Methods for Achieving Fast Query Times in Point Location Data Structures

13 years 5 months ago

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Given a collection S of n line segments in the plane, the planar point location problem is to construct a data structure that can e ciently determine for a given query point p the rst segment(s) in S intersected by vertical rays emanating out from p. It is well known that linear-space data structures can be constructed so as to achieve O(logn) query times. But applications, such as those common in geographic information systems, motivate a re-examination of this problem with the goal of improving query times further while also simplifying the methods needed to achieve such query times. In this paper we perform such a re-examination, focusing on the issues that arise in three di erent classes of pointlocation query sequences: sequences that arereasonablyuniform spatially and temporally (in which case the constant factors in the query times become critical), sequences that are non-uniform spatially or temporally (in which case one desires data structures that adapt to spatial and tempor...

Michael T. Goodrich, Mark W. Orletsky, Kumar Ramai

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