A Formal Algebra for OLAP Link

نویسندگان

  • Bart Kuijpers
  • Alejandro Vaisman
چکیده

Online Analytical Processing (OLAP) comprises tools and algorithms that allow querying multidimensional databases. It is based on the multidimensional model, where data can be seen as a cube, where each cell contains one or more measures can be aggregated along dimensions. Despite the extensive corpus of work in the field, a standard language for OLAP is still needed, since there is no well-defined, accepted semantics, for many of the usual OLAP operations. In this paper, we address this problem, and present a set of operations for manipulating a data cube. We clearly define the semantics of these operations, and prove that they can be composed, yielding a language powerful enough to express complex OLAP queries. We express these operations as a sequence of atomic transformations over a fixed multidimensional matrix, whose cells contain a sequence of measures. Each atomic transformation produces a new measure. When a sequence of transformations defines an OLAP operation, a flag is produced indicating which cells must be considered as input for the next operation. In this way, an elegant algebra is defined. Our main contribution, with respect to other similar efforts in the field is that, for the first time, a formal proof of the correctness of the operations is given, thus providing a clear semantics for them. We believe the present work will serve as a basis to build more solid practical tools for data analysis.

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

A Formal Algebra for OLAP

Online Analytical Processing (OLAP) comprises tools and algorithms that allow querying multidimensional databases. It is based on the multidimensional model, where data can be seen as a cube, where each cell contains one or more measures can be aggregated along dimensions. Despite the extensive corpus of work in the field, a standard language for OLAP is still needed, since there is no well-def...

متن کامل

Do the middle letters of “OLAP” stand for Linear Algebra (“LA”)?

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 inve...

متن کامل

A Database Array Algebra for Spatio-Temporal Data and Beyond

Recently multidimensional arrays have received considerable attention among the database community, applications ranging from GIS to OLAP. Work on the formalization of arrays frequently focuses on mapping sparse arrays to ROLAP schemata. Database modeling of further array types, such as image data, is done differently and with less rigid methods. A unifying formal framework for general array ha...

متن کامل

A Powerful and SQL-Compatible Data Model and Query Language for OLAP

In this paper we present the SQL OLAP data model, formal algebra, and query language that, unlike current OLAP data models and languages, are both powerful, meaning that they support irregular dimension hierarchies, automatic aggregation of data, and correct aggregation of data, and SQL-compatible, allowing seamless integration with relational technology. We also consider the requirements to th...

متن کامل

A Formal Framework of Aggregation for the OLAP-OLTP Model

OLAP applications are widely used in business applications. They are often (implicitly) defined on top of OLTP systems and extensively use aggregation and transformation functions. The main OLAP data structure is a multidimensional table with three kinds of attributes: so-called dimension attributes, implicit attributes given by aggregation functions and fact attributes. Domains of dimension at...

متن کامل

ذخیره در منابع من


  با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

عنوان ژورنال:

دوره   شماره 

صفحات  -

تاریخ انتشار 2017