A Data Model for Supporting
On-Line Analytical Processing
DataBase Lab. 석사1학기
홍은주
Abstract
Formalize MDD model for OLAP
Develop algebraic query language
→ grouping algebra
MDDB consists of


finite set of multidimensional cube
finite set of relations
Contents
연구 동기
Cubes and Grouping relations
MDDB and MDDB queries
Multidimensional cube algebra
Related Research
Conclusion
연구 동기
Query 1 : 각 상점별로 올해의 모든 날(day)
에 대한 total sales amount를 구하라
Query 2 : 각 지역별(east, west..)로 작년
매출순위 상위 5위의 지역을 찾으라
Query 1 (two grouping method)


By attribute (store를 의미함)
시간에 따른 position (day를 의미함)
→ 올해 day ‘d’까지 store ‘s’에 있던 sales amount로 산출
Query 2 (two grouping method)

By attribute (product)
 작년의 모든 product에 대한 각각의 sales를 계산

sales 계산 결과로 각 지역별로 매출 상위 5위를
뽑아냄
위와 같은 query들은 traditional relational
query language 로는 query가 한번에 해결되
지 않음 → 本 연구를 시작
Cubes and Grouping R : attribute name
D : dimension name
Relations
A는 dom(A)에 속함
Definition 1
V : null value를 포함한
scalar value
N-dimensional cube scheme is a set
{(D1,R1),…,(Dn,Rn)}
 cube는 (F,  )와 짝을 이룸

 F = {(D1,r1),…,(Dn,rn)} ri는 Ri로의 relation

 는 {{(D1,t1),…,(Dn,tn)}|∀1≤ i ≤ n : t i ∈ r i}
로부터 V로의 mapping
Analyze –Definition 1


ri는 Di의 dimension relation
Multidimensional -cube는
 dimension relations 집합과
 value mapping의 집합
※value mapping은 각 dimension의 각 tuple
combination을 scalar value로 mapping

Cube의 dimension 이름에 순서가 있다고
가정:
 Cube scheme list : <(D1,R1),…,(Dn,Rn)>
 Cube는 위와 같은 scheme 에 정의
Example


3-dimensional cube
SALES = (rs, rp, rd, amount)
 <(Store Rs), (Prod, Rp), (Date, Rd)> scheme
위에 존재
 Rs = {loc} (location)
Rp = {p, m} (item and manufacturer)
Rd = {y, m, d} (year, month, day)
 amount (ts, tp, td)
sales amount of product tp
reported by store ts
on day td
Definition 2



S = {(D1,R1),…, (Dn,Rn)} : 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∈Ri and Di=D for some i
Analyze-Definition 2

Non-dummy dimension attribute D.A가
D에 나타남
 D : dimension name in the cube scheme
 A : relation scheme for dimension D
Definition 3
G : grouping scheme
g = G의 grouping relation
X : subset of G
S = <(D1,R1),…(Dn,Rn)> : cube scheme
C = (r1,…,tn) : S의 cube
 Each tuple t in x (g ) gives the following
set of coordinates, denoted by XC , g (t ) :
{(t1,…,tn)| ti∈ri for each 1≤i≤n and
there exist t’ in  x=tr(x) such that
t’[R∩Ri]= ti[R∩Ri] for each 1≤i≤n

Example - Definition 3
MDDB and MDDB queries
MDDB


Finite set of multidimensional cube
Finite set of grouping relations
grouping algebra를 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}
Q.1 Find out the names of the last year’s
(1994) top 5 selling product (including all
manufacturer)

begin, step,length
O
(g)
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)
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 m1 and
m2, find the total sales amounts of this
year (1995)
Multidimenstional
cube algebra
cube algebra


cube 에서 cube로 mapping하는 6 operation
으로 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
1. Operation-Add dimension
 D(C)


Relation scheme이
empty set
Input cube C로부터 C’을 생성
C’ has new dimension named D
 relation for the dimension has only one tuple
Empty tuple
→ empty tuple []
 coordinate (t1,…,tn,[]) in C’
coordinate (t1,…,tn) in C

two cube를 union 하기위해 input cube가
다른 cube와 dimension을 갖도록 맞추는 것
이 목적
2. Operation - Transfer (1)


D2 , B
D1 , A
(C )
D1의 A를 D2의 새로운 attribute B로 transfer
※ D : dimension
A, B : attribute

첫번째 dimension의 A를 두 번째dimension
으로 project out
(by Cartesian product)
2. Operation - Transfer (2)
(Year (C))
EX) C’ = 
Example of transfer operations
Year , y
Date, y

D '1 , A1
D1 , A1
3. Operation - Union




union cubes C1 and C2 along the
dimension D1
두 cube의 coordinate을 union
each coordinate get its original value
새로운 coordinate에 null value 사용됨
4. Operation - Aggregate
R 'i1 ,, R 'i1
Di1 ,, Di1
 The above cube aggregation gives a
cube C’’ on the scheme
<(Di1,R’i1),…, (Dim,R’im)>
f
(C )
Cube Aggregation
sumDA1
5. Operation - rc join
6. Operation - Construct


join r (relation) into D1 of C (cube)
result : new cube with D1
 (r )
A
D

r(relation)에서 cube 생성
Example
Suppose,




Each store reports a cube
Ci = (rd,rp,amounti) to the headquarter
위의 cube들과 위치 relation 등이 headquarters
data warehouse에서 cube를 구축하는데 쓰임
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
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