# Dynamic Planar Point Location in External Memory

## TL;DR

This paper introduces a fully-dynamic external memory data structure for planar point location that achieves near-optimal query and update I/O performance, significantly improving upon previous methods.

## Contribution

It presents the first dynamic data structure for planar point location in external memory with near-optimal query costs, matching internal-memory bounds.

## Key findings

- Supports queries in O(log_B n (log log_B n)^3) I/Os
- Supports updates in O(log_B n (log log_B n)^2) amortized I/Os
- First dynamic external memory structure with almost-optimal query performance

## 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.