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authors Sarnak, Neil and Tarjan, Robert E.
year 1986
title Planar Point Location Using Persistent Search Trees
source Communications of the ACM July, 1986. vol. 29: pp. 669-679 : ill. includes bibliography.
summary 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. The authors propose a simple O(log n) 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 stillÔ h)0*0*0*°° Ԍ be accessed. A persistent form of binary search tree that supports insertions and deletions in the present and queries in the past is developed. The time per query or update is O(log m), where m is the total number of updates, and the space needed is O(1) per update. The planar point location algorithm is an immediate application of this data structure. The structure also provides an alternative to Chazelle's 'hive graph' structure, which has a variety of applications in geometric retrieval
keywords search, data structures, algorithms, point inclusion, computational geometry
series CADline
references Content-type: text/plain
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