A mathematical model of the OLAP cubes
Sergey Dmitrievich Kuznetsov, Yu. A. Kudryavtsev · Programming and Computer Software · 2009
In 1993, E. Codd introduced a concept of an OLAP (online analytical processing) system, which includes 12 rules of representing data for the user. As can be seen from the name, such systems are designed for analyzing data in an interactive mode. Hence, the basic goal of OLAP means is to represent large amount of data in the form convenient for the end-user analysis. Currently, the representation of data in the form of multidimensional cubes is a de facto standard of user work with large amount of data. In this paper, basic concepts of the OLAP systems are introduced and, then, formalized in terms of the lattice theory. In the frame-work of this formalization, the optimality (in terms of the amount of data stored) of the representation of the OLAP cubes by closed lattices or by quotient lattices (which are equivalent to the former) is proved.