Cube Algebra: A Generic User-Centric Model and Query Language for OLAP Cubes

Introduction

Nowadays, data warehouses are at the forefront of information technology applications as a way for organizations to effectively use and analyze information for business planning and decision making. Data warehouses are large repositories of analytical and subject-oriented data integrated from several heterogeneous sources over a large period of time. The technique of performing complex analysis over the information stored in the data warehouse is commonly called Online Analytical Processing (OLAP). A review of the evolution of data warehouse technology reveals that research and development has mainly focused on system aspects such as the construction of data warehouses, materialization, indexing, and the implementation of OLAP functionality. This system-centric view has led to well-established and commercialized technologies such as relational OLAP (ROLAP), multidimensional OLAP (MOLAP), and hybrid OLAP (HOLAP) at the logical and the physical levels.

However, the unskilled user such as the manager in a consulting company or the analyst in a financial institution is confronted with the problem that the handling of data warehouses and OLAP systems requires expert knowledge due to complicated data warehouse structures and the complexity of OLAP systems and query languages. Two main reasons are responsible for this problem. First, due to the lack of a generic, user-friendly, and comprehensible conceptual data model, data warehouse design is usually performed at the logical level and leads to the exposure of the logical design schemas that are difficult to understand by the unskilled user. In a ROLAP environment, for example, the user is faced with the logical design of relational tables in terms of star, snowflake, or fact constellation schemas. The proposal to alleviate the problem by providing extensions to the Entity-Relationship Model and the Unified Modeling Language, or by offering specific graphical user interfaces or dashboards for data warehouse design is not really convincing since ultimately they represent a reflection and visualization of relational technology concepts and, in addition, reveal their own problems. Second, available OLAP query and analysis languages such as MDX and SQL OLAP operate at the logical level and require the user’s deep understanding of the data warehouse structure in order to be able to formulate queries. These languages are quite complex, overwhelm the unskilled user, and are therefore inappropriate as end-user languages.

We conclude that a generic, conceptual, and user-centric data warehouse model that focuses on user requirements is missing and needed. Such a model should fulfill several design criteria. First, it should be located above the logical level. Second, it should abstract from and be independent of the models and technologies (ROLAP, MOLAP, HOLAP) at the logical level. Third, it should be able to cooperate with any of these logical models and technologies. Fourth, it should enable the user to generically and abstractly represent and query hierarchical multidimensional data. Fifth, it should have an associated query language based exclusively on the conceptual level, thus providing high-level query operations for the user. The goal of this article is to propose and formally describe a conceptual and user-centric data warehouse model and query language that satisfies these design criteria. Surprisingly, the conceptual view this model adopts is not new; on the contrary, it is well known. However, the way and resoluteness in which we offer this concept is novel. Our proposed conceptual model leverages the cube view of data warehouses but takes the cube metaphor literally. This means that the user’s conceptual world is solely the cube that the user can create, manipulate, update, and query. The cube is used as the user concept that completely abstracts from any logical and physical implementation details. Technically, this implies that cubes can be regarded as an abstract data type that provides cubes as the only kind of values (objects), offers high-level operations on cubes or between cubes such as slice, dice, drill-down, roll-up, and drill-across as the only available access methods, and hides any data representation and algorithmic details from the user, who can concentrate on her main interest, namely to analyze large volumes of data. Another characterization is to say that we define a universal algebra with cubes as the only sort and a collection of unary and binary operations on cubes. We therefore name our approach Cube Algebra. We will show that this algebra develops its full power and expressiveness if it is used as a high-level query language.