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External Memory Planar Point Location with Fast Updates

par Iacono, John ;Karsin, Benjamin ;Koumoutsos, Grigorios
Référence arXiv.org
Publication Publié, 2019-06-01

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Résumé :

We study dynamic planar point location in the External Memory Model or Disk Access Model (DAM). Previous work in this model achieves polylog query and polylog amortized update time. We present a data structure with O(log2BN) query time and O(1B1−ϵlogBN) amortized update time, where N is the number of segments, B the block size and ϵ is a small positive constant, under the assumption that all faces have constant size. This is a B1−ϵ factor faster for updates than the fastest previous structure, and brings the cost of insertion and deletion down to subconstant amortized time for reasonable choices of N and B. Our structure solves the problem of vertical ray-shooting queries among a dynamic set of interior-disjoint line segments; this is well-known to solve dynamic planar point location for a connected subdivision of the plane with faces of constant size.