Almost tight upper bounds for vertical decompositions in four dimensions.

We show that the complexity of the vertical decomposition of an arrangement of n fixed-degree algebraic surfaces or surface patches in four dimensions is O(n4+ϵ), for any ϵ > 0. This improves the best previously known upper bound for this problem by a near-linear factor, and s...

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Bibliographic Details

Published in:	Journal of the ACM 51, 5 (2004).
Main Author:	Koltun, Vladlen
Format:	Article
Language:	English
Subjects:	Mathematics of computing. Discrete mathematics. Combinatorics. Combinatorial algorithms. Counting problems. Computing methodologies. Computer graphics. Computational geometry and object modeling. Geometric algorithms, languages and systems. Algorithms. Theory.