ProPolyne: A Fast Wavelet-Based Algorithm for Progressive Evaluation of Polynomial Range-Sum Queries

Many range aggregate queries can be eÆciently derived from a class of fundamental queries: the polynomial range-sums. After demonstrating how any range-sum can be evaluated exactly in the wavelet domain, we introduce a novel pre-aggregation method called ProPolyne to evaluate arbitrary polynomial range-sums progressively. At each step of the computation, ProPolyne makes the best possible wavelet approximation of the submitted query. The result is a data-independent approximate query answering technique which uses data structures that can be maintained eÆciently and exactly. ProPolyne's performance as an exact algorithm is comparable to the best known MOLAP techniques. Experimental results show that this approach of approximating queries rather than compressing data produces consistent and superior approximate results when compared to typical wavelet-based data compression techniques.