On the Difficulty of Range Searching

The problem of range searching is fundamental and well studied, and a large number of solutions have been suggested in the literature. The only existing non-trivial 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 number 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 one-dimensional and rectilinear queries.