Algorithms and Data Structures for External Memory

8
Batched Problems in Computational Geometry
For brevity, in the remainder of this manuscript we deal only with
the single-disk case D = 1. The single-disk I/O bounds for the batched
problems can often be cut by a factor of Θ(D) for the case D ≥ 1
by using the load balancing techniques of Chapter 5. In practice, disk
striping (cf. Section 4.2) may be sufficient. For online problems, disk
striping will convert optimal bounds for the case D = 1 into optimal
bounds for D ≥ 1.
Problems involving massive amounts of geometric data are ubiquitous
in spatial databases [230, 299, 300], geographic information systems
(GIS) [16, 230, 299, 334], constraint logic programming [209, 210],
object-oriented databases [361], statistics, virtual reality systems, and
computer graphics [169].
For systems of massive size to be efficient, we need fast EM algorithms
and data structures for some of the basic problems in computational
geometry. Luckily, many problems on geometric objects can
be reduced to a small set of core problems, such as computing intersections,
convex hulls, or nearest neighbors. Useful paradigms have
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