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Planar Point Location Using Persistent Search Trees (1986)
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BibTeX
@MISC{Sarnak86planarpoint,
author = {Neil Sarnak and Robert E. Tarjan},
title = {Planar Point Location Using Persistent Search Trees},
year = {1986}
}
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Abstract
A classical problem in computational geometry is the planar point location problem. This problem calls for preprocessing a polygonal subdivision of the plane defined by n line segments so that, given a sequence of points, the polygon containing each point can be determined quickly on-line. Several ways of solving this problem in O(log n) query time and O(n) space are known, but they are all rather complicated. We propose a simple O(log f&query-time, O(n)-space solution, using persistent search trees. A persistent search tree differs from an ordinary search tree in that after an insertion or deletion, the old version of the tree can still be accessed. We develop a persistent form of binary search tree that supports insertions and deletions in the present and queries in the past. The time per query or update is
