 
Summary: I/Oefficient Point Location using Persistent BTrees
Lars Arge, Andrew Danner, and ShaMayn Teh
Department of Computer Science, Duke University
We present an external planar point location data structure that is I/Oefficient both in theory
and practice.
The developed structure uses linear space and answers a query in optimal O(logB N) I/Os,
where B is the disk block size. It is based on a persistent Btree, and all previously developed
such structures assume a total order on the elements in the structure. As a theoretical result of
independent interest, we show how to remove this assumption.
Most previous theoretical I/Oefficient planar point location structures are relatively compli
cated and have not been implemented. Based on a bucket approach, Vahrenhold and Hinrichs
therefore developed a simple and practical, but theoretically nonoptimal, heuristic structure. We
present an extensive experimental evaluation that shows that, on a range of realworld Geographic
Information Systems (GIS) data, our structure uses fewer I/Os than the structure of Vahrenhold
and Hinrichs to answer a query. On a synthetically generated worstcase dataset, our structure
uses significantly fewer I/Os.
1. INTRODUCTION
The planar point location problem is the problem of storing a planar subdivision
defined by N line segments such that the region containing a query point p can
be computed efficiently. Planar point location has many applications in, e.g., Ge
