1. Relaxing Join and Selection Queries
Rares Vernica
UC Irvine, USA
Joint work with Nick Koudas, Chen Li, and Anthony K. H. Tung

2. Rares Vernica, UC Irvine
Query Example
SELECT * FROM Jobs J, Candidates C
WHERE J.Salary <= 95
AND J.Zipcode = C.Zipcode
AND C.WorkExp >= 5;
Make a “real” story; companies are very eager to find the people they want.
We assume that closer zip codes mean closer areas.
Jobs
Candidates ID
Company
Zipcode
Salary
ExpSalary
WorkExp J1
Broadcom
92047 80 C1
93652
120 3 J2
Intel 95 C2
92612
130 6 J3
Microsoft
82632 C3
100 5 J4
IBM
90391 C4
150 1
... …
Rares Vernica, UC Irvine

3. What if the query answer is empty?
SELECT * FROM Jobs J, Candidates C
WHERE J.Salary <= 95
AND J.Zipcode = C.Zipcode
AND C.WorkExp >= 5;
Queries can return nothing
It is important to have results
Automatically do relaxation!
Adjust the conditions
What conditions to adjust?
How to adjust them?
Rares Vernica, UC Irvine

4. Example Percentages of Empty Result Queries
In a Customer Relationship Management (CRM) application developed by IBM
18.07% (3,396 empty result queries in 18,793 queries)
In a real estate application developed by IBM
5.75%
In a digital library application [JCM+00]
10.53%
In a bioinformatics application [RCP+98]
38%
Efficient Detection of Empty-Result Queries (p.1015)Gang Luo (IBM T.J. Watson Research Center, USA) VLDB 2006
Rares Vernica, UC Irvine

5. Rares Vernica, UC Irvine
Observations
Different ways to adjust the conditions: Select vs. Join
How much to adjust each condition? Salary <= 100 vs. Salary <= 120
Adjust join vs. Adjust both selections
Jobs
Candidates ID
Company
Zipcode
Salary
ExpSalary
WorkExp J1
Broadcom
92047 80 C1
93652
120 3 J2
Intel 95 C2
92612
130 6 J3
Microsoft
82632 C3
100 5 J4
IBM
90391 C4
150 1
... …
Salary <= 95
WorkExp >= 5
Rares Vernica, UC Irvine

6. Rares Vernica, UC Irvine
Contributions
Query relaxation framework for selections and joins
Lattice-based approach for query relaxation
Efficient relaxation algorithms
Efficiency is a big issue
Rares Vernica, UC Irvine

7. Rares Vernica, UC Irvine
Overview
Motivation
Query Relaxation
Lattice-based Relaxation
Relaxation Algorithms
Variations
Experiments
Rares Vernica, UC Irvine

8. Rares Vernica, UC Irvine
Query Relaxation
Top-k / Nearest neighbor
Weight for each condition
Skyline
No weights are needed
Conditions are not considered equal
Return non dominated points
Skyline is not the only way.
Skyline does not care which one is more important.
We are not comparing apples with oranges.
Rares Vernica, UC Irvine

9. Rares Vernica, UC Irvine
Query Relaxation
Skyline
Stephan Börzsönyi, Donald Kossmann, Konrad Stocker: The Skyline Operator. ICDE 2001
In this diagram we are not relaxing join conditions.
Each point is a join pair.
Rares Vernica, UC Irvine

10. Rares Vernica, UC Irvine
Overview
Motivation
Query Relaxation
Lattice-based Relaxation
Relaxation Algorithms
Variations
Experiments
Rares Vernica, UC Irvine

11. Lattice-based Relaxation
R – select on Jobs
J – join condition
S – select on Candidates
Sometimes we might not want to relax the join (e.g.: attribute is an ID)
Relaxation is done automatically by the system
Jobs
Candidates ID
Company
Zipcode
Salary
ExpSalary
WorkExp J1
Broadcom
92047 80 C1
93652
120 3 J2
Intel 95 C2
92612
130 6 J3
Microsoft
82632 C3
100 5 J4
IBM
90391 C4
150 1
... …
Salary <= 95
WorkExp >= 5
Rares Vernica, UC Irvine

12. Rares Vernica, UC Irvine
Overview
Motivation
Query Relaxation
Lattice-based Relaxation
Relaxation Algorithms
Variations
Experiments
Rares Vernica, UC Irvine

