Math @ Duke

Publications [#235569] of Pankaj K. Agarwal
Papers Published
 Agarwal, PK; Aronov, B, Counting facets and incidences,
Discrete & Computational Geometry, vol. 7 no. 1
(1992),
pp. 359369, ISSN 01795376 [doi]
(last updated on 2018/08/18)
Abstract: We show that m distinct cells in an arrangement of n planes in ℝ3 are bounded by O(m2/3n+n2) faces, which in turn yields a tight bound on the maximum number of facets bounding m cells in an arrangement of n hyperplanes in ℝd, for every d≥3. In addition, the method is extended to obtain tight bounds on the maximum number of faces on the boundary of all nonconvex cells in an arrangement of triangles in ℝ3. We also present a simpler proof of the O(m2/3nd/3+nd1) bound on the number of incidences between n hyperplanes in ℝd and m vertices of their arrangement. © 1992 SpringerVerlag New York Inc.


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