Abstract
We describe the “cobweb” partition scheme and show that it can split any planar set into eight regions of equal area.
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M. Adams and V. Guillemin.Measure Theory and Probability, Wadsworth, Monterey, CA, 1986.
B. Aronov, P. Erdös, W. Goddard, D. J. Kleitman, M. Klugerman, J. Pach, and L. J. Schulman. Crossing families. InProc. Seventh ACM Symp. on Computational Geometry, pp. 351–356, 1991.
R. C. Buck and E. F. Buck. Equartition of convex sets.Math. Mag., 22:195–198, 1987.
R. Courant and H. Robbins.What is Mathematics, pp. 317–319. Oxford University Press, Oxford, 1941.
H. Edelsbrunner and F. Huber. Dissecting Sets of Points in Two and Three Dimensions. Technical Report F138, Technische Universitat Graz, 1984.
J. Matoušek. Efficient partition trees. InProc. Seventh ACM Symp. on Computational Geometry, pp. 1–9, 1991.
J. R. Munkres.Topology: A First Course. Prentice-Hall, Englewood Cliffs, NJ, 1975.
W. Rudin.Principles of Mathematical Analysis, 3rd edn. McGraw-Hill, New York, 1976.
R. M. Switzer.Algebraic Topology—Homotopy and Homology. Springer-Verlag, Berlin, 1975.
D. E. Willard. Polygon retrieval.SIAM J. Comput., 11(1):149–165, February 1982.
A. C. Yao and F. F. Yao. A general approach tod-dimensional geometric queries. InProc. 17th Symp. on Theory of Computing, pp. 163–169, 1985.
F. F. Yao. Computational geometry. In J. van Leeuwen, ed.,Handbook of Theoretical Computer Science, Volume A, Chapter 7. Elsevier, Amsterdam, 1990.
F. F. Yao, D. P. Dobkin, H. Edelsbrunner, and M. S. Paterson. Partitioning space for range queries.SIAM J. Comput., 18(2):371–384, April 1989.
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This research was supported by an ONR graduate fellowship.
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Schulman, L.J. An equipartition of planar sets. Discrete Comput Geom 9, 257–266 (1993). https://doi.org/10.1007/BF02189322
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DOI: https://doi.org/10.1007/BF02189322