Optimization of Preference Queries with Multiple Constraints

Transcription

1 Optimization of Preference Queries with Multiple Constraints Markus Endres and Werner Kießling Speaker: Timotheus Preisinger University of Augsburg Germany 2nd International Workshop on Personalized Access, Profile Management, and Context Awareness: Databases Optimization of Preference Queries under Hard Sum Constraints PersDB 1 / 26

2 Outline 1 Motivation 2 Preference Algebra 3 Optimization Techniques Dominance Criterion Selection Operators Rewriting Technique 4 Experimental Results 5 Conclusion Optimization of Preference Queries under Hard Sum Constraints PersDB 2 / 26

3 Motivation Diet sheet Multiple Hard constraints nutritional requirements restriction on calories ( 1100 kcal) restriction on vitamin C ( 38 g) restriction on fat ( 9 g) Soft constraints - Preferences Chicken soup as starter Main course should be beef Beef with lowest cholesterol Red wine for beverage, less important Optimization of Preference Queries under Hard Sum Constraints PersDB 3 / 26

4 Motivation Diet Sheet - Database Query Database Query Query on USDA Database to retrieve diet sheet More than 7000 types of food Relations for Soups, Meats, Beverages Must consider hard and soft constraints Using Preference SQL Kießling & Köstler 2002 Combining hard and soft constraints Optimization of Preference Queries under Hard Sum Constraints PersDB 4 / 26

5 Motivation Diet Sheet - Preference SQL Preference SQL Kießling & Köstler 2002 SELECT S. name, M. name, B. name FROM Soups S, Meats M, Beverages B WHERE S.cal + M.cal + B.cal <= 1100 AND S.Vc + M.Vc + B.Vc >= 38 AND S.fat + M.fat + B.fat <= 9 multiple hard constraint PREFERRING soft constraints S. name IN ( Chicken soup ) AND (M. name IN ( Beef ) AND M. Cholesterol LOWEST ) PRIOR TO B. name IN ( Red wine ) Hard and Soft Constraints SQL query with multiple hard constraints extended by soft constraints - PREFERRING Optimization of Preference Queries under Hard Sum Constraints PersDB 5 / 26

6 Operator Tree Transform Preference SQL into Operator Tree Preference SQL SELECT S. name, M. name, B. name FROM Soups ss, Meats M, Beverages B WHERE S.cal + M.cal + B.cal <= 1100 AND S.Vc + M.Vc + B.Vc >= 38 AND S.fat + M.fat + B.fat <= 9 PREFERRING S. name IN ( Chicken soup ) AND (M. name IN ( Beef ) AND M. Cholesterol LOWEST ) PRIOR TO B. name IN ( Red wine ) Soft Constraints Hard Constraints Soups Meats Beverages Optimization of Preference Queries under Hard Sum Constraints PersDB 6 / 26

7 Problem Description High memory and computation costs State-of-the-art: Join algorithms, but without preferences Ilyas, Liu Optimization for one constraint with preferences Endres, Kießling Full cartesian product necessary Pair-wise operators can t remove intermediate results Hard constraints include different relations Soft Constraints Hard Constraints Soups Meats Beverages Optimization of Preference Queries under Hard Sum Constraints PersDB 7 / 26

8 Problem Description Soft Constraints Target Reduce memory and computation costs for Preference Queries with Multiple Constraints Hard Constraints Soups Meats Beverages Optimization of Preference Queries under Hard Sum Constraints PersDB 7 / 26

9 Outline 1 Motivation 2 Preference Algebra 3 Optimization Techniques Dominance Criterion Selection Operators Rewriting Technique 4 Experimental Results 5 Conclusion Formal description necessary Optimization of Preference Queries under Hard Sum Constraints PersDB 8 / 26

10 Preference Algebra Kießling 2002 Preference Model Necessary Preference is a strict partial order P = (A, < P ), < P dom(a) dom(a) x < P y means I like y more than x Preference constructors Numerical: Lowest, Highest, Around,... Categorical: POS, NEG,... Complex preferences Pareto: P 1 P 2 P 1 and P 2 are equally important Prioritized: P 1 & P 2 P 1 is more important than P 2 Optimization of Preference Queries under Hard Sum Constraints PersDB 9 / 26

11 The BMO Query Model Compute optimal outcome with respect to preference statements. Best-Matches-Only only the best matches w.r.t the strict partial order of a preference P all tuples in BMO are undominated by others regarding P preference selection (Chomicki s Winnow-Operator) σ[p](r) := {t R t R : t[a] < P t [A]} Optimization of Preference Queries under Hard Sum Constraints PersDB 10 / 26

