Inefficient query answering is the main drawback in Decision Support Systems (DSS), due to the very large size of the multidimensional data stored in the underlying Data Warehouse Server (DWS). Aggregate queries are the most frequent and useful kind for such systems, as they support several analysis based on the multidimensionality and multi-resolution of data. As a consequence, providing fast answers to aggregate queries (by trading off accuracy for efficiency, if possible) has become a very important requirement in improving the effectiveness of DSS-based applications. In this paper we present a technique based on an analytical interpretation of multidimensional data and on the well-known least squares approximation (LSA) method for supporting approximate aggregate query answering in OLAP, which represents the most common application interfaces for a DWS. Our technique consists in building data synopses by interpreting the original data distributions as a set of discrete functions. These synopses, called Δ-Syn, are obtained by approximating data with a set of polynomial coefficients, and by storing these coefficients instead of the original data. Queries are issued on the compressed representation, thus reducing the number of disk accesses needed to evaluate the answers.
