 
Summary: http://www.elsevier.com/locate/jcss
Journal of Computer and System Sciences 66 (2003) 207243
Indexing Moving Points$
Pankaj K. Agarwal,a,
*,1
Lars Arge,a,2
and Jeff Ericksonb,3
a
Center for Geometric Computing, Department of Computer Science, Duke University, Durham, NC 27708, USA
b
Department of Computer Science, University of Illinois, Urbana, IL 61801, USA
Received 13 December 2000; revised 6 February 2002
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 any query of the following form can be answered quickly: Given a rectangle R and
a real value t; report all K points of S that lie inside R at time t: We first present an indexing structure that,
for any given constant e > 0; uses OðN=BÞ disk blocks and answers a query in OððN=BÞ1=2þe
þ K=BÞ I/Os,
where B is the block size. 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 Oðlog2
