Adaptive Planar Point Location

Cheng, Siu-Wing; Lau, Man-Kit

doi:10.4230/LIPIcs.SoCG.2017.30

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Adaptive Planar Point Location

Authors Siu-Wing Cheng, Man-Kit Lau

Part of: Volume: 33rd International Symposium on Computational Geometry (SoCG 2017)
Part of: Series: Leibniz International Proceedings in Informatics (LIPIcs)
Part of: Conference: Symposium on Computational Geometry (SoCG)
License: Creative Commons Attribution 3.0 Unported license
Publication Date: 2017-06-20

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Document Identifiers

DOI: 10.4230/LIPIcs.SoCG.2017.30
URN: urn:nbn:de:0030-drops-71897

Subject Classification

Keywords

point location
planar subdivision
static optimality

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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).

Cite As Get BibTex

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

Author Details

Siu-Wing Cheng

Man-Kit Lau

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