Dynamic Planar Point Location in External Memory

Abstract

In this paper we describe a fully-dynamic data structure for the planar point location problem in the external memory model. Our data structure supports queries in $O({\log }_{B}n(\log {\log }_{B}n{)}^3))$ I/Os and updates in $O({\log }_{B}n(\log {\log }_{B}n{)}^2))$ amortized I/Os, where $n$ is the number of segments in the subdivision and $B$ is the block size. This is the first dynamic data structure with almost-optimal query cost. For comparison all previously known results for this problem require $O({\log }_B^{2}n)$ I/Os to answer queries. Our result almost matches the best known upper bound in the internal-memory model.

extended version of a SoCG'19 paper