# Lower bounds for dynamic range query problems that permit subtraction (extended abstract)

## Abstract

Fredman has shown that Θ(*log*^{k}N) lower bounds the complexity for doing aggregate orthogonal range queries on a set of N records in a dynamic environment, where the computing machine can use only addition for calculating aggregates [Fr81a,Me84]. We show that a natural generalization of [KMR85]'s contiguous segment assumption extends Fredman's formalism so that subtraction as well as addition may be included in the Θ(*log*^{k}N) lower bound. Since subtraction operarions are known to speed up orthogonal range queries in a static environment [Ch85a, Wi85a, Wi85b, Wi86], it is surprising that subtraction is not also helpful in a dynamic environment.

The techniques introduced in section 2 are stated in very general terms because they should have applications to other types of problems, besides those we consider.

## Keywords

Range Query Aggregate Query Dynamic Data Structure Letter Symbol Aggregate Counter## References

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