Overview of Query OptimizationHighlights of System R OptimizerSchema for ExamplesMotivating ExampleAlternative Plans 1 (No Indexes)Alternative Plans 2 With IndexesQuery Blocks: Units of OptimizationCost EstimationStatistics and CatalogsSize Estimation and Reduction FactorsRelational Algebra EquivalencesMore EquivalencesEnumeration of Alternative PlansCost Estimates for Single-Relation PlansExampleQueries Over Multiple RelationsEnumeration of Left-Deep PlansEnumeration of Plans (Contd.)Slide 19Nested QueriesSummarySummary (Contd.)Overview of Query OptimizationPlan: Tree of R.A. ops, with choice of alg for each op.–Each operator typically implemented using a `pull’ interface: when an operator is `pulled’ for the next output tuples, it `pulls’ on its inputs and computes them.Two main issues:–For a given query, what plans are considered?Algorithm to search plan space for cheapest (estimated) plan.–How is the cost of a plan estimated?Ideally: Want to find best plan. Practically: Avoid worst plans!We will study the System R approach.Highlights of System R OptimizerImpact:–Most widely used currently; works well for < 10 joins.Cost estimation: Approximate art at best.–Statistics, maintained in system catalogs, used to estimate cost of operations and result sizes.–Considers combination of CPU and I/O costs.Plan Space: Too large, must be pruned.–Only the space of left-deep plans is considered.Left-deep plans allow output of each operator to be pipelined into the next operator without storing it in a temporary relation.–Cartesian products avoided.Schema for ExamplesSimilar to old schema; rname added for variations.Reserves:–Each tuple is 40 bytes long, 100 tuples per page, 1000 pages.Sailors:–Each tuple is 50 bytes long, 80 tuples per page, 500 pages. Sailors (sid: integer, sname: string, rating: integer, age: real)Reserves (sid: integer, bid: integer, day: dates, rname: string)Motivating ExampleCost: 500+500*1000 I/OsBy no means the worst plan! Misses several opportunities: selections could have been `pushed’ earlier, no use is made of any available indexes, etc.Goal of optimization: To find more efficient plans that compute the same answer. SELECT S.snameFROM Reserves R, Sailors SWHERE R.sid=S.sid AND R.bid=100 AND S.rating>5ReservesSailorssid=sidbid=100 rating > 5snameReservesSailorssid=sidbid=100 rating > 5sname(Simple Nested Loops)(On-the-fly)(On-the-fly)RA Tree:Plan:Alternative Plans 1 (No Indexes)Main difference: push selects.With 5 buffers, cost of plan:–Scan Reserves (1000) + write temp T1 (10 pages, if we have 100 boats, uniform distribution).–Scan Sailors (500) + write temp T2 (250 pages, if we have 10 ratings).–Sort T1 (2*2*10), sort T2 (2*3*250), merge (10+250), total=1830 –Total: 3560 page I/Os.If we used BNL join, join cost = 10+4*250, total cost = 2770.If we `push’ projections, T1 has only sid, T2 only sid and sname:–T1 fits in 3 pages, cost of BNL drops to under 250 pages, total < 2000.ReservesSailorssid=sidbid=100 sname(On-the-fly)rating > 5(Scan;write to temp T1)(Scan;write totemp T2)(Sort-Merge Join)Alternative Plans 2With IndexesWith clustered index on bid of Reserves, we get 100,000/100 = 1000 tuples on 1000/100 = 10 pages.INL with pipelining (outer is not materialized). Decision not to push rating>5 before the join is based on availability of sid index on Sailors. Cost: Selection of Reserves tuples (10 I/Os); for each, must get matching Sailors tuple (1000*1.2); total 1210 I/Os. Join column sid is a key for Sailors.–At most one matching tuple, unclustered index on sid OK.–Projecting out unnecessary fields from outer doesn’t help.ReservesSailorssid=sidbid=100 sname(On-the-fly)rating > 5(Use hashindex; donot writeresult to temp)(Index Nested Loops,with pipelining )(On-the-fly)Query Blocks: Units of OptimizationAn SQL query is parsed into a collection of query blocks, and these are optimized one block at a time.Nested blocks are usually treated as calls to a subroutine, made once per outer tuple. (This is an over-simplification, but serves for now.)SELECT S.snameFROM Sailors SWHERE S.age IN (SELECT MAX (S2.age) FROM Sailors S2 GROUP BY S2.rating)Nested blockOuter block For each block, the plans considered are:– All available access methods, for each relation in FROM clause.– All left-deep join trees (i.e., all ways to join the relations one-at-a-time, with the inner relation in the FROM clause, considering all relation permutations and join methods.)Cost EstimationFor each plan considered, must estimate cost:–Must estimate cost of each operation in plan tree.Depends on input cardinalities.We’ve already discussed how to estimate the cost of operations (sequential scan, index scan, joins, etc.)–Must estimate size of result for each operation in tree!Use information about the input relations.For selections and joins, assume independence of predicates.We’ll discuss the System R cost estimation approach.–Very inexact, but works ok in practice.–More sophisticated techniques known now.Statistics and CatalogsNeed information about the relations and indexes involved. Catalogs typically contain at least:–# tuples (NTuples) and # pages (NPages) for each relation.–# distinct key values (NKeys) and NPages for each index.–Index height, low/high key values (Low/High) for each tree index.Catalogs updated periodically.–Updating whenever data changes is too expensive; lots of approximation anyway, so slight inconsistency ok.More detailed information (e.g., histograms of the values in some field) are sometimes stored.Size Estimation and Reduction FactorsConsider a query block:Maximum # tuples in result is the product of the cardinalities of relations in the FROM clause.Reduction factor (RF) associated with each term reflects the impact of the term in reducing result size. Result cardinality = Max # tuples * product of all RF’s.–Implicit assumption that terms are independent!–Term col=value has RF 1/NKeys(I), given index I on col–Term col1=col2 has RF 1/MAX(NKeys(I1), NKeys(I2))–Term col>value has RF (High(I)-value)/(High(I)-Low(I))SELECT attribute listFROM relation listWHERE term1 AND ... AND termkRelational Algebra EquivalencesAllow us to choose different join orders and to `push’ selections and projections ahead of joins.Selections:
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