An aggregation algorithm using a multidimensional file in multidimensional OLAP

Aggregation is an operation that plays a key role in multidimensional OLAP (MOLAP). Existing aggregation methods in MOLAP have been proposed for file structures such as multidimensional arrays. These file structures are suitable for data with uniform distributions, but do not work well with skewed distributions. In this paper, we consider an aggregation method that uses dynamic multidimensional files adapting to skewed distributions. In these multidimensional files, the sizes of page regions vary according to the data density in these regions, and the pages that belong to a larger region are accessed multiple times while computing aggregations. To solve this problem, we first present an aggregation computation model that uses the new notions of disjoint-inclusive partition and induced space filling curves. Based on this model, we then present a dynamic aggregation algorithm. Using these notions, the algorithm allows us to maximize the effectiveness of the buffer––we control the page access order in such a way that a page being accessed can reside in the buffer until the next access. We have conducted experiments to show the effectiveness of our approach. Experimental results for a real data set show that the algorithm reduces the number of disk accesses by Information Sciences 152 (2003) 121–138 www.elsevier.com/locate/ins Corresponding author. Fax: +82-42-869-3510. E-mail addresses: [email protected] (Y.-K. Lee), [email protected] (K.-Y. Whang), [email protected] (Y.-S. Moon), [email protected] (I.-Y. Song). 0020-0255/03/$ see front matter 2003 Published by Elsevier Science Inc. doi:10.1016/S0020-0255(03)00077-X up to 5.09 times compared with a naive algorithm. The results further show that the algorithm achieves a near optimal performance (i.e., normalized I/O1⁄4 1.01) with the total main memory (needed for the buffer and the result table) less than 1.0% of the database size. We believe our work also provides an excellent formal basis for investigating further issues in computing aggregations in MOLAP. 2003 Published by Elsevier Science Inc.