Improved dynamic geodesic nearest neighbor searching in a simple polygon

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  • Pankaj K. Agarwal, Duke University
  • ,
  • Lars Arge
  • Frank Staals, Utrecht University, Utrecht

We present an efficient dynamic data structure that supports geodesic nearest neighbor queries for a set S of point sites in a static simple polygon P. Our data structure allows us to insert a new site in S, delete a site from S, and ask for the site in S closest to an arbitrary query point q ∈ P. All distances are measured using the geodesic distance, that is, the length of the shortest path that is completely contained in P. Our data structure achieves polylogarithmic update and query times, and uses O(n log3 nlog m + m) space, where n is the number of sites in S and m is the number of vertices in P. The crucial ingredient in our data structure is an implicit representation of a vertical shallow cutting of the geodesic distance functions. We show that such an implicit representation exists, and that we can compute it efficiently.

Original languageEnglish
Title of host publication34th International Symposium on Computational Geometry, SoCG 2018
EditorsCsaba D. Toth, Bettina Speckmann
Number of pages14
PublisherSchloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing
Publication year2018
ISBN (Electronic)9783959770668
Publication statusPublished - 2018
Event34th International Symposium on Computational Geometry, SoCG 2018 - Budapest, Hungary
Duration: 11 Jun 201814 Jun 2018


Conference34th International Symposium on Computational Geometry, SoCG 2018
SeriesLeibniz International Proceedings in Informatics

    Research areas

  • Data structure, Geodesic distance, Nearest neighbor searching, Shallow cutting, Simple polygon

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