Prof. Bayer, DWH, Ch.4, SS Chapter 4: Dimensions, Hierarchies, Operations, Modeling

Prof. Bayer, DWH, Ch.4, SS Chapter 4.1 Hierarchical Dimensions Def: Hierarchical Dimensions are composite keys with an order on the key attributes. Prefixes are allowed as keys. Ex: dimension Time = ( Year, Month, Day) legal keys are: (Year)or (Year, Month)or (Year, Month, Day) Def: Basic facts are values in cells with full foreign keys

Prof. Bayer, DWH, Ch.4, SS Aggregations, Summaries Def: Aggregations are facts in cells with partial keys. These facts are derived by aggregation functions. In a cube with derived facts the aggregation function must be specified. Ex: Sales on a monthly basis Sales (Year, Month) =  Sales (Year, Month, Days) Aggregation Functions: count, sum, avg, min, max,...

Prof. Bayer, DWH, Ch.4, SS Note on Aggregations Aggregations may be stored explicitely in the cube, but then they should be secured by integrity constraints Aggregations may be virtual and must be computed on demand when needed i.e., classical tradeoff between storage space, performance, flexibility

Prof. Bayer, DWH, Ch.4, SS Relational Modeling Expand and complete partial key by ALL (Year, Month, ALL) (ALL, Month, ALL) (ALL, ALL, ALL) to obtain simple and complete relational keys via special symbol ALL Question: SQL to compute complete cube with all aggregations from base-cube?

Prof. Bayer, DWH, Ch.4, SS Hierarchy Example

Prof. Bayer, DWH, Ch.4, SS Chapter 4.2: OLAP Operations Def: Roll-up computes higher aggregations from lower aggregations or base facts according to hierarchies Ex: for base facts (Year, Month, Day) there are 3 hierarchical roll-up functions: Roll-up (Year, Month, ALL) Roll-up (Year, ALL, ALL) Roll-up (ALL, ALL, ALL) which are supported in general (canonical roll-ups)

Prof. Bayer, DWH, Ch.4, SS Additional Roll-ups: (ALL, Month, ALL) etc. therefore aggregations or in general 2 m -1 aggregations for m hierarchy levels Note: see later chapters for the support of arbitrary aggregations Note: for m dimensions with h 1, h 2,...h m hierarchy levels there are different aggregations for a given aggregation function.

Prof. Bayer, DWH, Ch.4, SS Size of base cube 2-dim example Dim1: (4, 5)= cardinality of the dimension levels Dim2: (6, 7, 2) (4 5) ( 6 7 2)1680 = Size of base cube

Prof. Bayer, DWH, Ch.4, SS Number of cells per aggregation function 1645 Size of hierarchically aggregated Cube

Prof. Bayer, DWH, Ch.4, SS Size of completely aggregated cube | |0 || 00|00 0| |0 || 0|000 ||| |0000 ||||| x 6 = x 168 = x x 1008 = x 1008 = = 5040 : :

Prof. Bayer, DWH, Ch.4, SS Computation with binary Tree

Prof. Bayer, DWH, Ch.4, SS Lemma: Given a data cube with m dimensions with h 1,..., h m hierarchy levels resp. Let the hierarchy levels of dimension i have Then the base cube has and the cube with all aggregations has Size of the Cube

Prof. Bayer, DWH, Ch.4, SS Size of the Cube (2) The aggregated cube is larger than the base cube by the factor

Prof. Bayer, DWH, Ch.4, SS Size of the hierarchically aggregated Cube For a hierarchy i with h i levels and there are hierarchical aggregation possibilities, i.e. Lemma: A hierarchically completely aggregated data cube has

Prof. Bayer, DWH, Ch.4, SS Ex: (4 5) (6 7 2) size of the hierarchically aggregated cube plus base cube = ( ) * ( ) = 25 * 133 = 3325 Ex: (4 5) (6 7 2)( 8 3) size of base cube:40,320 hierarchically aggregated cube plus base: = ( ) * ( ) * ( ) = 3325 * 33 = 109,725

Prof. Bayer, DWH, Ch.4, SS Ex: (4 5) (6 7 2)( 8 3)(5 9) size of base cube:1 814,400 hierarchically aggregated cube plus base: = 109,725 * ( ) = 5 595,975

