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