Flexible Data Cubes for Online Aggregation

Abstract

Abstract. Applications like Online Analytical Processing depend heavily on the ability to quickly summarize large amounts of information. Techniques were proposed recently that speed up aggregate range queries on MOLAP data cubes by storing pre-computed aggregates. These approaches try to handle data cubes of any dimensionality by dealing with all dimensions at the same time and treat the different dimensions uniformly. The algorithms are typically complex, and it is difficult to prove their correctness and to analyze their performance. We present a new technique to generate Iterative Data Cubes (IDC) that addresses these problems. The proposed approach provides a modular framework for combining one-dimensional aggregation techniques to create spaceoptimal high-dimensional data cubes. A large variety of cost tradeoffs for high-dimensional IDC can be generated, making it easy to find the right configuration based on the application requirements.

Space-Efficient Range-Sum Queries in OLAP

“…At just one recursion level, our structure would be the same as the SRPS. However, at two recursion levels, the structure would be formed in each of the inner regions as well (in order from left: [3,3,5], [5,9,10], [3,3,5] and [3,3,5]). Unfortunately, it takes a much larger example to actually form a two-level structure.…”

“…The data cube [3] is a popular data model for OLAP that allows the implementation of several important queries. Several query types have previously been studied, including range max/min [4,5] and range-sum [6][7][8][9][10]1].…”

“…The update time, however, is O(n d ) for data cubes of n d elements. Nevertheless, the prefix sum techniques provides a base for further improvements [9,[6][7][8]10]. Poon [12] has a very efficient structure with a query time of O((2L) d ) and update time of O((2Ln (1/L) ) d ), where L is a parameter.…”

How to evaluate multiple range-sum queries progressively

“…These exact methods produce considerable savings, but are based on the assumption that some relation must be scanned in order to answer the batch of queries. This will not be the case when relations are stored using pre-aggregation techniques such as prefixsums [8], wavelets [14], or general Iterative Data Cubes [12].…”

“…Extensive research has been done developing techniques for exact [2,3,8,12,14], approximate [4,6,10,15], and progressive [9,11,18] evaluation of single range-sum queries.…”