External Memory Planar Point Location with Fast Updates

05/07/2019

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by   John Iacono, et al.

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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( _B^2 N) query time and O(1/ B^1-ϵ_B N) amortized update time, where N is the number of segments, B the block size and ϵ is a small positive constant. This is a B^1-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.