Summary: PREPRINT. In Proceedings of the 4th Workshop on
AlgorithmsDatathms 25170 volume 955, pages 473­481. Springer Verlag, 1995.
On the Difficulty of Range Searching
Arne Andersson ? Kurt Swanson ?
Dept. of Computer Science, Lund University,
Box 118, S­221 00 LUND, Sweden
Abstract. The problem of range searching is fundamental and well
studied, and a large number of solutions have been suggested in the lit­
erature. The only existing non­trivial lower bound that closely matches
known upper bounds with respect to time/space tradeoff is given for the
pointer machine model. However, the pointer machine prohibits a num­
ber of possible and natural operations, such as the use of arrays and bit
manipulation. In particular, such operations have proven useful in some
special cases such as one­dimensional and rectilinear queries.
In this article, we consider the general problem of (2­dimensional) range
reporting allowing arbitrarily convex queries. We show that using a tra­
ditional approach, even when incorporating techniques like those used in
fusion trees, a (poly­) logarithmic query time can not be achieved unless
more than linear space is used. Our arguments are based on a new non­
trivial lower bound in a model of computation which, in contrast to the

Source: Andersson, Arne - Department of Information Technology, Uppsala Universitet

Collections: Computer Technologies and Information Sciences