No abstract

The author has granted a non exclusive license allowing Library and Archives Canada to reproduce, publish, archive, preserve, conserve, communicate to the public by telecommunication or on the Internet, loan, distrbute and sell theses worldwide, for commercial or non commercial purposes, in microform, paper, electronic and/or any other formats. AVIS: L'auteur a accorde une licence non exclusive permettant a la Bibliotheque et Archives Canada de reproduire, publier, archiver, sauvegarder, conserver, transmettre au public par telecommunication ou par I'lnternet, preter, distribuer et vendre des theses partout dans le monde, a des fins commerciales ou autres, sur support microforme, papier, electronique et/ou autres formats. Bien que ces formulaires aient inclus dans la pagination, il n'y aura aucun contenu manquant.

Summarizability in a multidimensional (MD) database refers to the correct reusability of pre-computed aggregate queries (or views) when computing higher-level aggregations or rollups. A dimension instance has this property if and only if it is strict and homogeneous. A dimension instance may fail to satisfy either of these two semantics conditions, and has to be repaired, restoring strictness and homogeneity. In this work, we take a relational approach to the problem of repairing dimension instances. A dimension repair is obtained by translating the dimension instance into a relational instance, repairing the latter using established techniques in the relational framework, and properly inverting the process. We show that the common relational star and snowflake schemas for MD databases are not the best choice for this process. Actually, for this purpose, we propose and formalize the path relational schema, which becomes the basis for obtaining dimensional repairs. The path schema turns out to have useful properties in general, as a basis for a relational representation and implementation of MD databases and data warehouses. It is also particularly suitable for restoring MD summarizability through relational repairs. We compare the dimension repairs so obtained with existing repair approaches for MD databases.