1. A Data Model for Supporting On-Line Analytical Processing DataBase Lab. 석사 1 학기 홍 은 주

2. Abstract Formalize MDD model for OLAP Develop algebraic query language → grouping algebra MDDB consists of finite set of multidimensional cube finite set of relations

3. Contents 연구 동기 Cubes and Grouping relations MDDB and MDDB queries Multidimensional cube algebra Related Research Conclusion

4. 연구 동기 Query 1 : 각 상점별로 올해의 모든 날 (day) 에 대한 total sales amount 를 구하라 Query 2 : 각 지역별 (east, west..) 로 작년 매 출순위 상위 5 위의 지역을 찾으라

5. Query 1 (two grouping method) By attribute (store 를 의미함 ) 시간에 따른 position (day 를 의미함 ) → 올해 day ‘ d ’ 까지 store ‘ s ’ 에 있던 sales amount 로 산출 Query 2 (two grouping method) By attribute (product)  작년의 모든 product 에 대한 각각의 sales 를 계산 sales 계산 결과로 각 지역별로 매출 상위 5 위를 뽑 아냄 위와 같은 query 들은 traditional relational query language 로는 query 가 한번에 해결되지 않음 → 本 연구를 시작

6. Cubes and Grouping Relations Definition 1 N-dimensional cube scheme is a set {(D 1,R 1 ), …,(D n,R n )} cube 는 (F, ) 와 짝을 이룸  F = {(D 1,r 1 ), …,(D n,r n )} r i 는 R i 로의 relation  는 {{(D 1,t 1 ), …,(D n,t n )}| ∀ 1≤ i ≤ n : t i ∈ r i } 로부터 V 로의 mapping R : attribute name D : dimension name A 는 dom(A) 에 속함 V : null value 를 포함한 scalar value

7. Analyze – Definition 1 r i 는 Di 의 dimension relation Multidimensional -cube 는  dimension relations 집합과  value mapping 의 집합 ※ value mapping 은 각 dimension 의 각 tuple combination 을 scalar value 로 mapping Cube 의 dimension 이름에 순서가 있다고 가정 :  Cube scheme list :  Cube 는 위와 같은 scheme 에 정의

8. Example 3-dimensional cube SALES = (r s, r p, r d, amount)  scheme 위 에 존재  R s = {loc} (location) R p = {p, m} (item and manufacturer) R d = {y, m, d} (year, month, day)  amount (t s, t p, t d ) sales amount of product t p reported by store t s on day t d

9. Definition 2 S = {(D 1,R 1 ), …, (D n,R n )} : cube scheme G : grouping relation scheme G is said to be applicable to S if for each non-dummy dimension attribute D.A ∈ G, A ∈ R i and D i =D for some i Analyze-Definition 2 Non-dummy dimension attribute D.A 가 D 에 나타남  D : dimension name in the cube scheme  A : relation scheme for dimension D

10. Definition 3 G : grouping scheme g = G 의 grouping relation X : subset of G S = : cube scheme C = (r 1, …,t n ) : S 의 cube Each tuple t in gives the following set of coordinates, denoted by : {(t 1, …,t n )| t i ∈ r i for each 1≤i≤n and there exist t ’ in x=tr(x) such that t ’ [R∩R i ]= t i [R∩R i ] for each 1≤i≤n

11. Example - Definition 3

12. MDDB and MDDB queries MDDB Finite set of multidimensional cube Finite set of grouping relations grouping algebra 를 표현하는 4 MDDB queries MDDB on the scheme (D, C, G) D = {Date, Prod, Store}, C = {Sales} G = {Region} Region is on the scheme {reg, Store.loc}

13. Q.1 Find out the names of the last year ’ s (1994) top 5 selling product (including all manufacturer) Q.2 For each member store, find out the year-to-date total sales amounts for each day this year (the daily cumulative sales amounts over 1995)

14. Q.3 Find the year-to-date total sales amounts, in each region, of each product whose last year ’ s nation-wide total sales amount was ranked among top five Q.4 For all those products that are in the set of products manufactured by m 1 and m 2, find the total sales amounts of this year (1995)

15. Multidimenstional cube algebra cube algebra cube 에서 cube 로 mapping 하는 6 operation 으 로 구성 Purpose  construct data from local databases into suitable multidimensional cubes 종류  1. add dimension, 2. transfer, 3. Union 4. cube aggregation 5. rc-join 6. construct

16. D(C) Input cube C 로부터 C ’ 을 생성 C ’ has new dimension named D  relation for the dimension has only one tuple → empty tuple []  coordinate (t 1, …,t n,[]) in C ’ coordinate (t 1, …,t n ) in C two cube 를 union 하기위해 input cube 가 다 른 cube 와 dimension 을 갖도록 맞추는 것이 목 적 Relation scheme 이 empty set 1. Operation-Add dimension Empty tuple

17. 2. Operation - Transfer(1) D 1 의 A 를 D 2 의 새로운 attribute B 로 transfer ※ D : dimension A, B : attribute 첫번째 dimension 의 A 를 두 번째 dimension 으로 project out (by Cartesian product)

18. 2. Operation - Transfer(2) EX) C ’ = Example of transfer operations

19. 3. Operation - Union union cubes C 1 and C 2 along the dimension D 1 두 cube 의 coordinate 을 union each coordinate get its original value 새로운 coordinate 에 null value 사용됨

20. 4. Operation - Aggregate The above cube aggregation gives a cube C ’’ on the scheme Cube Aggregation

21. 5. Operation - rc join 6. Operation - Construct join r (relation) into D 1 of C (cube) result : new cube with D 1 r(relation) 에서 cube 생성

22. Example Suppose, Each store reports a cube C i = (r d,r p,amount i ) to the headquarter 위의 cube 들과 위치 relation 등이 headquarters data warehouse 에서 cube 를 구축하는데 쓰임

23. Related Research In DB research, systems similar to OLAP systems have been studied in the domain of statistical and scientific databases(SSDB) Optimization techniques Pre-aggregation new grouping operation CUBE for the SQL group-by clause

24. Conclusion The query language is flexible in expressing many intuitive OLAP queries, including order-related queries. Issued on Nov.1996 by Chang Li, X.Sean Wang George Mason University