CSE 562 Database Systems

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1 Outline Query Optimization CSE 562 Database Systems Query Processing: Algebraic Optimization Some slides are based or modified from originals by Database Systems: The Complete Book, Pearson Prentice Hall 2 nd Edition 2008 Garcia-Molina, Ullman, and Widom Overview elational algebra level Algebraic Transformations Detailed query plan level Estimate Costs Estimating size of results Estimating # of IOs Generate and compare plans UB CSE 562 UB CSE elational Algebra Optimization Algebraic ewritings: Commutative and Associative Laws Transformation rules (preserve equivalence) What are good transformations? Cartesian Product Commutative S S Associative T S T S Natural Join S S Question 1: Do the above hold for both sets and bags? Question 2: Do commutative and associative laws hold for arbitrary Theta Joins? S T S T UB CSE UB CSE

2 Algebraic ewritings: Commutative and Associative Laws Algebraic ewritings for Selection: Decomposition of Logical Connectives Commutative Associative Union S S S T T S Intersection S S S T T S Does it apply to bags? Question 1: Do the above hold for both sets and bags? Question 2: Is difference commutative and associative? UB CSE UB CSE Algebraic ewritings for Selection: Decomposition of Negation Pushing Selection Through Binary Operators: Union and Difference Question Complete Union Difference Exercise: Do the rules for intersection UB CSE UB CSE

3 Pushing Selection Through Cartesian Product and Join ules: π + σ combined The right direction requires that cond refers to S attributes only Let X = subset of attributes Z = attributes in predicate P (subset of attributes) The right direction requires that cond refers to S attributes only The right direction requires that all the attributes used by cond appear in both and S Exercise: Do the rule for theta join UB CSE UB CSE Pushing Simple Projections Through Binary Operators: Union Pushing Simple Projections Through Binary Operators: Join and Product A projection is simple if it only consists of an attribute list Union B is the list of attributes that appear in A Similar for C Question 1: Does the above hold for both bags and sets? Question 2: Can projection be pushed below intersection and difference? Answer for both bags and sets UB CSE Question: What is B and C? Exercise: Write the rewriting rule that pushes projection below theta join UB CSE

4 ules: π + σ + combined Projection Decomposition Let X = set of attributes Y = set of attributes XY = X U Y Z = Z U {attributes used in cond} UB CSE UB CSE Projection Decomposition Some ewriting ules elated to Aggregation: SUM σ cond [SUM GroupbyList;GroupedAttribute esultattribute ()] SUM GroupbyList;GroupedAttribute esultattribute [σ cond ()] if cond involves only the GroupbyList SUM GL;GA A ( S) PLUS A1,A2:A [(SUM GL;GA A1 ) (SUM GL;GA A2 S)] SUM GL2;A1 A2 [SUM GL1;GA A1 ()] SUM GL2:GA A2 () Question: does the above hold for both bags and sets? UB CSE UB CSE

5 Derived ules: σ + combined Derivation for first one More ules can be Derived: σp q ( S) = [σp ()] [σq (S)] σp q m ( S) = σm[σp () σq (S)] σpvq ( S) = [σp () S] U [ σq (S)] σp q ( S) = σp[σq ( S)] = σp[ σq (S)] = [σp ()] [σq (S)] p only at q only at S m at both and S UB CSE UB CSE Which are good transformations? Conventional Wisdom: Do Projects Early σp1 p2 () σp1[σp2 ()] σp ( S) [σp ()] S S S πx[σp ()] πx{σp[πxz ()]} UB CSE UB CSE

6 But More Transformations in Textbook What if we have A, B indexes? B = cat A=3 Eliminate common sub-expressions Other operations: duplicate elimination Intersect pointers to get pointers to matching tuples UB CSE UB CSE Bottom line No transformation is always good at the logical query plan level Usually good: early selections elimination of Cartesian products elimination of redundant sub-expressions Many transformations lead to promising plans Commuting/rearranging joins In practice too combinatorially explosive to be handled as rewriting of logical query plan UB CSE