1. Automated Ranking of
Database Query Results
Sanjay Agrawal, Surajit Chaudhari, Gautam Das,
Aristides Gionis
Presented By: Upa Gupta

2. Contents
 Introduction
 IDF Similarity
 QF Similarity
 Breaking Ties
 Implementation
 ITA Algorithm
 Conclusion

3. Introduction
 Database is Boolean Query Model
 E.g.. Select * WHERE MFR_Country = “Germany”
AND Type = “Sports” AND Manufacture =
“Volkswagon”
 Problems in Database
 Empty Answers
 Too selective query leading to Null Result Set
 Many Answers
 General query leading to too many results

4. Introduction
 Ranking of Database Query Results using IR
techniques.
 Applying TF-IDF concept to database that is
based on the frequency of the attribute values.
 Need to extend the TF-IDF to Numerical Domains
 IDF Similarity is discussed in paper
 Collecting WORKLOAD and using it for ranking.
 QF Similarity, leveraging Workload Information

5. Introduction
 Many Answers Problem is solved using Top-K
Query Processing
 Index-based Threshold Algorithm (ITA)
developed exploiting IDF/QF Similarity.

6. IDF Similarity
 What is TF-IDF Technique?
 Given a set of documents and a query,
documents are ranked based on TF and IDF of
the words of the document.
 Adapting IDF concept to Database
containing only categorical Attributes
t=<t1,……tm>  values of Attribute A
n  Number of tuples in the database

7. IDF Similarity
 For all the values of t:
 Frequency F(t) is defined as no. of tuples having
Attribute A = t
 IDF is calculated as:
IDF(t) = log(n/F(t))
 For pair of values u and v in Attribute A domain
S(u,v) = IDF (u) if u=v otherwise 0
 For tuple T and Query Q for all the Attributes
(A1…Ak) m
SIM(T,Q) = S ( t , q )
k k k
k 1

8. IDF Similarity
 Example:
CAR_ID MODEL MFR MFR_Country Type
1 SLR Mercedes Germany Sports
2 A6 Audi Germany Executive
3 R8 Audi Germany Sports
4 Gallardo Lamborghini Italy Sports
Query Q: Select * WHERE MFR_Country =
“Germany” AND Type = “Sports” AND MFR =
“Volkswagon”

9. IDF Similarity
n=4
F (MFR_Country = Germany) = 3
IDF(MFR_Country = Germany) = log(n/F(MFR_Country = Germany))
= log(4/3) = 0.287
Similarly,
IDF(MFR_Country=Italy) = 1.38 IDF(MFR = Audi) = 0.69
IDF(MFR = Lamborghini) = 1.38 IDF(MFR = Mercedes) =
1.38
IDF(Type = Sports) = 0.287 IDF(Type = Executive) = 1.38
Similarity of 1st tuple with Q = SIM(T,Q)
= S(Germany, Germany) + S(Sports, Sports) + S(Mercedes, Volkswagen)
= IDF(MFR_Country = Germany) + IDF(Type = Sports) + 0
= 0.287+0.287+0 = 0.574

10. IDF Similarity
 Consider a Numeric Attribute in DB e.g. PRICE
 SIMPLE SOLUTION: Discretize the data between ranges
 Consider two Range: (0, 50) and (51, 100)
 Values 49 and 52 are considered completely dissimilar.
 Frequency of a numeric value t of an attribute is defined as
2
ti t
n 1/ 2
h
sum of contributions to t
F(t) = e from every ti database.
i
IDF(t) = log(n/F(t)) h = bandwidth parameter
S(t,q) = density at t of a Gaussian Distribution centered q.
2
ti t
1/ 2
h
S(t,q) = e IDF ( q )

11. IDF Similarity
 Consider following Query:
 Select * where MFR IN (“Germany”, “Italy”,
”Japan”) m
 SIM(T,Q) = max S k ( t k , q )
q Qk
k 1

12. QF Similarity
 Problems with IDF:
 In a realtor database, more homes are built in
recent years such as 2007 and 2008 as
compared to 1980 and 1981.Thus recent years
have small IDF. Yet newer homes have higher
demand.
 In a bookstore DB, demand for an author is due
to factor other than no. of books he has written

13. QF Similarity
 WORKLOAD: Past Queries
 Importance of attribute values is determined
by frequency of their occurrence in workload.
 As in above eg, frequency of queries
requesting homes in 2010 are more than of
the year 1981

