Optimal Deterministic Algorithms for 2-d and 3-d Shallow Cuttings

We present optimal deterministic algorithms for constructing shallow cuttings in an arrangement of lines in two dimensions or planes in three dimensions. Our results improve the deterministic polynomial-time algorithm of Matoušek (Comput Geom 2(3):169–186, 1992 ) and the optimal but randomized algor...

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Bibliographic Details
Published in:	Discrete & computational geometry Vol. 56; no. 4; pp. 866 - 881
Main Authors:	Chan, Timothy M., Tsakalidis, Konstantinos
Format:	Journal Article
Language:	English
Published:	New York Springer US 01.12.2016 Springer Nature B.V
Subjects:	Algorithms Chips Combinatorics Computational geometry Computational Mathematics and Numerical Analysis Convexity Hulls Linear programming Mathematics Mathematics and Statistics Optimization Peeling Planes Searching Halfspace range reporting Shallow cuttings Derandomization Geometric data structures
ISSN:	0179-5376, 1432-0444
Online Access:	Get full text
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