Algorithms for bivariate medians and a Fermat–Torricelli problem for lines

Computational Geometry - Tập 26 - Trang 69-79 - 2003
Greg Aloupis1, Stefan Langerman1, Michael Soss2, Godfried Toussaint1
1School of Computer Science, McGill University, 3480 University Street, rm. 318, Montreal, QC, H3A 2A7, Canada
2Chemical Computing Group, 1010 Sherbrooke St, Montreal, QC, H3A 2R7, Canada

Tài liệu tham khảo

G. Aloupis, On computing geometric estimators of location, M. Sc. Thesis, McGill University, 2001 Aloupis, 2002, Lower bounds for computing statistical depth, Computational Statistics and Data Analysis, 40, 223, 10.1016/S0167-9473(02)00032-4 G. Aloupis, M. Soss, G. Toussaint, On the computation of the bivariate median and a Fermat–Torricelli problem, Technical Report SOCS-01.2, School of Computer Science, McGill University, February 2001 Barbara, 2000, The Fermat–Torricelli points of n lines, Math. Gazette, 84, 24, 10.2307/3621470 Dalla, 2001, A note on the Fermat–Torricelli point of a d-simplex, J. Geom., 70, 38, 10.1007/PL00000991 P. de Fermat, Abhandlungen über maxima und minima, in: M. Miller (Ed.), Ostwalds Klassiker der exacten Wissenschaften, p. 238 Edelsbrunner, 1987 Edelsbrunner, 1989, Topologically sweeping an arrangement, J. Comput. System Sci., 38, 165, 10.1016/0022-0000(89)90038-X Gill, 1992, Geometric medians, Discrete Math., 108, 37, 10.1016/0012-365X(92)90658-3 Groß, 1998, On generalizations of conics and on a generalization of the Fermat–Torricelli problem, Amer. Math. Monthly, 105, 732, 10.2307/2588990 Khuller, 1989, On a triangle counting problem, Inform. Process. Lett., 33, 319, 10.1016/0020-0190(90)90217-L Kupitz, 1997, Geometric aspects of the generalized Fermat–Torricelli problem, Intuitive Geometry, Bolyai Society Math. Studies, 6, 55 Langerman, 2000, Computing a maximal depth point in the plane S. Langerman, W. Steiger, Optimization in arrangements, Technical Report SOCS-02.7, School of Computer Science, McGill University, 2002. To appear at the 20th International Symposium on Theoretical Aspects of Computer Science (STACS 2003) Lee, 1985, The power of geometric duality revisited, Inform. Process. Lett., 21, 117, 10.1016/0020-0190(85)90015-8 Liu, 1990, On a notion of data depth based upon random simplices, Ann. Statist., 18, 405, 10.1214/aos/1176347507 Liu, 1999, Multivariate analysis of data depth: descriptive statistics, graphics and inference, Ann. Statist., 27, 783, 10.1214/aos/1018031260 1919 Niinimaa, 1992, Algorithm AS 277: The Oja bivariate median, Appl. Statist., 41, 611, 10.2307/2348099 Niinimaa, 1990, The finite-sample breakdown point of the Oja bivariate median and of the corresponding half-samples version, Statist. Probab. Lett., 10, 325, 10.1016/0167-7152(90)90050-H Oja, 1983, Descriptive statistics for multivariate distributions, Statist. Probab. Lett., 1, 327, 10.1016/0167-7152(83)90054-8 Rousseeuw, 1996, Bivariate location depth, Appl. Statist., 45, 516, 10.2307/2986073 Small, 1990, A survey of multidimensional medians, Internat. Statist. Rev., 58, 263, 10.2307/1403809