Multidimensional or Relational? / How to Organize an On-line Analytical Processing Database (1103.3863v3)

Abstract: In the past few years, the number of OLAP applications increased quickly. These applications use two significantly different DB structures: multidimensional (MD) and table-based. One can show that the traditional model of relational databases cannot make difference between these two structures. Another model is necessary to make the differences visible. One of these is the speed of the system. It can be proven that the multidimensional DB organization results in shorter response times. And it is crucial, since a manager may become impatient, if he or she has to wait say more than 20 seconds for the next screen. On the other hand, we have to pay for the speed with a bigger DB size. Why does the size of MD databases grow so quickly? The reason is the sparsity of data: The MD matrix contains many empty cells. Efficient handling of sparse matrices is indispensable in an OLAP application. One way to handle sparsity is to take the structure closer to the table-based one. Thus the DB size decreases, while the application gets slower. Therefore, other methods are needed. This paper deals with the comparison of the two DB structures and the limits of their usage. The new results of the paper: (1) It gives a constructive proof that all relations can be represented in MD arrays. (2) It also shows when the MD array representation is quicker than the table-based one. (3) The MD representation results in smaller DB size under some conditions. One such sufficient condition is proved in the paper. (4) A variation of the single count header compression scheme is described with an algorithm, which creates the compressed array from the ordered table without materializing the uncompressed array. (5) The speed of the two different database organizations is tested with experiments, as well. The tests are done on benchmark as well as real life data. The experiments support the theoretical results.