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Optimal search in planar subdivisions (1983)
| Venue: | SIAM JOURNAL OF COMPUTING, VOLTUNE |
| Citations: | 273 - 3 self |
BibTeX
@ARTICLE{Kirkpatrick83optimalsearch,
author = {David Kirkpatrick},
title = {Optimal search in planar subdivisions},
journal = {SIAM JOURNAL OF COMPUTING, VOLTUNE},
year = {1983},
volume = {12},
number = {1},
pages = {28--35}
}
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Abstract
A planar subdivision is any partition of the plane into (possibly unbounded) polygonal regions. The subdivision search problem is the following: given a subdivision S with n line segments and a query point P, determine which region of S contains P. We present a practical algorithm for subdivision search that achieves the same (optimal) worst case complexity bounds as the significantly more complex algorithm of Lipton and Tarjan, namely O (log n) search time with O (n) storage. Our subdivision search structure can be constructed in linear time from the subdivision representation used in many applications.
Keyphrases
planar subdivision optimal search computational geometry line segment polygonal region subdivision representation point location many application complex algorithm linear time subdivision search structure subdivision search practical algorithm planar graph case complexity hierarchical search key word search time query point subdivision search problem
