1. © 1999 FORWISS General Research Report Implementation and Optimization Issues of the ROLAP Algebra F. Ramsak, M.S. (UIUC) Dr. V. Markl Prof. R. Bayer, Ph.D.

2. © 1999 FORWISS Contents l Motivation l ROLAP Algebra Recap l Optimization Issues – Handling of Restrictions – Aggregation Networks l Future Work & Summary

3. © 1999 FORWISS Example DW Model

4. © 1999 FORWISS User‘s View of a Report Grouping combinations used to fill pivot table: (1){Y,Q,R,N} (2){Y,Q,R} (3) {Y,Q} (4) {Y,R,N}(5){Y,R} (6){Y} (7) {R,N}(8) {R} (9){} = ALL

5. © 1999 FORWISS POT: Pivot Organized Tuples l We may also write for POT(R,G,F). G,FG,F (R)(R)

6. © 1999 FORWISS POT-Example POT(R,{{A},{A,B}},{sum(D)}) yields the table: AB Sum( D ) a 1 ALL*** … n ALL*** a 1 b 1 …… a n …… a 1 b m …… a n b m a

7. © 1999 FORWISS POT Extension: Group Filtering l Filtering of generated groups (like with the HAVING clause in SQL) with H containing a predicate H[g] for each grouping g in G

8. © 1999 FORWISS Group Filtering Example l Report Years, Product-Group sales totals and sales/year for PGs with less than 10 Mio sales

9. © 1999 FORWISS Straight Forward SQL Generation l POT(R,{{A},{A,B}},{sum(D)}) maps directly to: SELECT A, ‘ALL’, sum(D) FROM R GROUP BY A UNION SELECTA, B, sum(D) FROM R GROUP BY A,B l Disadvantages: – Efficient execution depends on optimizer of underlying DBMS – no UB-Tree support on SQL interface guaranteed

10. © 1999 FORWISS Handling Restrictions l Semantic of ALL value l Pushing Restrictions Down – Pushing Through POT: Restrictions on all groups – Pushing down inside POT: Restrictions on individual groups may be pushed down (i.e., before grouping) if they do not contain constraints on the aggregation results

11. © 1999 FORWISS )(Salessum   )(, ALLpad MonthYear  MonthYear,  )(Salessum  FACT   )(, ALLpad MonthYear  )19981997( 

12. © 1999 FORWISS )( Salessum   )(, ALLpad MonthYear  MonthYear,  )( Salessum  FACT   )(, ALLpad MonthYear  )19981997( 

13. © 1999 FORWISS Aggregation Networks l Efficient generation of multiple groups – Usage of previous generated (more finer) groups instead of fact table as starting point – Only one access to the fact table for multiple groups l Problems: Size of aggregation nets – Hierarchy semantic reduces aggregation nets significantly l UB-Tree & Tetris techniques have high potential to optimize aggregation nets – Grouping requires sorting – Sorted writing of large temporary results saves additional processing time

14. © 1999 FORWISS Example of an Aggregation Network (Year, Month, Productgroup) (Year)(Productgroup) (Month) (Year, Month)(Year, Productgroup)(Month, Productgroup) ( )

15. © 1999 FORWISS Aggregation Net with Hierarchies (Year, Month, Productgroup) (Year)(Productgroup) (Year, Month)(Year, Productgroup) ( ) Tetris: sort according to Y Sort according to PG (or sorted writing+Scan)

16. © 1999 FORWISS POT and Aggregation Nets

17. © 1999 FORWISS Optimization Issues of AggregationNets l Find minimal spanning tree for the specified groupings – Vertices: groupings – Edge weights: cost of computing new group# l Cost factors: – Group size – Required sorting –...

18. © 1999 FORWISS Optimization Issues of Aggregation Nets (Year, Month, Productgroup) (Year)(Productgroup) (Year, Month)(Year, Productgroup) ( ) C1C1 C2C2 C5C5 C4C4 C3C3 C6C6 C7C7

19. © 1999 FORWISS Summary and Future Work l Aggregation networks have a very potential to speed up POT operations l Standard grouping/aggregation algorithms may benefit significantly from UB-Tree/Tetris techniques l Upon availability of resources: Implementation of basic ROLAP algebra processing as part of a master thesis