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 IDPriceQuantity Simple PTIME algorithms to compute

Data Integration Probabilistic Schema Mappings

Data Integration 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

Data Integration Goals/Objectives  Impact Analysis of Probabilistic Schemas on Aggregate Queries  Aggregate Query Algorithms  Time Complexity Analysis  Evaluation

Data Integration Aggregation Methods Range Distribution Expected Value

Data Integration Method Relationships  Distribution  Most time consuming  Most information  Range  Computed directly from distribution  Expected Value  Computed directly from distribution More efficient ways to compute

Data Integration By-Table Algorithm All PTIME computable

Data Integration By-Tuple Algorithm (COUNT) O(n * m)

Data Integration Example By-Tuple (COUNT)

Data Integration Time Complexity

Data Integration Evaluation  Empirical Evaluation  Real-world dataset (eBay)  Synthetic dataset  Evaluate Time Complexity  Vary tuple numbers  Vary attribute mappings

Data Integration Evaluation Results

Data Integration Evaluation Results

Data Integration Evaluation Results

Data Integration Analysis  Strengths  Effect of probabilistic schemas on aggregates  Nice PTIME algorithms  Weaknesses  Evaluation was obvious  By-Table results biased by database optimizations  Future Work  Improve algorithms  Extend to sub-queries  Heuristics