I/O-efficient dynamic planar point location

We present an I/O-efficient dynamic data structure for point location in a general planar subdivision. Our structure uses O(N/B) disk blocks of size B to store a subdivision of size N. Queries can be answered in O(log(B)(2) N) I/Os in the worst-case, and insertions and deletions can be performed in O(log(B)(2) N) and O(log(B) N) I/Os amortized, respectively. Part of our data structure is based on an external version of the so-called logarithmic method that allows for efficient dynamization of static external-memory data structures with certain characteristics. Another important part of our structure is an external data structure for vertical ray-shooting among line segments in the plane with endpoints on rootB + 1 vertical lines, developed using an external version of dynamic fractional cascading. We believe that these methods could prove helpful in the development of other dynamic external memory data structures. (C) 2004 Elsevier B.V. All rights reserved.