12 Preference Model Example Preference SQL SELECT S. name, M. name, B. name FROM Soups S, Meats M, Beverages B WHERE S.cal + M.cal + B.cal <= 1100 AND S.Vc + M.Vc + B.Vc >= 38 AND S.fat + M.fat + B.fat <= 9 PREFERRING S. name IN ( Chicken soup ) AND (M. name IN ( Beef ) AND AND M. Cholesterol LOWEST ) PRIOR TO B. name IN ( Red wine ) Preference Algebra σ[p 1 P 2 & P 3 ] σ S.cal + M.cal + B.cal 1100 S.Vc + M.Vc + B.Vc 38 S.fat + M.fat + B.fat 9 (S M B) with P 1 = POS(S.name, {Chicken soup}) P 2 = POS(M.name, {Beef }) LOWEST (cholesterol) P 3 = POS(B.name, {Red wine}) Optimization of Preference Queries under Hard Sum Constraints PersDB 11 / 26

13 Outline 1 Motivation 2 Preference Algebra 3 Optimization Techniques Dominance Criterion Selection Operators Rewriting Technique 4 Experimental Results 5 Conclusion Extension of MPref 2008 Paper Optimization of Preference Queries under Hard Sum Constraints PersDB 12 / 26

14 A Dominance Criterion Example Preference SQL SELECT S. name, M. name, B. name FROM Soups S, Meats M, Beverages B WHERE S.cal + M.cal + B.cal <= 1100 AND S.Vc + M.Vc + B.Vc >= 38 AND S.fat + M.fat + B.fat <= 9 PREFERRING S. name IN ( Chicken soup ) AND... Dominance Criterion S4 < P1 S3 S4.cal S3.cal S4.Vc S3.Vc S4.fat S3.fat Soups ID Name Cal Vc Fat S1 Vegetable S2 Chicken S3 Chicken //// S4 ////////// Noodle ///// 453 //1 //// 17 Optimization of Preference Queries under Hard Sum Constraints PersDB 13 / 26

15 Query A Dominance Criterion Definition Q := σ[p 1 Φ... Φ P r ] σ F1... F n (R 1... R r ) R i (A i1,..., A in, B i ), P i = (B i, < Pi ), Φ {, &}, F i hard constraints with Θ {<,, >,, =, }, If tuples t, t R i such that t[b i ] < Pi t [B i ] t[a i1 ] ˆΘ1 t [A i1 ]... and ˆΘ j defined as 8 < ˆΘ j := : t[a ir ] ˆΘ r t [A ir ] iff Θ j {, <} iff Θ j {, >} = iff Θ j {=, } then an optimal solution exists without the tuple t R i. Optimization of Preference Queries under Hard Sum Constraints PersDB 14 / 26

16 Query A Dominance Criterion Definition Q := σ[p 1 Φ... Φ P r ] σ F1... F n (R 1... R r ) R i (A i1,..., A in, B i ), P i = (B i, < Pi ), Φ {, &}, F i hard constraints with Θ {<,, >,, =, }, If tuples t, t R i such that t[b i ] < Pi t [B i ] t[a i1 ] ˆΘ1 t [A i1 ]... and ˆΘ j defined as 8 < ˆΘ j := : t[a ir ] ˆΘ r t [A ir ] iff Θ j {, <} iff Θ j {, >} = iff Θ j {=, } then an optimal solution exists without the tuple t R i. CUTOFF Preference Constructor Strict partial order P c := CUTOFF (P) : Evaluation of the Dominance Criterion Optimization of Preference Queries under Hard Sum Constraints PersDB 14 / 26

17 Outline 1 Motivation 2 Preference Algebra 3 Optimization Techniques Dominance Criterion Selection Operators Rewriting Technique 4 Experimental Results 5 Conclusion Additional hard selection operators Optimization of Preference Queries under Hard Sum Constraints PersDB 15 / 26

18 Constraints: Selection Operators Domain Knowledge S.cal + M.cal + B.cal 1100 kcal S.Vc + M.Vc + B.Vc 38 g S.fat + M.fat + B.fat 9 g Introduce NEW Constraints S.Cal + M.Cal + B.Cal 1100 S.Cal 1100 (M.Cal + B.Cal) A tuple with S.Cal 1100 (min(m.cal) + min(b.cal)) can t fulfill the hard constraint Optimization of Preference Queries under Hard Sum Constraints PersDB 16 / 26

