1. Eftychia Baikousi Panos Vassiliadis
View Usability and Safety for the Answering of Top-k Queries via Materialized Views
Eftychia Baikousi
Panos Vassiliadis
University of Ioannina
Dept. of Computer Science

2. Forecast
Problem of answering a top-k query through materialized top-n views
Theoretical guarantees when a top-n materialized view can answer a top-k query
Algorithmic techniques for answering a top-k query from a materialized view
Properties of the safe areas of views
DOLAP 2009, Hong Kong, 6 Nov 2009

3. Contents Motivation & Problem Definition Overview of the Method
Theoretical guarantees
Strictness of theorem
Safe area properties
Experiments
Conclusions
Future extensions
DOLAP 2009, Hong Kong, 6 Nov 2009

4. Contents Motivation & Problem Definition Overview of the Method
Theoretical guarantees
Strictness of theorem
Safe area properties
Experiments
Conclusions
Future extensions
DOLAP 2009, Hong Kong, 6 Nov 2009

5. Top-k query Find k tuples with highest grades according to Q Given
a relation R (id, x1, x2, x3) and
a query Q, sum(x1, x2, x3)
Find k tuples with highest grades according to Q R id x1 x2 x3 a
0.3
0.6
0.7 b
0.2
0.4 c
0.5
0.9 d
0.1
sum
1.6
0.9
1.8
1.4
Top-2 tuples
DOLAP 2009, Hong Kong, 6 Nov 2009

6. Motivating Example Telecommunication Company Given a relation
Executives see sale reports in PDAs
Given a relation
Region (id, name, today_traffic, yesterday_traffic, budget, ..)
a materialized view V of top-2 regions according to the query
Q: 0.6*difftraffic + 0.4*budget V
Region id
Name
t_traffic
y_traffic
budget V 1 LA 18 20 21
7.2 2 NY 42 54 15
-1.2 3
Dallas 26 22 8
4.4 4
Chicago 30 28 11
5.6
name V LA
7.2
Dallas
4.4
Can a new top-k query (e.g. 0.5*difftraffic + 0.3*budget)
be answered from V ?
DOLAP 2009, Hong Kong, 6 Nov 2009

7. Problem definition Given a base relation R (ID, X, Y)
a materialized view V (ID, X, Y, s)
that contains top-n tuples of the form (id, s) where s is defined as
s = w (a·x + y) and w, a are positive parameters
a query Q (ID, X, Y, sQ )
that requests for top k ≤ n tuples of the form (id, sQ) where sQ is defined as
sQ = wQ (aQ·x + y) and wQ, aQ are positive parameters
Introduce
an algorithm
that decides whether V by itself is suitable to answer Q
and compute Q’s answer
DOLAP 2009, Hong Kong, 6 Nov 2009

8. Related Work “Answering Top-k Queries Using Views”, VLDB ’06
Gautam Das, Dimitrios Gunopulos, Nick Koudas, Dimitris Tsirogiannis :
“Answering Top-k Queries Using Views”, VLDB ’06
Answer top-k query Q by making use of ranking views V
LPTA in 2-steps
SelectViews (V, Q)
Selects efficient subset of views U for answering Q,
U contains the sorted lists over each attribute of the relation
Answer Q from U
Linear programming adaptation of TA algorithm
Stopping condition : solution of linear program ≤ min (top-k)
DOLAP 2009, Hong Kong, 6 Nov 2009

9. Related Work – Geometric Representation (0)
Assume
Relation R (ID, X, Y)
Two views Vu( id, Score1) and Vd( id, Score2)
Query Q( id, Score)
Scoring functions of the form Score = w ( a·x +y)
Depicted as y = a-1·x
DOLAP 2009, Hong Kong, 6 Nov 2009

10. Related Work – Geometric Representation (1)
M : the kth tuple in Q
Stopping condition: sweeping line ( ) crosses position A1B
Any point below line AB has smaller score than M in regards to Q
DOLAP 2009, Hong Kong, 6 Nov 2009

11. Related Work – Geometric Representation (2)
Stopping condition: intersection point S of sweeping lines ( , ) lies on line AB
Any point below line AB has smaller score than M in regards to Q
DOLAP 2009, Hong Kong, 6 Nov 2009

12. Related Work SelectViews (V,Q) is Data dependant
based on estimation of the last tuple of Q according to the data distribution
No theoretically established guarantees that the set of views will answer Q
DOLAP 2009, Hong Kong, 6 Nov 2009

13. Contents Motivation & Problem Definition Overview of the Method
Theoretical guarantees
Strictness of theorem
Safe area properties
Experiments
Conclusions
Future extensions
DOLAP 2009, Hong Kong, 6 Nov 2009

14. Overview of the method
Theoretical guarantees of Answering a query Q via a view VU
Theoretical guarantees are too strict
Parallelism of safe areas
DOLAP 2009, Hong Kong, 6 Nov 2009

15. Example V top-3 with score x+2y Q top-1 with score 2x+y R id x y V a 74 15 b 2 16 c 8 d 1 3 Q 18 11 10 3
DOLAP 2009, Hong Kong, 6 Nov 2009

