Abstract
In this paper we face the problem of computing a conservative approximation of a set of isothetic rectangles in the plane by means of a pair of enclosing isothetic rectangles. We propose an O(n log n) time algorithm for finding, given a set M of n isothetic rectangles, a pair of isothetic rectangles (s,t) such that s and t enclose all rectangles of M and area(s) + area(t) is minimal. Moreover we prove an O(n log n) lower bound for the one-dimensional version of the problem.
Work partially supported by grants no. Wi810/2-5 from the Deutsche Forschungsgemeinschaft, by the ESPRIT II Basic Research Actions Program of the European Community, Working Group “Basic GOODS”, and by the Italian PFI National Project “Obiettivo Multidata”.
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References
H. Alt, J. Blomer, M. Godau, and H. Wagener. Approximation of convex polygons. In Automata, Languages and Programming (Proc. of the 17th ICALP, Univ. of Warwick, England, July 1990), Lecture Notes in Computer Science 443, pages 703–716, 1990.
L. Guibas, J. Hershberger, and J. Snoeyink. Compact interval trees: A data structure for convex hulls. International Journal of Computational Geometry & Applications, 1:1–22, 1991.
J. O'Rourke, A. Aggarwal, S. Maddila, and M. Baldwin. An optimal algorithm for finding minimal enclosing triangles. Journal of the Algorithms, 7:258–269, 1986.
Th. Ottmann, E. Soisalon-Soininen, and D. Wood. On the definition and computation of rectilinear convex hulls. Information Sciences, 33:157–171, 1984.
F. P. Preparata and M. I. Shamos. Computational Geometry, an Introduction. Springer-Verlag, New York, 1985.
O. Schwarzkopf, U. Fuchs, G. Rote, and E. Welzl. Approximation of convex figures by pairs of rectangles. Report B 89-15, Freie Universitaet Berlin, Department of Mathematics, 1989.
S. Skyum. A simple algorithm for computing the smallest enclosing circle. Report DAIMI 314, Aarhus University, Computer Science Department, 1990.
R. B. Tilove. Set membership classification: A unified approach to geometric intersection problems. IEEE Trans. on Computers, pages 874–883, 1980.
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© 1991 Springer-Verlag Berlin Heidelberg
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Becker, B., Franciosa, P.G., Gschwind, S., Ohler, T., Thiem, G., Widmayer, P. (1991). An optimal algorithm for approximating a set of rectangles by two minimum area rectangles. In: Bieri, H., Noltemeier, H. (eds) Computational Geometry-Methods, Algorithms and Applications. CG 1991. Lecture Notes in Computer Science, vol 553. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-54891-2_2
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DOI: https://doi.org/10.1007/3-540-54891-2_2
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