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New results on dynamic planar point location

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2 Author(s)
Siu-Wing Cheng ; Dept. of Comput. Sci., Minnesota Univ., Minneapolis, MN, USA ; Janardan, R.

A point location scheme is presented for an n-vertex dynamic planar subdivision whose underlying graph is only required to be connected. The scheme uses O(n) space and yields an O(log2n) query time and an O(log n) update time. Insertion [respectively, deletion] of an arbitrary k-edge chain inside a region can be performed in O( k log(n+k)) [respectively, O(k log n)] time. The scheme is then extended to speed up the insertion/deletion of a k-edge monotone chain to O(log 2n log log n+k) time [or O(log n log log n+k) time for an alternative model of input], but at the expense of increasing the other time bounds slightly. All bounds are worst case. Additional results include a generalization to planar subdivisions consisting of algebraic segments of bounded degree and a persistent scheme for planar point location

Published in:

Foundations of Computer Science, 1990. Proceedings., 31st Annual Symposium on

Date of Conference:

22-24 Oct 1990