Data Integration

Aggregate Query Answering under Uncertain Schema Mappings

Avigdor Gal, Maria Vanina Martinez, Gerardo I. Simari, VS Subrahmanian

Presented By Stephen Lynn

Data Integration

Overview Aggregate Queries Probabilistic Schema Mapping Goals/Objectives Aggregate Processing (3 proposals) By-Table Algorithm By-Tuple Algorithm Evaluation Analysis

Data Integration

Aggregate Queries

COUNT, MIN, MAX, SUM, AVG

ID Price Quantity1 2.30 2

2 3.20 4

3 7.34 1

4 8.29 20

5 3.32 3

Simple PTIME algorithms to compute

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Probabilistic Schema Mappings

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By-Table vs By-Tuple

Tuple – consider all possible mappings for each tuple

Table – single mapping for entire table P(date→postedDate) = 0.7 P(date→reducedDate) = 0.3

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Goals/ObjectivesImpact Analysis of Probabilistic Schemas on Aggregate Queries

Aggregate Query AlgorithmsTime Complexity AnalysisEvaluation

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Aggregation Methods

RangeDistribution

Expected Value

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Method Relationships Distribution

Most time consumingMost information

RangeComputed directly from distribution

Expected ValueComputed directly from distribution

More efficient ways to compute

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By-Table Algorithm

All PTIME computable

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By-Tuple Algorithm (COUNT)

O(n * m)

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Example By-Tuple (COUNT)

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Time Complexity

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Evaluation Empirical Evaluation

Real-world dataset (eBay)Synthetic dataset

Evaluate Time ComplexityVary tuple numbersVary attribute mappings

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Evaluation Results

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Evaluation Results

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Evaluation Results

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Analysis Strengths

Effect of probabilistic schemas on aggregatesNice PTIME algorithms

WeaknessesEvaluation was obviousBy-Table results biased by database optimizations

Future Work Improve algorithmsExtend to sub-queriesHeuristics