 
Summary: Indexing Moving Points
(Extended Abstract)
Pankaj K. Agarwal \Lambda Lars Arge y Jeff Erickson z
Abstract
We propose three indexing schemes for storing a set S of N
points in the plane, each moving along a linear trajectory, so
that a query of the following form can be answered quickly:
Given a rectangle R and a real value tq , report all K points
of S that lie inside R at time tq . We first present an indexing
structure that, for any given constant '' ? 0, uses O(N=B)
disk blocks, where B is the block size, and answers a query in
O((N=B) 1=2+'' +K=B) I/Os. It can also report all the points
of S that lie inside R during a given time interval. A point
can be inserted or deleted, or the trajectory of a point can
be changed, in O(log 2
B N) I/Os. Next, we present a general
approach that improves the query time if the queries arrive
in chronological order, by allowing the index to evolve over
time. We obtain a tradeoff between the query time and
the number of times the index needs to be updated as the
