Evaluating Top-k Queries over Web-Accessible Databases

Nicolas BrunoLuis GravanoAmélie MarianColumbia University

2/27/2002 2

“Top-k” Queries Natural in Many Scenarios

Example: NYC Restaurant Recommendation Service.Goal: Find best restaurants for a user:

Close to address: “2290 Broadway”Price around $25Good rating

Query: Specification of Flexible Preferences

Answer: Best k Objects for Distance Function

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Attributes often Handled by External Sources

MapQuest returns the distance between two addresses.NYTimes Review gives the price range of a restaurant.Zagat gives a food rating to the restaurant.

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“Top-k” Query Processing Challenges

Attributes handled by external sources (e.g., MapQuest distance).External sources exhibit a variety of interfaces (e.g., NYTimes Review, Zagat).Existing algorithms do not handle all types of interfaces.

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Processing Top-k Queries over Web-Accessible Data Sources

Data and query modelAlgorithms for sources with different interfacesOur new algorithm: UpperExperimental results

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Data ModelTop-k Query: assignment of weights

and target values to attributes

< $25, “2290 Broadway”, very good >

preferred price close to address preferred rating

weights: <4, 1, 2>

price: most important attribute

Combined in scoring function

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Sorted Access Source S

Return objects sorted by scores for a given query.

Example: Zagat

GetNextS interface

S-SourceAccess Time: tS(S)

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Random Access Source R

Return the score of a given object for a given query.

Example: MapQuest

R-SourceAccess Time: tR(R)

GetScoreR interface

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Query Model

Attributes scores between 0 and 1. Sequential access to sources.Score Ties broken arbitrarily.No wild guesses.One S-Source (or SR-Source) and multiple R-sources. (More on this later.)

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Query Processing Goals

Processing top-k queries over R-Sources.Returning exact answer to top-k query q.Minimizing query response time.Naïve solution too expensive (access all sources for all objects).

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Example: NYC Restaurants

S-Source:Zagat: restaurants sorted by food rating.

R-Sources:MapQuest: distance between two input addresses.User address: “2290 Broadway”

NYTimes Review: price range of the input restaurant.Target Value: $25

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TA Algorithm for SR-Sources

Perform sorted access sequentially to all SR-Sources Completely probe every object found for all attributes using random access.Keep best k objects.Stop when scores of best k objects are no less than maximum possible score of unseen objects (threshold).

Fagin, Lotem, and Naor (PODS 2001)

Does NOT handle R-Sources

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Our Adaptation of TA Algorithm for R-Sources: TA-Adapt

Perform sorted access to S-Source S.Probe every R-Source Ri for newly found object.Keep best k objects.Stop when scores of best k objects are no less than maximum possible score of unseen objects (threshold).

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An Example Execution of TA-AdaptObject

S(Zagat) R1(MQ)

R2(NYT)

Final Score

tS(S)=tR(R1)=tR(R2)=1, w=<3, 2, 1>, k=1

Final Score = (3.scoreZagat + 2.scoreMQ + 1.scoreNYT)/6

Threshold = 1

Total Execution Time = 9

o1

GetNextS(q) Threshold =

0.95

0.9

score

o1

GetScoreR1(q,o1)

Threshold = 0.95

0.1

score

o1

GetScoreR2(q,o1)

Threshold = 0.95

0.5 0.56

score

o1

x

GetNextS(q) Threshold =

0.9

o2 0.8

score

o1

x

o2

GetScoreR1(q,o2)

Threshold = 0.9

0.7

score

o1

x

o2

GetScoreR2(q,o2)

Threshold = 0.9

0.7 0.75

score

o1

x

o2

x

GetNextS(q) Threshold =

0.725

o3 0.45

score

o1

x

o2

x

o3

GetScoreR1(q,o

3) Threshold =

0.725

0.6

score

o1

x

o2

x

o3

GetScoreR2(q,o

3) Threshold =

0.725

0.3 0.55

score

o1

x

o2

x

o3

x

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Improvements over TA-Adapt

Add a shortcut test after each random-access probe (TA-Opt).Exploit techniques for processing selections with expensive predicates (TA-EP).

Reorder accesses to R-Sources.Best weight/time ratio.

