Points and triangles in the plane and halving planes in space

B. Aronov, B. Chazelle, H. Edelsbrunner, L. Guibas, M. Sharir, R. Wenger, in:, ACM, 1990, pp. 112–115.

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Abstract
We prove that for any set S of n points in the plane and n3-α triangles spanned by the points of S there exists a point (not necessarily of S) contained in at least n3-3α/(512 log25 n) of the triangles. This implies that any set of n points in three - dimensional space defines at most 6.4n8/3 log5/3 n halving planes.
Publishing Year
Date Published
1990-01-01
Page
112 - 115
Conference
SCG: Symposium on Computational Geometry
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Aronov B, Chazelle B, Edelsbrunner H, Guibas L, Sharir M, Wenger R. Points and triangles in the plane and halving planes in space. In: ACM; 1990:112-115. doi:10.1145/98524.98548
Aronov, B., Chazelle, B., Edelsbrunner, H., Guibas, L., Sharir, M., & Wenger, R. (1990). Points and triangles in the plane and halving planes in space (pp. 112–115). Presented at the SCG: Symposium on Computational Geometry, ACM. https://doi.org/10.1145/98524.98548
Aronov, Boris, Bernard Chazelle, Herbert Edelsbrunner, Leonidas Guibas, Micha Sharir, and Rephael Wenger. “Points and Triangles in the Plane and Halving Planes in Space,” 112–15. ACM, 1990. https://doi.org/10.1145/98524.98548.
B. Aronov, B. Chazelle, H. Edelsbrunner, L. Guibas, M. Sharir, and R. Wenger, “Points and triangles in the plane and halving planes in space,” presented at the SCG: Symposium on Computational Geometry, 1990, pp. 112–115.
Aronov B, Chazelle B, Edelsbrunner H, Guibas L, Sharir M, Wenger R. 1990. Points and triangles in the plane and halving planes in space. SCG: Symposium on Computational Geometry 112–115.
Aronov, Boris, et al. Points and Triangles in the Plane and Halving Planes in Space. ACM, 1990, pp. 112–15, doi:10.1145/98524.98548.

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