Repairing dimension hierarchies under inconsistent reclassification

Abstract

On-Line Analytical Processing (OLAP) dimensions are usually modelled as a hierarchical set of categories (the dimension schema), and dimension instances. The latter consist in a set of elements for each category, and relations between these elements (denoted rollup). To guarantee summarizability, a dimension is required to be strict, that is, every element of the dimension instance must have a unique ancestor in each of its ancestor categories. In practice, elements in a dimension instance are often reclassified, meaning that their rollups are changed (e.g., if the current available information is proved to be wrong). After this operation the dimension may become non-strict. To fix this problem, we propose to compute a set of minimal r-repairs for the new non-strict dimension. Each minimal r-repair is a strict dimension that keeps the result of the reclassification, and is obtained by performing a minimum number of insertions and deletions to the instance graph. We show that, although in the general case finding an r-repair is NP-complete, for real-world dimension schemas, computing such repairs can be done in polynomial time. We present algorithms for this, and discuss their computational complexity. © 2011 Springer-Verlag.