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The Upper Algorithm

Selects a pair (object,source) to probe next.Based on the property:

The object with the highest upper bound will be probed before top-k solution is

reached.score

Object is one of top-k objects

score

x Object is not one of top-k objects

score

x

score

x

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Threshold = 1

An Example Execution of Upper

Object

Upper Bound

S(Zagat)

R1(MQ)

R2(NYT)

Final Score

Total Execution Time = 6

0.95

GetNextS(q) Threshold = 0.95

o1 0.9

score

o1

0.10.65

GetScoreR1(q,o1) Threshold = 0.95

score

o1

o2 0.80.9

GetNextS(q) Threshold =

0.9

score

o1 o2

0.7

GetScoreR1(q,o2

) Threshold = 0.9

0.8

score

o1 o2

o3

0.45

0.725

GetNextS(q) Threshold =

0.725

0.8

score

o1 o2

o3

0.750.7

GetScoreR2(q, o2) Threshold = 0.725

0.75

score

o1 o2

x

o3

tS(S)=tR(R1)=tR(R2)=1, w=<3, 2, 1>, k=1

Final Score = (3.scoreZagat + 2.scoreMQ + 1.scoreNYT)/6

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The Upper AlgorithmChoose object with highest upper bound.If some unseen object can have higher upper bound:

Access S-Source SElse:

Access best R-Source Ri for chosen object

Keep best k objectsIf top-k objects have final values higher than maximum possible value of any other object, return top-k objects.Interleaves accesses on objects

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Selecting the Best SourceUpper relies on expected values to make its choices.Upper computes “best subset” of sources that is expected to:

1. Compute the final score for k top objects.2. Discard other objects as fast as possible.

Upper chooses best source in “best subset”.

Best weight/time ratio.

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Experimental Setting: Synthetic Data

Attribute scores randomly generated (three data sets: uniform, gaussian and correlated).tR(Ri): integer between 1 and 10.tS(S) {0.1, 0.2,…,1.0}.Query execution time: ttotalDefault: k=50, 10000 objects, uniform data.Results: average ttotal of 100 queries.Optimal assumes complete knowledge(unrealistic, but useful performance bound)

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Experiments: Varying Number of Objects Requested k

0

30

60

90

120

150

180

210

0 20 40 60 80 100

k

t tota

l

Optimal

Upper

TA-EP

TA-Opt

TA-Adapt

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Experiments: Varying Number of Database Objects N

0

50

100

150

200

250

300

350

0 20000 40000 60000 80000 100000

Number of objects in S-Source S

t tota

l

Optimal

Upper

TA-EP

TA-Opt

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Experimental Setting: Real Web Data

S-Source: Verizon Yellow Pages (sorted by distance)

R-Sources: Subway Navigator Subway time

Altavista Popularity

MapQuest Driving time

NYTimes Review Food and price ratings

Zagat Food, Service, Décor and Price ratings

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Experiments: Real-Web Data

0

1000

2000

3000

4000

5000

6000

nR

Upper

TA-EP

TA-Opt

# o

f R

an

dom

Acc

ess

es

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Evaluation Conclusions

TA-EP and TA-Opt much faster than TA-Adapt.Upper significantly better than all versions of TA.Upper close to optimal.Real data experiments: Upper faster than TA adaptations.

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Conclusion

Introduced first algorithm for top-k processing over R-Sources.Adapted TA to this scenario.Presented new algorithms: Upper and Pick (see paper)

Evaluated our new algorithms with both real and synthetic data.

Upper close to optimal

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Current and Future Work

Relaxation of the Source ModelCurrent source model limitedAny number of R-Sources and SR-SourcesUpper has good results even with only SR-Sources

ParallelismDefine a query model for parallel access to sourcesAdapt our algorithms to this model

Approximate Queries

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ReferencesTop-k Queries:

Evaluating Top-k Selection Queries, S. Chaudhuri and L. Gravano. VLDB 1999

TA algorithm: Optimal Aggregation Algorithms for Middleware, R. Fagin, A. Lotem, and M. Naor. PODS 2001

Variations of TA:Query Processing Issues on Image (Multimedia) Databases, S. Nepal and V. Ramakrishna. ICDE 1999Optimizing Multi-Feature Queries for Image Databases, U. Güntzer, W.-T. Balke, and W.Kießling. VLDB 2000

Expensive PredicatesPredicate Migration: Optimizing queries with Expensive Predicates, J.M. Hellerstein and M. Stonebraker. SIGMOD 1993

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Real-web Experiments

0

1000

2000

3000

4000

5000

6000

t total Upper

TA-EP

TA-Opt

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Real-web Experiments with Adaptive Time

0

200

400

600

800

1000

1200

Query 1 Query 2 Query 3 Query 4

t to

tal (

se

co

nd

s)

TA-Opt TA-EP Upper

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Relaxing the Source Model

0

20000

40000

60000

80000

100000

120000

140000

160000

180000

200000

0 1 2 3 4 5 6 7

Number of SR-Sources (out of 6 sources)

t tota

l

Upper_Weight Upper-Relaxed TA-Upper TAz-EP-NODUP TAz-EP

Upper

TA-EP

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Upcoming Journal Paper

Variations of UpperSelect best source

Data StructuresComplexity AnalysisRelaxing Source Model

Adaptation of our AlgorithmsNew Algorithms

Variations of Data and Query Model to handle real web data

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Optimality

TA instance optimal over:Algorithms that do not make wild guesses.Databases that satisfy the distinctness property.

TAZ instance optimal over:Algorithms that do not make wild guesses.

No complexity analysis of our algorithms, but experimental evaluation instead