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 $O(\log_B n(\log\log_B n)<sup>3))$ I/Os and updates in $O(\log_B n(\log\log_B n)<sup>2))$ 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 $O(\log_B² n)$ I/Os to answer queries. Our result almost matches the best known upper bound in the internal-memory model.