19 Selection Operators Example Constraint S.Cal + M.Cal + B.Cal 1100 Soups ID Name Cal Vc Fat S1 Vegetable S2 Chicken S3 Chicken S4 Noodle Meats ID Name Cal Vc Fat Chol M1 Turkey M2 Beef M3 Pork Beverages ID Name Cal Vc Fat B1 Red Wine B2 Red Wine B3 Coke B4 Lemonade B5 Red Wine Optimization of Preference Queries under Hard Sum Constraints PersDB 17 / 26

20 Selection Operators Example Constraint S.Cal + M.Cal + B.Cal 1100 min(m.cal) + min(b.cal) = 903 S.Cal <= 197 Soups ID Name Cal Vc Fat S1 Vegetable S2 Chicken S.Cal > 197 //// S3 /////////// Chicken ///// 198 //9 //2 S.Cal > 197 //// S4 ////////// Noodle ///// 453 //1 //// 17 Meats ID Name Cal Vc Fat Chol M1 Turkey M2 Beef M3 Pork Beverages ID Name Cal Vc Fat B1 Red Wine B2 Red Wine B3 Coke B4 Lemonade B5 Red Wine Optimization of Preference Queries under Hard Sum Constraints PersDB 17 / 26

21 Selection Operators Example Constraint S.Cal + M.Cal + B.Cal 1100 min(s.cal) + min(b.cal) = 144 M.Cal <= 956 Soups ID Name Cal Vc Fat S1 Vegetable S2 Chicken S.Cal > 197 //// S3 /////////// Chicken ///// 198 //9 //2 S.Cal > 197 //// S4 ////////// Noodle ///// 453 //1 //// 17 Meats ID Name Cal Vc Fat Chol M1 Turkey M2 Beef M3 Pork Beverages ID Name Cal Vc Fat B1 Red Wine B2 Red Wine B3 Coke B4 Lemonade B5 Red Wine Optimization of Preference Queries under Hard Sum Constraints PersDB 17 / 26

22 Selection Operators Example Constraint S.Cal + M.Cal + B.Cal 1100 min(s.cal) + min(m.cal) = 877 B.Cal <= 223 Soups ID Name Cal Vc Fat S1 Vegetable S2 Chicken S.Cal > 197 //// S3 /////////// Chicken ///// 198 //9 //2 S.Cal > 197 //// S4 ////////// Noodle ///// 453 //1 //// 17 Meats ID Name Cal Vc Fat Chol M1 Turkey M2 Beef M3 Pork Beverages ID Name Cal Vc Fat B1 Red Wine B2 Red Wine B3 Coke B.Cal > 223 //// B4 ////////////// Lemonade ///// 281 //// 17 //2 B.Cal > 223 //// B5 Red//////// Wine ///// 400 //4 //0 Optimization of Preference Queries under Hard Sum Constraints PersDB 17 / 26

23 Selection Operators Example Constraint ALL additional selection operators and dominance criterion Soups ID Name Cal Vc Fat S1 Vegetable S.Vc < 3 //// S2 /////////// Chicken ///// 110 //2 //4 S.Cal > 197 //// S3 /////////// Chicken ///// 198 //9 //2 DC, S.Cal > 197 //// S4 ////////// Noodle ///// 453 //1 //// 17 Meats ID Name Cal Vc Fat Chol M1 Turkey M2 Beef DC ///// M3 /////// Pork ///// 911 //// 12 //// 12 //// 15 Beverages ID Name Cal Vc Fat B.Vc < 12 //// B1 Red//////// Wine //// 85 //1 //0 B2 Red Wine B3 Coke B.Cal > 223 //// B4 ////////////// Lemonade ///// 281 //// 17 //2 B.Cal > 223 //// B5 Red//////// Wine ///// 400 //4 //0 Optimization of Preference Queries under Hard Sum Constraints PersDB 17 / 26

24 Outline 1 Motivation 2 Preference Algebra 3 Optimization Techniques Dominance Criterion Selection Operators Rewriting Technique 4 Experimental Results 5 Conclusion Query optimizer integration Optimization of Preference Queries under Hard Sum Constraints PersDB 18 / 26

25 Rewriting Technique Operator Tree σ[p 1 Φ... Φ P r ] σ F1... F r R 1 R 2 R r Query Transformation 1) 2) Optimization of Preference Queries under Hard Sum Constraints PersDB 19 / 26

26 Rewriting Technique Operator Tree σ[p 1 Φ... Φ P r ] σ F1... F r σ A1 Θ 1 b 1 σ Ar Θ r b r σ A2 Θ 2 b 2 R r Query Transformation 1) Get lower and upper bounds and insert additional selection operators R 1 R 2 Optimization of Preference Queries under Hard Sum Constraints PersDB 19 / 26