Prof. Bayer, DWH, Ch.4, SS Additional comments on aggregations 1. In addition to the size of the complete cube there is a factor of 5 for the various aggregation functions, e.g. sum, avg, min, max, count, So far we did not consider general restrictions, e.g. „all Saturdays in March“ or „vacation months July and August“, which cross bounds of hierarchy levels Interactive query formulation results in an unlimited number of aggregations Optimization: restrictions corresponding to hierarchy levels shoud be pushed down, since they lead to query boxes

Prof. Bayer, DWH, Ch.4, SS Note: See later chapters for multidimensional indexes and MHC techniques and optimization of ROLAP-algebra to support hierarchical canonical aggregations like Roll-up (Year, Month, ALL) Roll-up (Year, ALL, ALL) Roll-up (ALL, ALL, ALL) but not Roll-up ( ALL, Month, ALL)

Prof. Bayer, DWH, Ch.4, SS Optimization Problem Non-hierarchical aggregation, e.g. March for all years decompose into union of several restrictions, e.g.  Sales (Year, Month, Day) where Month = March and (Year = 1996 or Year = 1997 or Year = 1998) see later for translation into ROLAP expression and transformations for optimization

Prof. Bayer, DWH, Ch.4, SS Multiple Hierarchies e.g. the time hierarchy Aggregation for month e.g. by covering QB of weeks and postfiltering

Prof. Bayer, DWH, Ch.4, SS Navigation Operations Drill Down: first show single result for aggregated value, e.g. sales per day, then show: hourly values for days with very high or very low sales in order to plan working hours for sales people better Other Examples: daily sales during Christmas season vacation bookings for skiing on fasching

Prof. Bayer, DWH, Ch.4, SS Roll-up: Compute Aggregations

Prof. Bayer, DWH, Ch.4, SS Slicing Selection of a smaller data cube or even reduction of a multidimensional datacube to fewer dimensions by a point restriction in some dimension (becomes pivot element)

Prof. Bayer, DWH, Ch.4, SS Dicing (würfeln) rotate result, to show another view, e.g. exchanging rows and columns Slice management precomputing and caching of several slices for later or special use, e.g. for a special sales person

Prof. Bayer, DWH, Ch.4, SS Chapter 4.3 Modeling Methodology Purpose: analysis of business processes, characteristic facts (Kennzahlen) for managers to support decisions (DSS) Steps of Decision Process: 1. Which business processes to model and analyze? 2. What are the measures, where do they come from? 3. Which degree of details, e.g. minutes like in SAP? Which precision is required for OLAP? 4. Common properties of measures to determine dimensions? Brand, Time, geogr. Region, Productgroup? Dependencies between levels of hierarchies?

Prof. Bayer, DWH, Ch.4, SS Attributes of dimensions, e.g. of products screen size of TV & computers cc and PS for cars focal length for camera Problem: how common are properties to dimensions? Non common properties cannot be modeled by levels of dimensions, are called features at GfK (up to 50), they are numbered, their meaning dependent on a specific dimension element, e.g. TV: screen size color audio system Car:transmission ccPS#cyl...

Prof. Bayer, DWH, Ch.4, SS Constant or changing attributes of dimensions? E.g. New models of car makers new powersource: electrical, hydrogen, solar attributes are rather stable, but still should be planned ahead! (mergers like Daimler-Crysler) 7. Sparsity: one hypercube or several, i.e. multicube model? Influences storage requirements, query formulation and performance, cannot be hidden easily from user, maybe by views?

Prof. Bayer, DWH, Ch.4, SS Caching and management of aggregates? Time Optimal Number of aggregates

Prof. Bayer, DWH, Ch.4, SS Chapter 4.4 Comparison of OLAP Architectures 1.MOLAP: Multidimensional OLAP 2.ROLAP: Relational OLAP 3. HOLAP: Hybrid OLAP

Prof. Bayer, DWH, Ch.4, SS MOLAP Architecture

Prof. Bayer, DWH, Ch.4, SS MDDBMS in ANSI-X3-Sparc

Prof. Bayer, DWH, Ch.4, SS Logical components of a MDDBMS

Prof. Bayer, DWH, Ch.4, SS ROLAP Architecture

Prof. Bayer, DWH, Ch.4, SS HOLAP Architecture

Prof. Bayer, DWH, Ch.4, SS Reasons for MOLAP performance write access Data Marts functional power Reasons for ROLAP scalability flexible precomputations, partial aggregates parallelism DB-mamagement and ACID