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The changing data requirements of today's dynamic business environments are not handled well by current On-Line Analytical Processing (OLAP) systems. Physically integrating unexpected, external data into OLAP cubes, i.e., the data warehousing approach, is a long and time-consuming process, making logical, on-the-fly, integration the better choice in many situations. However, OLAP systems have no operations for integrating existing multidimensional cube data with external data.In this paper we present a novel multidimensional algebra operator, the decoration operator, which allows external data to be integrated in OLAP cubes as new dimensions, i.e., the cube is "decorated" with new dimensions which can subsequently be used just as the regular dimensions. We formally specify the semantics of the decoration operator, ensuring that semantic problems do not occur in the data integration process. We also provide a comprehensive set of algebraic rewrite rules, specifying how the decoration operator interacts with other operators in the cube algebra.

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