Repair-oriented relational schemas for multidimensional databases

Abstract

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.

A multidimensional data model with subcategories for flexibly capturing summarizability

“…This is the concept that has been the focus of previous research in the literature [6,7,11,10,19,29]. In particular, it has been established that for a dimension to be strict-summarizable, it must satisfy three conditions [20,29]. First, the dimension schema must have a single base category, which contains the all elements that have no children.…”

“…Instance-based repairs have been introduced and studied in [6,7,11,9,29], and in some sense, but not as repairs, in [28,18]. In this case, consistency is restored by modifying data elements or links between them in the original dimension instance.…”

“…These repairs have been proposed to deal mainly with non-strictness, and usually assuming homogeneity [6,9]. When both non-strictness and heterogeneity are addressed [7,11,29], the latter has been confronted through the insertion of null values [18,28,29].…”

“…With data repairs, a single change on a dimension instance directly results in several changes on records in the underlying database (the number of changes depends on the underlying ROLAP schema, and is usually larger when changes are made at higher levels of the instance [29]). With structural repairs this is not the case, which is advantageous for users who do not want their records changed.…”

“…An HM instance is considered to be summarizable if a cube view on any category c can be computed a from pre-computed cube view for each one of its descendant categories c ′ (as if the cube view for c ′ were a fact table) [6,7,11,10,19,29]. We will refer to this notion of summarizability (i.e.…”