Flexible Data Cube for Range-Sum Queries in Dynamic OLAP Data Cubes

1. Flexible Data Cube for Range-Sum Queries in Dynamic OLAP Data Cubes Authors: C.-I Lee and Y.-C. Li Speaker: Y.-C. Li Date :Dec. 19, 2002

2. Outline • Introduction • Related works • Analysis of the average query and update costs • Flexible data cube • Performance analysis • Conclusions

3. Introduction • Data cubes are frequently adopted to implement OLAP and provides aggregate information • Data cube: also known as Multi-dimensional Database(MDDB) • Measure attributes: be chosen as metrics of interest • Functional attributes(dimensions): other attributes of records. • Cells: store measure attribute values • Range-Sum Query: add all cells in query region

4. Car-sales example • Measure attribute → Sale_Volume • Dimensions → Year and Age of customers

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6. Several previous approaches are used to accelerate the response time • But they slow down the update speed and require further space overhead • This study considers both query and update costs to construct data cubes • No extra space overhead • Choice the best cube in any query or update ratio • We also present a FDC method • No extra space overhead (for dense data cube) • Select or integrate some pre-aggregation techniques for each dimension

7. Hierarchical Cube (HC) [Chan & Ioannidis, 1999] Double RPS[Liang et al., 2000] Iterative Data Cube (IDC)[Riedewal et al., 2001] Relative Prefix Sum (RPS) [Geffer et al., 1999a] Space-Efficient Data Cube (SEDC)[Riedewal et al., 2000] Dynamic Data Cube (DDC)[Geffer et al., 1999b] 1997 1998 1999 2000 2001 Related works • The history of pre-aggregate range-sum queries Prefix Sum(PS) [Ho et al., 1997]

8. Prefix Sum(PS) ( Ho et al., 1997 ) • 3+5+1+2+7+3+2+6+2+4+2+3=40 • A: 2+3+3+3+1+5+3+5+1+3+3+4=36 • P: 103-50-35+18=36

9. Prefix Sum(PS)

10. Other methods • RPS ( Geffer et al., 1999a) • Two levels(Local PS and overlay boxes) but extra space overhead • HC ( Chan & Ioannidis, 1999 ) • Hierarchical method • DDC ( Geffer et al., 1999b ) • Hierarchical method but need extra space overhead • SEDC ( Riedewald et al., 2000 ) • No exrtra space overhead of RPS and DDC (SRPS and SDDC) • Double RPS ( Liang et al., 2000 ) • Three levels but need extra space overhead • IDC ( Riedewald et al., 2001 ) • No extra space overhead (different method in different dimension)

11. Our work focuses mainly on methods that do not require any extra space overhead for dense data cubes.

12. Analysis of the average query and update costs • Assume query ratio + update ratio =100% • Average query cost: • Average update cost: Cu(n) / n

14. Flexible Data Cube(FDC) • Exponential time is required to find the optimal pre-aggregated data cube • Proposed the FDC method that is a heuristic method to select or integrate any two pre-aggregation techniques for each dimension.

15. A, LPS or PS A, LPS or PS k’=6 A, LPS or PS A, LPS or PS A, LPS or PS k’=4 k’=7 A, LPS or PS A, LPS or PS k’=5 A, LPS or PS k’=0 A, LPS or PS PS A k’=4 A, LPS or PS k’=3 A, LPS or PS A, LPS or PS k’=1 A, LPS or PS A, LPS or PS k’=2 A, LPS or PS The FDC Method • In certain situation • Size • Query ratio • FDCopt = min average cost{FDC candidates} • FDCopt =min{q×CaqFDC + u×CauFDC} • Time complexity O(9n)=O(n)

16. Performance analysis • Average cost at different query ratios d = 2, n = 16, 64

17. Average cost for different dimension sizes: d = 4, q = 1, 0.9

18. Average cost for different dimension sizes: d = 4, q = 0.1, 0

19. Conclusions • Take both the query and update costs into consideration to select the suitable data cube. • Propose the FDC method • select or integrate pre-aggregating techniques for each dimension. • Outperform other methods for any query (or update) ratio situation • linear time: determine the best FDC structure. • In the future, develop new techniques to support sparse data sets

20. Thank You