List of Figures

Chapter I: Basic Notions

Figure 1: Phases of the Aggregation Process

Figure 2: Simple MADS

Figure 3: The "Geography" Primitive Dimension

Figure 4: The 2-D Representation of a Multidimensional MADS

Figure 5: A Complex MADS

Figure 6: A Composite MADS

Figure 7: A Complex-Composite MADS

Figure 8: Spaces and Levels of ADAMO

Figure 9: Graphical Representation of a MAD in ADAMO

Figure 10: Graphical Notations of Different Summarizability Characteristics

Figure 11: Table Example

Figure 12: Graphical Representation of Marginals and Implicit Dimensions

Figure 13: Graphical Representation of the ID-Dependency

Figure 14: Composite Table

Figure 15: The Graphical Representation of an Alias Node

Figure 16: Different Total Levels

Figure 17: Graphical Representation of Butterfly Node with Alias and Marginals

Figure 18: Example of Star Model Representation

Chapter II: Multidimensionality in Statistical, OLAP, and Scientific Databases

Figure 1a: An "Employee" Table

Figure 1b: A 3-D View of the Table

Figure 2a: A Summary Database in 2D Space

Figure 2b: The Database Further Summarized on Each Dimension

Figure 3a: A Graphical Representation of a Summary Database

Figure 3b: An Inverted Graphical à Representation Using UML Notation

Figure 3c: A Star Schema Representation of the Summary Database

Figure 4: Using Links to Federate "Object" and "Summary" Databases

Figure 5a: Representing a Category Hierarchy in a Tabular Form

Figure 5b: An Alternative, More Compact Representation

Figure 5c: A Normalized Version of the Category Hierarchy

Figure 6a: A Schematic of an Object Model for Supporting Category-Hierarchy Class

Figure 6b: A Schematic of an Object Model to Support a Multidimensional Class Whose Dimensions Are Two Category-Hierarchy Classes

Chapter III: Conceptual Multidimensional Models

Figure 1: An Example of Star Schema

Figure 2: Dimension Scheme in the MD Model

Figure 3: Two Data Cube Schemes Over the Dimensions in Figure 2

Figure 4: A Sample Instance Over the Multidimensional Scheme of Example 4:

Chapter IV: Hierarchies

Figure 1: Examples of non-hierarchical structures

Figure 2: Example of the MAD occupation

Figure 3: Example of non-completeness

Figure 4: Temporal Summarization by Function and Summary Attribute Type

Figure 5: Non Temporal Summarization by Function and Summary Attribute Type

Figure 6: Example of a Data Cube

Figure 7: The Hierarchy Along Dimensions: Beverages and Location (on the Left) and the Relative Domain Value (on the Right)

Figure 8: Domain Values of the Level City

Figure 9: Example of a Multiple Hierarchy

Figure 10: Example of Path Generation Between Levels

Figure 11: A Multidimensional View of the Drink Sales Data Cube

Figure 12: The result of the query

Figure 13: Example of an Insert Level

Chapter V: Operators for Multidimensional Aggregate Data

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Chapter VI: Time in Multidimensional Databases

Figure 1: A Geography Dimension

Figure 2: Updated Geography Dimension

Figure 3: The Temporal Dimension "Store"

Figure 4: A Series of Updates to Dimension "Product"

Figure 5: A Snapshot at "d4"

Figure 6: Dimension Product for the Running Example

Figure 7: Data Warehouse Versioning

Figure 8: Dimensions in the Case Study

Figure 9: Browsing Dimension "Patient"

Chapter VII: Dynamic Multidimensional Data Cubes

Figure 1: Data Cube Example

Figure 2: Original Data Cube A and Corresponding Prefix Cube PS with Range Sum Query

Figure 3: Aggregation Regions of Cells for RPS

Figure 4: Original Data Cube A and Corresponding RPS Cube with Range Sum Query (Middle) and Update (Right)

Figure 5: Original Data Cube A and Corresponding DDC Cube with Range Sum Query

Figure 6: Tree Structure of the DDC Cube (Query Endpoint Hatched, Accessed Cells Shaded)

Figure 7: Original Data Cube A and a Possible HBC Cube

Figure 8: Original Array A and Corresponding RPS (Block Size 3) and PS Arrays (Query Range and Updated Cell in A Are Framed, Accessed Cells Are Shaded)

Figure 9: Original Data Cube A, Intermediate Result, and Final IDC Cube (Fat Lines Indicate Partitioning into Blocks by RPS)

Figure 10: Processing Queries and Updates on an Iterative Data Cube (RPS Technique Used for Both Dimensions)

Figure 11: pCube with R-Tree Based Structure for the Aggregate Function COUNT

Figure 12: Processing a Query on a Simple pCube for Aggregate Operator SUM

Figure 13: Cuboids of a Three-Dimensional Example Cube

Figure 14: Cube as a Multidimensional Data Cube; Cuboids of Figure 13 Indicated

Chapter VIII: Materialized Views in Multidimensional Databases

Figure 1: Entity-Relationship Representation of an MDDB

Figure 2: Data-Cube Lattice with Associated Queries

Figure 3: MD-Lattice of the Store Dimension

Figure 4: A Configuration of Materializations

Figure 5: A Configuration of Materializations

Chapter IX: Querying Multidimensional Data

Figure 1: Star and Snowflake Schemes

Figure 2: The Dimension Hierarchies for Fcalls

Figure 3: Relational and Multidimensional Operations on Tables

Figure 4: A Graphical Query of the MD Model

Chapter X: Incomplete Information in Multidimensional Databases

Figure 1: A Multidimensional Space

Figure 2: A Hierarchy in the Multidimensional Space

Figure 3: Options for Handling an Unknown Value (in a Max Aggregate)

Figure 4: Options for Handling an Imprecise Value (in a Max Aggregate)

Figure 5: Options for Handling an Exclusive Disjunctive Value (in a Max Aggregate)

Figure 6: Suggesting an Alternative, Complete Query

Figure 7: A Mapping Table from Items to Food Groups

Figure 8: Repairing a Non-Covering Mapping

Figure 9: Repairing a Non-Strict Hierarchy

Chapter XI: Privacy in Multidimensional Databases

Figure 1: The Graph Associated with Three Queries

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Figure 3: A Simple Bond of a Bipartite Graph

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Figure 32: A Data Map.

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Chapter XIII: Cooperation with Geographic Databases

Figure 1: A GDB Schema with Full-Contains Relationships

Figure 2: Example of Cube "Car_Sales"

Figure 3: Example of Binding Attributes in the Geographic Class Schema MUNICIPALITY

Figure 4: Instances of the Binding Attributes, "Car_Sales" and "Toy_Sales"

Figure 5: The Inheritance of Binding Attribute

Figure 6: Example of Inferring Binding Attribute

Figure 7: Example of Different Steps for the Generation of Specialized Geographic Classes