations can be freely chosen.
geometric covering
parallelogram annulus
two-line center
double-strip
Theory of computation~Computational geometry
25:1-25:14
Regular Paper
https://arxiv.org/abs/1911.07504
Sang Won
Bae
Sang Won Bae
Division of Computer Science and Engineering, Kyonggi University, Suwon, Korea
https://orcid.org/0000-0002-8802-4247
Supported by Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education (2018R1D1A1B07042755).
10.4230/LIPIcs.ISAAC.2019.25
M. Abellanas, Ferran Hurtado, C. Icking, L. Ma, B. Palop, and P.A. Ramos. Best Fitting Rectangles. In Proc. Euro. Workshop Comput. Geom. (EuroCG 2003), 2003.
P. Agarwal and M. Sharir. Planar geometric location problems. Algorithimca, 11:185-195, 1994.
P.K. Agarwal and M. Sharir. Efficient randomized algorithms for some geometric optimization problems. Discrete Comput. Geom., 16:317-337, 1996.
P.K. Agarwal, M. Sharir, and S. Toledo. Applications of parametric searching in geometric optimization. J. Algo., 17:292-318, 1994.
Sang Won Bae. Computing a Minimum-Width Square Annulus in Arbitrary Orientation. Theoret. Comput. Sci., 718:2-13, 2018.
Sang Won Bae. On the Minimum-Area Rectangular and Square Annulus Problem. CoRR, 2019. URL: http://arxiv.org/abs/1904.06832.
http://arxiv.org/abs/1904.06832
Mark de Berg, Mark van Kreveld, Mark Overmars, and Otfried Schwarzkopf. Computationsl Geometry: Alogorithms and Applications. Springer-Verlag, 2nd edition, 2000.
Alex Glozman, Klara Kedem, and Gregory Shpitalnik. On some geometric selection and optimization problems via sorted matrices. Comput. Geom.: Theory Appl., 11(1):17-28, 1998.
Olga N. Gluchshenko, Horst W. Hamacher, and Arie Tamir. An optimal O(n log n) algorithm for finding an enclosing planar rectilinear annulus of minimum width. Operations Research Lett., 37(3):168-170, 2009.
J. Hershberger. Finding the upper envelope of n line segments in O(nlog n) time. Inform. Proc. Lett., 33:169-174, 1989.
Jerzy Jaromczyk and Miroslaw Kowaluk. The Two-Line Center Problem from a Polar View: A New Algorithm and Data Structure. In Proc. 4th Int. Workshop Algo. Data Struct. (WADS 1995), volume 955 of Lecture Notes Comput. Sci., pages 13-25, 1995.
J. Mukherjee, P.R.S. Mahapatra, A. Karmakar, and S. Das. Minimum-width rectangular annulus. Theoretical Comput. Sci., 508:74-80, 2013.
U. Roy and X. Zhang. Establishment of a pair of concentric circles with the minimum radial separation for assessing roundness error. Computer-Aided Design, 24(3):161-168, 1992.
G.T. Toussaint. Solving geometric problems with the rotating calipers. In Proc. IEEE MELECON, 1983.
Sang Won Bae
Creative Commons Attribution 3.0 Unported license
https://creativecommons.org/licenses/by/3.0/legalcode