Adaptive Planar Point Location

10/01/2018

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by   Siu-Wing Cheng, et al.

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We present self-adjusting data structures for answering point location queries in convex and connected subdivisions. Let n be the number of vertices in a convex or connected subdivision. Our structures use O(n) space. For any convex subdivision S, our method processes any online query sequence σ in O(OPT + n) time, where OPT is the minimum time required by any linear decision tree for answering point location queries in S to process σ. For connected subdivisions, the processing time is O(OPT + n + |σ|(^* n)). In both cases, the time bound includes the O(n) preprocessing time.