On levels in arrangements of lines, segments, planes, and triangles
Published
Journal Article
We consider the problem of bounding the complexity of the kth level in an arrangement of n curves or surfaces, a problem dual to, and an extension of, the well-known k-set problem. Among other results, we prove a new bound, O(nk5/3), on the complexity of the kth level in an arrangement of n planes in ℝ3, or on the number of k-sets in a set of n points in three dimensions, and we show that the complexity of the kth level in an arrangement of n line segments in the plane is O(n-√kα(n/k)), and that the complexity of the kth level in an arrangement of n triangles in 3-space is O(n2k5/6α(n/k)).
Full Text
Duke Authors
Cited Authors
- Agarwal, PK; Aronov, B; Chan, TM; Sharir, M
Published Date
- January 1, 1998
Published In
Volume / Issue
- 19 / 3
Start / End Page
- 315 - 331
International Standard Serial Number (ISSN)
- 0179-5376
Digital Object Identifier (DOI)
- 10.1007/PL00009348
Citation Source
- Scopus