27 σ[p 1 Φ... Φ P r ] σ F1... F r Rewriting Technique Operator Tree σ[p rc ] σ[p 1c ] σ[p 2c ] σ Ar Θ r b r σ A1 Θ 1 b 1 σ A2 Θ 2 b 2 R r Query Transformation 1) Get lower and upper bounds and insert additional selection operators 2) Apply dominance criterion R 1 R 2 Optimization of Preference Queries under Hard Sum Constraints PersDB 19 / 26

28 Outline 1 Motivation 2 Preference Algebra 3 Optimization Techniques Dominance Criterion Selection Operators Rewriting Technique 4 Experimental Results 5 Conclusion Optimization of Preference Queries under Hard Sum Constraints PersDB 20 / 26

29 Experimental Results USDA - National Nutrient Database for Standard Reference USDA - A Real-World Database More than 7000 types of food 3 relations: 500 soups meats beverages about possible combinations Preference SQL engine (Java) Integrated Preference Optimizer With and without rewriting Optimization of Preference Queries under Hard Sum Constraints PersDB 21 / 26

30 Experimental Results Different Hard Constraints Test query SELECT S. name, M. name, B. name FROM Soups S, Meats M, Beverages B WHERE S.cal + M.cal + B.cal <= max cal AND S.Vc + M.Vc + B.Vc >= min vc AND S.fat + M.fat + B.fat <= max fat PREFERRING S. name IN ( Chicken soup ) AND (M. name IN ( Beef ) AND M. Cholesterol LOWEST ) PRIOR TO B. name IN ( Red wine ) Optimization of Preference Queries under Hard Sum Constraints PersDB 22 / 26

31 Test query Experimental Results Different Hard Constraints SELECT S. name, M. name, B. name FROM Soups S, Meats M, Beverages B WHERE S.cal + M.cal + B.cal <= max cal AND S.Vc + M.Vc + B.Vc >= min vc AND S.fat + M.fat + B.fat <= max fat PREFERRING S. name IN ( Chicken soup ) AND (M. name IN ( Beef ) AND M. Cholesterol LOWEST ) PRIOR TO B. name IN ( Red wine ) Response time (s) Response time (s) No rewriting SO DC DC+SO max_cal x100 DC DC+SO max_cal x100 Optimization of Preference Queries under Hard Sum Constraints PersDB 22 / 26

32 Experimental Results Different Relation Sizes Test query SELECT S. name, M. name, B. name FROM Soups S, Meats M, Beverages B WHERE S.cal + M.cal + B.cal <= 1100 AND S.Vc + M.Vc + B.Vc >= 38 AND S.fat + M.fat + B.fat <= 9 PREFERRING S. name IN ( Chicken soup ) AND (M. name IN ( Beef ) AND M. Cholesterol LOWEST ) PRIOR TO B. name IN ( Red wine ) Optimization of Preference Queries under Hard Sum Constraints PersDB 23 / 26

33 Test query Experimental Results Different Relation Sizes SELECT S. name, M. name, B. name FROM Soups S, Meats M, Beverages B WHERE S.cal + M.cal + B.cal <= 1100 AND S.Vc + M.Vc + B.Vc >= 38 AND S.fat + M.fat + B.fat <= 9 PREFERRING S. name IN ( Chicken soup ) AND (M. name IN ( Beef ) AND M. Cholesterol LOWEST ) PRIOR TO B. name IN ( Red wine ) Response time (s) Response time (s) No rewriting SO DC DC+SO 0 1.5M 22.5M 40.0M 62.5M 87.5M Number of combinations DC DC+SO 0 1.5M 22.5M 40.0M 62.5M 87.5M Number of combinations Optimization of Preference Queries under Hard Sum Constraints PersDB 23 / 26

34 Outline 1 Motivation 2 Preference Algebra 3 Optimization Techniques Dominance Criterion Selection Operators Rewriting Technique 4 Experimental Results 5 Conclusion Optimization of Preference Queries under Hard Sum Constraints PersDB 24 / 26

35 Summary and Outlook Summary Preference queries with multiple hard constraints Diet sheet, tourism (overall price), planning tasks,... Optimization based on dominance criterion Additional selection operators Experimental results on USDA real-world DB Outlook Consider further optimization techniques Develop special join algorithms to avoid complete cartesian product Optimization of Preference Queries under Hard Sum Constraints PersDB 25 / 26

36 {endres, kiessling, Optimization of Preference Queries under Hard Sum Constraints PersDB 26 / 26