This is a preview of subscription content, log in via an institution to check access.
Preview
Unable to display preview. Download preview PDF.
References
N. N. Doroshko, The solution of two mainline problems in the plane. Manuscript Deposited in VINITI USSR (14.06.1984), Reg. no. 39614 (1984), 15 pp.
N. N. Doroshko, N. M. Korneenko, N. N. Metel'skij, Optimizing line location with respect to a planar point system. Preprint Inst. Math. Acad. Sci. BSSR, Minsk, USSR, no. 23 (1984), 19 pp.
N. N. Doroshko, N. M. Korneenko, N. N. Metel'skij, Mainline problems in the plane. Doklady AN BSSR 29 (1985), 872–873.
B. Chazelle, L. Guibas, D. T. Lee, The power of geometric duality. Proc. 24th Ann. IEEE Symp. Found. Computer Sci., 217–225 (1983), also in BIT 25 (1985), 76–90.
H. Edelsbrunner, J. O'Rourke, R. Seidel, Constructing arrangements of lines and hyperplanes with applications. Proc. 24th Ann. IEEE Symp. Found. Computer Sci., 83–91, also in SIAM J. Comput. 15 (1986), 341–363.
H. Edelsbrunner, L. Guibas, Topologically sweeping the arrangement. Proc. 18th ACM Symp. Theory of Computing, 389–403 (1986).
H. Edelsbrunner, E. Mücke, Simulation of simplicity: A technique to cope with degenerate cases in geometric algorithms. Proc. 4th ACM SYmp. Computational Geometry, Baltimore, USA, 118–133 (1987).
H. Edelsbrunner, Algorithms in Combinatorial Geometry. Springer-Verlag, New York, 1987.
N. M. Korneenko, Optimal straight lines for planar point sets. 33rd Internat. Wiss. Koll. TH Ilmenau, DDR, Posterbeitr. sekt. C1, 15–18 (1988).
N. M. Korneenko, Optimal lines in the plane: a survey. In: Geobild '89, Proc. 4th Workshop Geom. Problems of Image Processing, Georgenthal, DDR, 43–52, Akademie-Verlag, Berlin, 1989.
N. M. Korneenko, H. Martini, Least-distances lines and flats and related topics. Submitted.
D. T. Lee, Y. T. Ching, The power of geometric duality revisited. Inform Process. Lett. 21 (1985), 117–122.
H. Martini, Some results and problems around zonotopes. Coll. Math. Soc. J. Bolyai 48 (Intuitive Geometry, Siofok 1985), 383–418. Eds. K. Böröczky and G. Fejes Toth, North-Holland, 1987.
R. D. McBridge, J. S. Yormark, An implicit enumeration algorithm for quadratic integer programming. Management Sci. 26 (1980), 282–296.
P. McMullen, On zonotopes. Trans. Amer. Math. Soc. 159 (1971), 91–110.
N. Megiddo, A. Tamir, On the Complexity of locating linear facilities in the plane. Operations Research Lett. 1 (1982), 5, 194–197.
N. Megiddo, A. Tamir, Finding least-distance lines. SIAM J. Algebr. Discrete Meth. 4 (1983), 207–211.
J. G. Morris, J. P. Norback, A simple approach to linear facilities location. Transp. Sci. 14 (1980), 1–8.
J. P. Norback, J. G. Morris, Fitting hyperplanes by minimizing orthogonal deviations. Math. Progr. 19 (1980), 102–105.
E. M. Reingold, J. Nievergelt, N. Deo, Combinatorial Algorithms: Theory and Practice. Prentice-Hall, Englewood Cliffs, NJ, 1977.
R. Schneider, W. Weil, Zonoids and related topics. Convexity and Its Applications, Eds. P. Gruber and J. M. Wills, Birkhäuser, Basel 1983, 296–317.
G. Wesolowski, Location of the median line for weighted points. Environ. Planning A 7 (1975), 163–170.
P. Yammamoto, K. Kato, K. Imai, H. Imai, Algorithms for vertical and orthogonal L1 approximation of points. Proc. 4th ACM Symp. Computational Geometry, 1988, 352–361.
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 1990 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Korneenko, N.M., Martini, H. (1990). Approximating finite weighted point sets by hyperplanes. In: Gilbert, J.R., Karlsson, R. (eds) SWAT 90. SWAT 1990. Lecture Notes in Computer Science, vol 447. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-52846-6_96
Download citation
DOI: https://doi.org/10.1007/3-540-52846-6_96
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-52846-3
Online ISBN: 978-3-540-47164-6
eBook Packages: Springer Book Archive