Range Searching and Point Location among Fat Objects (1994)
| Venue: | Journal of Algorithms |
| Citations: | 8 - 0 self |
BibTeX
@ARTICLE{Overmars94rangesearching,
author = {Mark H. Overmars and A. Frank van der Stappen},
title = {Range Searching and Point Location among Fat Objects},
journal = {Journal of Algorithms},
year = {1994},
volume = {21},
pages = {629--656}
}
OpenURL
Abstract
We present a data structure that can store a set of disjoint fat objects in d-space such that point location and bounded-size range searching with arbitrarily-shaped ranges can be performed efficiently. The structure can deal with either arbitrary (fat) convex objects or non-convex polytopes. The multi-purpose data structure supports point location and range searching queries in time O(log d\Gamma1 n) and requires O(n log d\Gamma1 n) storage, after O(n log d\Gamma1 n log log n) preprocessing. The data structure and query algorithm are rather simple. 1 Introduction Fatness turns out to be an interesting phenomenon in computational geometry. Several papers present surprising combinatorial complexity reductions [3, 15, 22, 26, 32] and efficiency gains for algorithms [1, 4, 19, 28, 33] if the objects under consideration have a certain fatness. Fat objects are compact to some extent, rather than long and thin. Fatness is a realistic assumption, since in many practical instances of ...







