An array-based algorithm for simultaneous multidimensional aggregates

Abstract

Computing multiple related groupbys and aggregates is one of the core operations of On-Line Analytical Processing (OLAP) applications. Recently, Gray et al. [GBLP95] proposed the "Cube" operator, which computes group-by aggregations over all possible subsets of the specified dimensions. The rapid acceptance of the importance of this operator has led to a variant of the Cube being proposed for the SQL standard. Several efficient algorithms for Relational OLAP (ROLAP) have been developed to compute the Cube. However, to our knowledge there is nothing in the literature on how to compute the Cube for Multidimensional OLAP (MOLAP) systems, which store their data in sparse arrays rather than in tables. In this paper, we present a MOLAP algorithm to compute the Cube, and compare it to a leading ROLAP afgorithm. The comparison between the two is interesting, since although they are computing the same function, one is value-based (the ROLAP algorithm) whereas the other is position-based (the MOLAP algorithm.) Our tests show that, given appropriate compression techniques, the MOLAP algorithm is significantly faster than the RO-LAP algorithm. In fact, the difference is so pronounced that this MOLAP algorithm may be usefuf for ROLAP systems as wefl as MOLAP systems, since in many cases, instead of cubing a table directly, it is faster to fist convert the table to an array, cube the array, then convert the result back to a table.

Graph OLAP: a multi-dimensional framework for graph data analysis

“…In bottom-up computation, which can be contrasted with BUC [2] in traditional OLAP, high-level cells are calculated first, before drilling-down to low-level cells they cover. In top-down computation, which can be contrasted with Multi-Way [31] in traditional OLAP, we calculate low-level cells first, and then aggregate to high-level cells. Finally, which approach to adopt will depend on various parameters, including the size of the network, data sparsity, the measures to be computed, and the available constraints.…”

“…It randomly picks an augmenting path from s to t until no such paths exist. To accommodate top-down computation, where high-level cells are computed after low-level cells so that intermediate results can be utilized, we integrate our attenuation scheme with the classic Multi-Way aggregation method for cube computation [31]. .…”

“…There have been a lot of works that deal with the efficient computation of a 6 The effect of optimization w.r.t. dimension cardinality data cube, such as [2,31], whereas the wealth of literature cannot be enumerated. However, all these researches target conventional spreadsheet data, i.e., OLAP analysis is performed on independent data tuples that mathematically form a set.…”

“…OLAP (On-Line Analytical Processing) [2,7,11,12,31] is an important notion in data analysis. Given the underlying data, a cube can be constructed to provide a multi-dimensional and multi-level view, which allows for effective analysis of the data from different perspectives and with multiple granularities.…”

Stream Cube: An Architecture for Multi-Dimensional Analysis of Data Streams

“…Data are aggregated either completely or partially in multiple dimensions and multiple levels, and are stored in the form of either relations or multi-dimensional arrays [1,29]. The dimensions in a data cube are of categorical data, such as products, region, time, etc., and the measures are numerical data, representing various kinds of aggregates, such as sum, average, variance of sales or profits, etc.…”