Answering Top-k Queries
Using Views
Gautam Das (Univ. of Texas),
Dimitrios Gunopulos (Univ. of California Riverside),
Nick Koudas (Univ. of Toronto),
Dimitris Tsirogiannis (Univ. of Toronto)
Introduction
R
tid
X1
X2
X3
tid
Score
1
82
1
59
2
612
2
53
19
83
1
543
3
29
99
15
4
370
4
80
45
8
3
360
5
28
32
39
5
343
fQ

Preferences expressed as scoring functions on
the attributes of a relation, e.g
fQ  3X1  2X 2  5X 3
Top-k: k tuples with the highest score
VLDB '06
Related Work

TA [Fagin et. al. ‘96]



PREFER [Hristidis et. al. ‘01]



Deterministic stopping condition
Always the correct top-k set
Stores multiple copies of base relation R
Utilizes only one
We complement existing approaches
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Motivation




Query answering using views
Space-Performance tradeoff
Improved efficiency
Can we exploit the same tradeoffs for
top-k query answering?
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Problem Statement
Ranking Views: Materialized results of previously
asked top-k queries
Problem: Can we answer new ad-hoc top-k queries
efficiently using ranking views?
fQ  3X1  2X 2  5X 3 fV1  2X1  5X2 fV 2  X2  4X3
R
tid
X1
X2
X3
1
82
1
59
2
53
19
83

3
29
99
15
4
80
45
8
5
28
32
39
V1
tid
Score
3
4
V2
tid
Score
553
2
351
385
237
5
 216
1
5
177
2
201
3
159
1
169
4
88
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Outline


LPTA Algorithm
View Selection Problem




Cost Estimation Framework
View Selection Algorithms
Experimental Evaluation
Conclusions
VLDB '06
LPTA - Setting

Linear additive scoring functions e.g.
fQ  3X1  2X 2  5X 3

Set of Views:
Materialized result of a previously executed
 top-k query
 Arbitrary subset of attributes
 Sorted access on pairs tid,scoreQ tid




Random access on the base table R
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

LPTA - Example
Top-1
R(X1, X2)
V1
1
1
tid12
1
tid3
1

tid
s12
tid s
4
T  (0,1)
V2
1
1

2
1
4
2
4
tid s
2
4
2
5
2
5




1
1
tid s
Q
R  (1,1)
tid
tid s
1
3
 1 1
tid5 s5
 
stopping
condition
2
1
tid 22 s22
2
tid 3 s32
s

1
s
V1
X1


2
1
tid
O  (0,0)
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
P  (1,0)
V2
X2
LPTA
Linear Programming adaptation of TA
R(X1, X 2 )
fV1  2X1  5X2 fV 2  X1  2X2
V1


s1d
 
max( f Q )
V2
tid Score tid Score

tid1d
Q: fQ  3X1  10X 2
tid d2
sd2
0  X1, X 2  1

2X1  5X 2  s1d
d iteration
X 2  2X 2  sd2
unseen max  topkmin
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LPTA - Example (cont’)
R(X1, X2)
V1
tid11 s11
tid12 s12
1
2
1
3
1
2
1
3
tid 2 s2
tid 32 s32
4
tid 42 s42
tid s
tid s

tid1 
s1
4
 1 1
tid5 s5
 


X1
Top-1
V2
V1
T  (0,1)
stopping
condition
1
1
Q
R  (1,1)
tid
tid12
2 2


tid 22

tid12
V2
tid 52 s52

O  (0,0)
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
P  (1,0)
X2
Outline


LPTA Algorithm
View Selection Problem




Cost Estimation Framework
View Selection Algorithms
Experimental Evaluation
Conclusions
VLDB '06
View Selection Problem


Given a collection of views V  {V1, ,Vr}
and a query Q, determine the most
efficient subset U  V to execute Q on.
Conceptual discussion



Two dimensions
Higher
dimensions
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View Selection - 2d
Q
Y
T  (0,1)
A1

V1
Min top-k tuple
A
R  (1,1)
M
V2

B
O  (0,0)
B1
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P  (1,0)
X
View Selection - Higher d

Theorem: If V  {V1, ,Vr} is a set of views
for an m-dimensional dataset and Q a
query, the optimal execution of LPTA
requires
a subset of views U  V such

that U  m.
Question: How do we
 select the optimal
 subset of views?
VLDB '06
Outline


LPTA Algorithm
View Selection Problem




Cost Estimation Framework
View Selection Algorithms
Experimental Evaluation
Conclusions
VLDB '06
Cost Estimation Framework


What is the cost of running LPTA when a
specific set of views is used to answer a
query?
Cost = number of sequential accesses
V1
Min top-k tuple
Q
Cost = 6 sequential
A
B
V2 accesses
Can we find that cost
without actually running
LPTA?
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Simulation of LPTA on
Histograms
HQ: approximates the score
distribution of the query Q
HQ
HV1 HV2
Cost
1.
topkmin
2.
Use HQ to estimate the
score of the k highest
tuple (topkmin).
Simulate LPTA in a
bucket by bucket lock
step to estimate the
cost.
b buckets
n/b tuples per bucket
VLDB '06
Outline


LPTA Algorithm
View Selection Problem




Cost Estimation Framework
View Selection Algorithms
Experimental Evaluation
Conclusions
VLDB '06
View Selection Algorithms


Exhaustive (E): Check all possible
r
p

m
subsets of size
, p .
Greedy (SV): Keep expanding the set of
views to use until the estimated cost
stops reducing.



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
Select Views Spherical (SVS)
Requires the solution of a single linear
program.
(0,1)
max( f Q )
fV j  s
s
Q
T
s s
s
(0,0)
s
Selected Views

(1,0)
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Select Views By Angle (SVA)
Select Views By Angle (SVA): Sort the views by
increasing angle with respect to Q.
(0,1)
V4
V3
4

3
V2
2
1


(0,0)
Q
Selected Views
V1
1  2  3  4

(1,0)
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General Queries and Views

Views that materialize their top-k tuples.


Truncate the view histograms.
Accommodating range conditions


Select the views that cover the range
conditions.
Truncate each attribute’s histogram.
VLDB '06
Outline


LPTA Algorithm
View Selection Problem




Cost Estimation Framework
View Selection Algorithms
Experimental Evaluation
Conclusions
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Experiments


Datasets (Uniform, Zipf, Real)
Experiments:




Performance comparison of LPTA,
PREFER and TA
Accuracy of the cost estimation framework
Performance of LPTA using each of the
view selection algorithms
Scalability of the LPTA algorithm
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Performance comparison of
LPTA, PREFER and TA
Real dataset, 2d
Uniform dataset, 3d
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Cost Estimation Accuracy
2d
(buckets = 0.5% of n)
(buckets = 1% of n)
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Performance of LPTA using
View Selection Algorithms
(2d)
500K tuples, top-100 (3d)
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Scalability Experiments on
LPTA
(2d, uniform dataset)
(500K tuples, top-100)
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Conclusions




Using views for top-k query answering
LPTA: linear programming adaptation of
TA
View selection problem, cost estimation
framework, view selection algorithms
Experimental evaluation
VLDB '06
(Thank You!)
Questions?
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