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Lecture 10 Query Optimization II Automatic Database Design

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Recap: Query Planning Use analytical cost to estimate time needed for a query execution plan tree Selectivity (fraction of tuples returned from input): – col = value: 1/ICARD– 1/nth of # of unique col values, 1/10 if no index – col > value: (value – max) / (max – min) or 1/3 – col1 = col2: 1/max(ICARD(c1), ICARD(c2)) or 1/10

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Selinger Heuristics Push down all filters and projections Skip cross-joins Left-deep plans only Get from O(n!) to O(2^n) optimization time

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Selinger Optimizer Algorithm algorithm: compute optimal way to generate every sub-join: size 1, size 2,... n (in that order) e.g. {A}, {B}, {C}, {AB}, {AC}, {BC}, {ABC} R set of relations to join For i in {1...|R|}: for S in {all length i subsets of R}: optjoin(S) = a join (S-a), where a is the relation that minimizes: cost(optjoin(S-a)) + min. cost to join optjoin(S-a) to a + min. access cost for a Precomputed in previous iteration!

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Selinger, as code R set of relations to join For i in {1...|R|}: for S in {all length i subsets of R}: optcost s = ∞ optjoin S = ø for a in S: //a is a relation c = optcost s-a + min. cost to join optjoin s-a to a + min. access cost for a if c < optcost s optcost s = c optjoin s = optjoin s-a joined optimally w/ a This is the same algorithm as on the previous slide, written differently Pre-computed in previous iteration!

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Example 4 Relations: ABCD (only consider NL join) Optjoin: A = best way to access A (e.g., sequential scan, or predicate pushdown into index...) B = " " " " B C = " " " " C D = " " " " D {A,B} = AB (or BA) {A,C} = AC (or CA) {B,C} = BC (or CB) {A,D} … {B,D} {C,D} R set of relations to join For i in {1...|R|}: for S in {all length i subsets of R}: optjoin(S) = a join (S-a), where a is the relation that minimizes: cost(optjoin(S-a)) + min. cost to join (S-a) to a + min. access cost for a Optjoin

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Example (con’t) Optjoin {A,B,C} = remove A: ({B,C})A remove B: ({A,C})B remove C: ({A,B})C {A,C,D} = … {A,B,D} = … {B,C,D} = … … {A,B,C,D} = remove A: ({B,C,D})A remove B: ({A,C,D})B remove C: ({A,B,D})C remove D: ({A,B,C})D R set of relations to join For i in {1...|R|}: for S in {all length i subsets of R}: optjoin(S) = a join (S-a), where a is the relation that minimizes: cost(optjoin(S-a)) + min. cost to join (S-a) to a + min. access cost for a Optjoin

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Complexity Number of subsets of set of size n = |power set of n| = 2 n (here, n is number of relations) How much work per subset? Have to iterate through each element of each subset, so this at most n n2 n complexity (vs n!) n=12 49K vs 479M R set of relations to join For i in {1...|R|}: for S in {all length i subsets of R}: optjoin(S) = a join (S-a), where a is the relation that minimizes: cost(optjoin(S-a)) + min. cost to join (S-a) to a + min. access cost for a Optjoin

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Interesting Orders Push down sorts when it is profitable – Merge joins usually faster than NLJ Another round of dynamic programming For k interesting orders, have complexity kn2 n

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Study Break – Join Ordering For the query: SELECT * FROM A,B,C,D WHERE A.v = B.v and B.w = C.w and C.w = D.w; How many left-deep plans are possible? How many plans or subsets of plans do we evaluate using the opt algo? Which one(s) can we eliminate as cross products?

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Automatic DB Design Key idea: optimize data layout for performance Make a well-known set of queries execute fast Use cost models to estimate utility of different designs

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Materialized Views sales : (saleid, date, time, register, product, price,...) CREATE MATERIALIZED VIEW sales_by_date AS SELECT date, product, sum(price), count(*) AS quantity FROM sales GROUP BY date, product Key properties: Kept up to date as data is added Selected for use automatically by optimizer when appropriate

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Conclusions Use dynamic programming to efficiently enumerate costs of different query plans – Start with one table and add more Physical db design is complicated! – Picking the right indexes and materialized views – Combinations of heuristics and what-if cost modeling needed – Designs may be adaptive to changing workloads

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