13. Relaxing Selection Conditions
INCORRECT
Algorithm:
Compute Skyline on Jobs
Compute Skyline on Candidates
Join the Skylines
Skyline as a relational algebra operator with various properties
Jobs
Candidates ID
Company
Zipcode
Salary
ExpSalary
WorkExp J1
Broadcom
92047 80 C1
93652
120 3 J2
Intel 95 C2
92612
130 6 J3
Microsoft
82632 C3
100 5 J4
IBM
90391 C4
150 1
... …
Salary <= 95
WorkExp >= 5
Empty Join
Skyline
Skyline
Skyline
Rares Vernica, UC Irvine

14. Relaxing Selection Conditions
Join First Algorithm:
Compute the join (disregarding the selections)
Compute Skyline on join results
Jobs
Candidates ID
Company
Zipcode
Salary
ExpSalary
WorkExp J1
Broadcom
92047 80 C1
93652
120 3 J2
Intel 95 C2
92612
130 6 J3
Microsoft
82632 C3
100 5 J4
IBM
90391 C4
150 1
... …
Salary <= 95
WorkExp >= 5
Join
Skyline
Rares Vernica, UC Irvine

15. Relaxing Selection Condition
Variations
Pruning Join
Build the Skyline during the join
Pruning Join+
Build the local Skyline before the join
Sorted Access Join
Fagin’s Top-k: sort the columns on relaxation
Compute the join Skyline
Main idea of the algorithms. For more details see the paper.
Rares Vernica, UC Irvine

16. Relaxing all conditions
Multi-Dim.-Index-based-Relaxation Algorithm:
Traverse the index structure top-down
Form pairs of nodes or records
Build the Skyline
Queue
Skyline
Index exists, e.g., R-tree; works with other types of multi-dimensional indices
Children
Queue: Enqueue, Dequeue
Rares Vernica, UC Irvine

17. Rares Vernica, UC Irvine
Overview
Motivation
Query Relaxation
Lattice-based Relaxation
Relaxation Algorithms
Variations
Experiments
Rares Vernica, UC Irvine

18. Rares Vernica, UC Irvine
Variations
Computing Top-k over Skyline
Weight to each condition
Queries with multiple joins
Conditions on nonnumeric attributes
Dominance checking function
Explain the Top-k over Skyline
Rares Vernica, UC Irvine

19. Rares Vernica, UC Irvine
Overview
Motivation
Query Relaxation
Lattice-based Relaxation
Relaxation Algorithms
Variations
Experiments
Rares Vernica, UC Irvine

20. Rares Vernica, UC Irvine
Experimental Setting
Datasets
Real
Internet Movie Database (IMDB)
Movies (120k) & ActorInMovies (1.2m)
Census-Income – UCI KDD Repository
Census (200k)
Synthetic
Independent, Correlated, and Anticorrelated
Implementation
GNU C++
Spatial Index Library (R-tree)
Linux, AMD Opteron 240, 1GB RAM
Rares Vernica, UC Irvine

21. Different algorithms, different behaviors
We present just a few of our results, for more details see the paper.
IMDB Dataset
Rares Vernica, UC Irvine

22. Different datasets, different behaviors
Correlated Dataset
Anticorrelated Dataset
Independent Dataset
Rares Vernica, UC Irvine

23. Rares Vernica, UC Irvine
How big is the Skyline?
Skyline size depends on cardinality, number of selections, and data size.
Rares Vernica, UC Irvine

24. Relaxing join takes time
Self-join on Census Dataset
Rares Vernica, UC Irvine

25. Rares Vernica, UC Irvine
Top-k over Skyline
IMDB Dataset
Rares Vernica, UC Irvine

26. Rares Vernica, UC Irvine
Related Work
Muslea et al.
Alternate forms of conjunctive expressions
Efficient Skyline algorithms
Selection queries
Efficient Top-k algorithms
Require weights for conditions
Muslea deals primarily with expressibility issues without paying attention to the data management issues involved.
We relax queries with selection and join conditions.
Other studies assume that the attributes and ordering of the values are already pre-determined in a single table; our work require us to compute skyline dynamically for a set of tables which are to be join and whose attribute values must be determined on the fly.
Our work considers both the selection and join conditions for relaxation.
Rares Vernica, UC Irvine

27. Rares Vernica, UC Irvine
Conclusions
Query relaxation framework for selections and joins
Lattice-based approach for query relaxation
Efficient relaxation algorithms
Efficiency is a big issue
Rares Vernica, UC Irvine

28. Rares Vernica, UC Irvine
Future Work
Optimum use of the lattice structure
Relax conditions on string attributes
Algorithms applicable outside the databases
Rares Vernica, UC Irvine

29. Questions ?

30. Rares Vernica, UC Irvine

31. Rares Vernica, UC Irvine
Skyline vs. Top-k
Rares Vernica, UC Irvine

32. Skyline vs. Top-k over Skyline
Rares Vernica, UC Irvine