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Adaptive Planar Point Location

Authors Siu-Wing Cheng, Man-Kit Lau



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Siu-Wing Cheng
Man-Kit Lau

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Siu-Wing Cheng and Man-Kit Lau. Adaptive Planar Point Location. In 33rd International Symposium on Computational Geometry (SoCG 2017). Leibniz International Proceedings in Informatics (LIPIcs), Volume 77, pp. 30:1-30:15, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2017)
https://doi.org/10.4230/LIPIcs.SoCG.2017.30

Abstract

We present a self-adjusting point location structure for convex subdivisions. Let n be the number of vertices in a convex subdivision S. Our structure for S uses O(n) space and processes any online query sequence sigma in O(n + OPT) time, where OPT is the minimum time required by any linear decision tree for answering point location queries in S to process sigma. The O(n + OPT) time bound includes the preprocessing time. Our result is a two-dimensional analog of the static optimality property of splay trees. For connected subdivisions, we achieve a processing time of O(|sigma| log log n + n + OPT).
Keywords
  • point location
  • planar subdivision
  • static optimality

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