14. QF Similarity
 For categorical data
 RQF(q) = raw frequency of occurrence of value q of
attribute A in query strings of workload
 RQFMax = raw frequency of most frequently occurring
value in workload
 Query frequency QF(q) = RQF(q)/RQFMax
 s(t, q) = QF(q), if q = t otherwise 0
 QF resembles TF

15. QF Similarity
 Consider Workload containing following
values of Attribute TYPE:
{Sports, Executive, Luxury, Sports, Sports, Executive}
QF(Executive) = RQF(Executive)/RQFMax
= 2/3

16. QF Similarity
 Similarity between pairs of different categorical
attribute values can also be derived from workload
eg. To find S(Audi, Mercedes)
 Similarity coefficient between t and q in this case is
defined by jaccard coefficient scaled by QF factor
as shown below.
S(t,q)=J(W(t),W(q))/QF(q)
 W(t) = Subset of queries in workload W in which
categorical value t occurs in an IN clause

17. QF-IDF
 For QF-IDF Similarity
S(t,q)=QF(q) *IDF(q) when t=q otherwise 0

18. BREAKING TIES
 IF SIM(t1, q) = SIM (t2, q)
 Which Should be ranked Higher??
 QF and IDF partitions database into classes
CAR_ID MODEL MFR MFR_Country Type
1 SLR Mercedes Germany Sports
2 A6 Audi Germany Executive
3 R8 Audi Germany Sports
4 Gallardo Lamborghini Italy Sports
 Q: SELECT * WHERE Type = “Sports” AND MFR_Country
= “Germany”

19. Breaking Ties with QF
 Determine weights of missing attribute values that
reflect their “global importance” using workload.
 Global Imp = log( QF ( t k )) tk= missing attribute
k
 Missing Attributes for Q: MFR and Model

20. Breaking Ties with QF
 Considering Workload with following values of MFR and
Model
MFR{Audi, Audi, Lamborghini, Mercedes, Lamborghini, Audi}
Model{R8, A6, Gallardo, SLR, Gallardo, A6}
 QF(SLR) = ½ = 0.5 QF(Mercedes) = 1/3 = 0.33
1 SLR Mercedes Germany Sports
 Global Imp = log(0.5) + log(0.33).
 NEGATIVE VALUES of Global Imp ??

21. Breaking Ties with IDF
 Tuples with large IDF(occuring infequently) of
missing attributes are ranked higher
 Cars which are not popular are ranked higher
 Tuples with small IDF of missing attributes
are ranked higher
 Cars having Moonroof will be ranked less which
is a desirable feature.

22. Implementation
 Pre-processing component
 Query–processing component

23. Implementation
 Pre Processing Component
 Compute and store a representation of similarity
function(QF-IDF, QF, IDF) in auxiliary database
tables

24. Implementation
 Query Processing Component
 Job: Retrieving Top-K results from Database
 ITA Algorithm: Use of Fagin’s Threshold Algorithm
and Similarity function
 Sorted Access: Along any attribute Ak, TIDs of tuples
are retrieved.
 Random Access: entire tuple corresponding to a TID
is retrieved.

25. ITA Algorithm
 Repeat
 Initialize Top-K Buffer to empty
 For each k = 1 to p
 TID = Index of the next Tuple is retrieved from the ordered
Lists
 T = Complete Tuple is retrieved for TID
 Compute value of Ranking Function
 If Rank of T is higher than the rank of lowest ranking tuple in
Top-K Buffer, then update Top-K Buffer
 If Stopping Condition has been reached then Exit
 End For
 Until all index of the tuples have been seen.

26. ITA Algorithm
Stopping Condition
Hypothetical tuple – current value a1,…, ap
for A1,… Ap, corresponding to index seeks on
L1,…, Lp and qp+1,….. qm for remaining
columns from the query directly.
Termination – Similarity of hypothetical tuple
to the query< tuple in Top-k buffer with least
similarity.

27. ITA for Numeric columns
 Consider a query has condition Ak = qk for a
numeric column Ak.
 Two index scan is performed on Ak.
 First retrieve TID’s > qk in incresing order.
 Second retrieve TID’s < qk in decreasing order.
 We then pick TID’s from the merged stream.

28. Conclusion
 Automated Ranking Infrastructure for SQL
databases.
 Extended TF-IDF based techniques from
Information retrieval to numeric and mixed
data.
 Implementation of Ranking function that
exploited Fagin’s TA

29. THANK YOU