Do the middle letters of “OLAP” stand for Linear Algebra (“LA”)?
نویسندگان
چکیده
Inspired by pointfree relational data processing, this paper addresses the foundations of an alternative roadmap for parallel online analytical processing (OLAP) based on a separation of concerns: rather than depending on standard database technology and heavy machinery, OLAP operations are performed by encoding data in matrix format and relying thereupon solely on LA operations. The paper investigates, in particular, how the generation of aggregation operations such as cross tabulations and data cubes in OLAP can be expressed in terms of matrix multiplication, transposition and the Khatri-Rao variant of the Kronecker product. This offers much potential for parallel OLAP, as such matrix operations have a well-defined parallelization theory. Last but not least, the approach offers a formal semantics for data aggregation which is useful in reasoning about OLAP operation as a whole.
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