Summary: Time Responsive External Data Structures
for Moving Points
Pankaj K. Agarwal 1? , Lars Arge 1?? , and Jan Vahrenhold 2? ? ?
1 Center for Geometric Computing, Department of Computer Science, Duke
University, Durham, NC 27708, USA. EMail: fpankaj,firstname.lastname@example.org.
2 Westf¨alische WilhelmsUniversit¨at M¨unster, Institut f¨ur Informatik, 48149
M¨unster, Germany. EMail: email@example.com.
Abstract. We develop external data structures for storing points in one
or two dimensions, each moving along a linear trajectory, so that a range
query at a given time tq can be answered efficiently. The novel feature
of our data structures is that the number of I/Os required to answer a
query depends not only on the size of the data set and on the number
of points in the answer but also on the difference between tq and the
current time; queries close to the current time are answered fast, while
queries that are far away in the future or in the past may take more time.
I/Ocommunication, and not internal memory computation time, is often the
bottleneck in a computation when working with datasets larger than the avail
able main memory. Recently, external geometric data structures have received
considerable attention because massive geometric datasets arise naturally in