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The upper envelope of piecewise linear functions: Tight bounds on the number of faces

Discrete & Computational Geometry (1989) 4(1) 337-343
DOI: 10.1007/BF02187734
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Abstract

This note proves that the maximum number of faces (of any dimension) of the upper envelope of a set of n possibly intersecting d-simplices in d+1 dimensions is Θ(ndα(n)). This is an extension of a result of Pach and Sharir [PS] who prove the same bound for the number of d-dimensional faces of the upper envelope. © 1989 Springer-Verlag New York Inc.

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APA

Edelsbrunner, H. (1989). The upper envelope of piecewise linear functions: Tight bounds on the number of faces. Discrete & Computational Geometry, 4(1), 337–343. https://doi.org/10.1007/BF02187734

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