16. Construction of safe area
VU(ID, X, Y, sU)
Containing top n tuples
with score sU=wU(aU·x+y)
tN the nth tuple in VU
LU :xNUyNU line perpendicular to VU passing from tN and meeting axes X and Y
LQ:xNUyQ line perpendicular to Q passing from xNU
DOLAP 2009, Hong Kong, 6 Nov 2009

17. Safe area Safe area defined as the area “above” line LQ (shaded area)
Observations
Any tuple in safe area has score (in regards to Q) higher than any tuple outside the safe area
Tuples in safe area belong in both VU and Q
DOLAP 2009, Hong Kong, 6 Nov 2009

18. Answering Q from VU THEOREM 1
VU can answer Q if safe area contains at least k tuples
Inverse does not always hold
DOLAP 2009, Hong Kong, 6 Nov 2009

19. Overview of the method
Theoretical guarantees of Answering a query Q via a view VU
Theoretical guarantees are too strict
Parallelism of safe areas
DOLAP 2009, Hong Kong, 6 Nov 2009

20. Answering Q from VU cont.
THEOREM 2
It is possible that VU can answer Q if safe area contains less than k tuples
This holds when:
area defined by (yellow triangle)
line LU, X-axis and
line L1 producing the lowest possible score for Q from tuples of VU
Is void of tuples
DOLAP 2009, Hong Kong, 6 Nov 2009

21. Algorithm TestViewSuitability
Three main steps
Step 1:
Compute safe area (Q, V)
Step 2:
Count tuples in V that belong in the safe area
Step 3:
If there are more than k, then return (true)
Else return (false)
DOLAP 2009, Hong Kong, 6 Nov 2009

22. Overview of the method
Theoretical guarantees of Answering a query Q via a view VU
Theoretical guarantees are too strict
Parallelism of safe areas
DOLAP 2009, Hong Kong, 6 Nov 2009

23. Combining two views Lines LQU , LQD Q
characterizing the safe areas for VU and VD
LQU ║ LQD
safe area of one view (VU ) encompassed in safe area of the other view (VD)
DOLAP 2009, Hong Kong, 6 Nov 2009

24. Combining two views THEOREM 3
If two views are not safe for answering Q by themselves,
then the combination of them cannot safely guarantee the answer to Q, in regards to the safe areas.
DOLAP 2009, Hong Kong, 6 Nov 2009

25. Contents Motivation & Problem Definition Overview of the Method
Theoretical guarantees
Strictness of theorem
Safe area properties
Experiments
Conclusions
Future extensions
DOLAP 2009, Hong Kong, 6 Nov 2009

26. Experimental methodology
Test the following methods
Our algorithm
TA algorithm (it can guarantee view usability correctness)
For the following goals
Effectiveness
Number of queries answered by views
Efficiency
Time savings from usage of queries
DOLAP 2009, Hong Kong, 6 Nov 2009

27. Experimental methodology
Experimental parameters:
Size of source table R (tuples)
|R|
1x104, 5x104, 1x105
Max size of mat. View (tuples) k
10, 50, 100, 500, 1000
Number of queries asked
|Q|
100, 1000
Synthetic data sets:
Random data sets of different sizes for a relation of the form
R (ID, X, Y)
Sequence of queries with random coefficients and result size k
DOLAP 2009, Hong Kong, 6 Nov 2009

28. Effectiveness Percentage of views used for 100 queries
DOLAP 2009, Hong Kong, 6 Nov 2009

29. Effectiveness Percentage of views used for different time spans
DOLAP 2009, Hong Kong, 6 Nov 2009

30. Efficiency
Time savings from the usage of queries for different database sizes and requested results
Conflicting case
The number of stored results rises, while the savings drop
Due to the size of used memory
Memory allocation becomes slow
Probably one view is able to answer lot of queries
Savings increase for reasonable k’s of size 0.1%
DOLAP 2009, Hong Kong, 6 Nov 2009

31. Contents Motivation & Problem Definition Overview of the Method
Theoretical guarantees
Strictness of theorem
Safe area properties
Experiments
Conclusions
Future extensions
DOLAP 2009, Hong Kong, 6 Nov 2009

32. Conclusions
We have provided theoretical and algorithmic results for the problem of answering top-k queries via materialized views
Theoretical – algorithmic results:
Theorem1: Theoretical guarantees for a view to answer a top-k query,
Theorem2: Strictness of Theorem1
Parallelism of safe areas
DOLAP 2009, Hong Kong, 6 Nov 2009

33. Contents Motivation & Problem Definition Overview of the Method
Theoretical guarantees
Strictness of theorem
Safe area properties
Experiments
Conclusions
Future extensions
DOLAP 2009, Hong Kong, 6 Nov 2009

34. Future Work Optimization in case of time and storage constraints
View Caching
Hierarchical structures for the set of views
Sorting techniques
DOLAP 2009, Hong Kong, 6 Nov 2009

35. Thank you for your attention!
… many thanks to our hosts!
DOLAP 2009, Hong Kong, 6 Nov 2009

36. Auxiliary Time Savings
DOLAP 2009, Hong Kong, 6 Nov 2009