Selecting Vertices in Arrangements of Hyperplanes

Report
Author:Salowe, Jeffrey, Department of Computer ScienceUniversity of Virginia
Abstract:

Given any arrangement of n hyperplanes in Rd. there are O(n‘l vertices. This paper shows that the time complexity of selecting the vertex with k‘" smallest z_1-coordinate in such an arrangement is O(nd‘1log3" n), which is sublinear in the number of vertices. This extends the result of from 2 - dimensions to d-dimensions.
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Rights:
All rights reserved (no additional license for public reuse)
Language:
English
Source Citation:

Salowe, Jeffrey. "Selecting Vertices in Arrangements of Hyperplanes." University of Virginia Dept. of Computer Science Tech Report (1987).

Publisher:
University of Virginia, Department of Computer Science
Published Date:
1987