Query Processing
Zachary G. IvesUniversity of Pennsylvania
CIS 550 – Database & Information Systems
April 20, 2023
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Making Use of the Data + Indices:Query Execution
Query plans & exec strategies Basic principles Standard relational operators Querying XML
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Making Use of the Data + Indices:Query Execution
Query plans & exec strategies Basic principles Standard relational operators Querying XML
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Query Plans
Data-flow graph of relational algebra operators
Typically: determined by optimizer
Select
Client = “Atkins”
Join
PressRel.Symbol = Clients.Symbol
Scan
PressRel
Scan
Clients
Join
PressRel.Symbol = EastCoast.CoSymbol
Project
CoSymbol
Scan
EastCoast
SELECT *FROM PressRel p, Clients CWHERE p.Symbol = c.Symbol AND c.Client = ‘Atkins’ AND c.Symbol IN (SELECT CoSymbol FROM EastCoast)
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Iterator-Based Query Execution
Execution begins at root open, next, close Propagate calls to
childrenMay call multiple child
nexts
Efficient scheduling & resource usage
Can you think of alternatives and their benefits?
Select
Client = “Atkins”
Join
PressRel.Symbol = Clients.Symbol
Scan
PressRel
Scan
Clients
Join
PressRel.Symbol = EastCoast.CoSymbol
Project
CoSymbol
Scan
EastCoast
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Execution Strategy Issues
Granularity & parallelism: Pipelining vs. blocking Materialization
Select
Client = “Atkins”
Join
PressRel.Symbol = Clients.Symbol
Scan
PressRel
Scan
Clients
Join
PressRel.Symbol = EastCoast.CoSymbol
Project
CoSymbol
Scan
EastCoast
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Basic Principles
Many DB operations require reading tuples, tuple vs. previous tuples, or tuples vs. tuples in another table
Techniques generally used: Iteration: for/while loop comparing with all tuples on disk
Index: if comparison of attribute that’s indexed, look up matches in index & return those
Sort/merge: iteration against presorted data (interesting orders)
Hash: build hash table of the tuple list, probe the hash table
Must be able to support larger-than-memory data
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Basic Operators
One-pass operators: Scan Select Project
Multi-pass operators: Join
Various implementations Handling of larger-than-memory sources
Semi-join Aggregation, union, etc.
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1-Pass Operators: Scanning a Table
Sequential scan: read through blocks of table
Index scan: retrieve tuples in index order May require 1 seek per tuple! When?
Cost in page reads – b(T) blocks, r(T) tuples b(T) pages for sequential scan Up to r(T) for index scan if unclustered index Requires memory for one block
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1-Pass Operators: Select()
Typically done while scanning a file If unsorted & no index, check against predicate:
Read tupleWhile tuple doesn’t meet predicate
Read tupleReturn tuple
Sorted data: can stop after particular value encountered
Indexed data: apply predicate to index, if possible If predicate is:
conjunction: may use indexes and/or scanning loop above (may need to sort/hash to compute intersection)
disjunction: may use union of index results, or scanning loop
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1-Pass Operators: Project ()
Simple scanning method often used if no index:Read tupleWhile tuple exists
Output specified attributesRead tuple
Duplicate removal may be necessary Partition output into separate files by bucket, do
duplicate removal on those If have many duplicates, sorting may be better
If attributes belong to an index, don’t need to retrieve tuples!
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Multi-pass Operators: Join (⋈) – Nested-Loops Join
Requires two nested loops:For each tuple in outer relation
For each tuple in inner, compareIf match on join attribute, output
Results have order of outer relation Can do over indices Very simple to implement, supports any joins
predicates Supports any join predicates Cost: # comparisons = t(R) t(S)
# disk accesses = b(R) + t(R) b(S)
Join
outer inner
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Block Nested-Loops Join
Join a page (block) at a time from each table:For each page in outer relation
For each page in inner, join both pages If match on join attribute, output
More efficient than previous approach: Cost: # comparisons still = t(R) t(S)
# disk accesses = b(R) + b(R) * b(S)
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Index Nested-Loops Join
For each tuple in outer relationFor each match in inner’s index Retrieve inner tuple + output joined tuple
Cost: b(R) + t(R) * cost of matching in S For each R tuple, costs of probing index are
about: 1.2 for hash index, 2-4 for B+-tree and:
Clustered index: 1 I/O on average Unclustered index: Up to 1 I/O per S tuple
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Two-Pass Algorithms
Sort-basedNeed to do a multiway sort first (or have an
index)Approximately linear in practice, 2 b(T) for table
T
Hash-basedStore one relation in a hash table
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(Sort-)Merge Join
Requires data sorted by join attributesMerge and join sorted files, reading sequentially a block at a time
Maintain two file pointers While tuple at R < tuple at S, advance R (and vice
versa) While tuples match, output all possible pairings
Preserves sorted order of “outer” relation Very efficient for presorted data Can be “hybridized” with NL Join for range joins May require a sort before (adds cost + delay) Cost: b(R) + b(S) plus sort costs, if necessary
In practice, approximately linear, 3 (b(R) + b(S))
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Hash-Based Joins
Allows partial pipelining of operations with equality comparisons
Sort-based operations block, but allow range and inequality comparisons
Hash joins usually done with static number of hash buckets Generally have fairly long chains at each
bucket What happens when memory is too small?
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Hash Join
Read entire inner relation into hash table (join attributes as key)
For each tuple from outer, look up in hash table & join
Very efficient for equality
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Running out of Memory
Resolution: When hash tables fullSplit hash table into files along bucket boundaries
Partition remaining data in same wayRecursively join partitions with diff. hash fn!
Hybrid hash join: flush “lazily” a few buckets at a time
Cost: <= 3 * (b(R) + b(S))
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Aggregation ()
Need to store entire table, coalesce groups with matching GROUP BY attributes
Compute aggregate function over group: If groups are sorted or indexed, can iterate:
Read tuples while attributes match, compute aggregate
At end of each group, output result Hash approach:
Group together in hash table (leave space for agg values!)
Compute aggregates incrementally or at end At end, return answers
Cost: b(t) pages. How much memory?
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Other Operators
Duplicate removal very similar to grouping All attributes must match No aggregate
Union, difference, intersection: Read table R, build hash/search tree Read table S, add/discard tuples as required Cost: b(R) + b(S)
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SQL Operations
In a whirlwind, you’ve seen most of relational operators: Select, Project, Join Group/aggregate Union, Difference, Intersection Others are used sometimes:
Various methods of “for all,” “not exists,” etc Recursive queries/fixpoint operator etc.
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What about XQuery?
Major difference: bind variables to subtrees; treat each set of bindings as a tuple
Select, project, join, etc. on tuples of bindings
Plus we need some new operators: XML construction:
Create element (add tags around data) Add attribute(s) to element (similar to join) Nest element under other element (similar to join)
Path expression evaluation – create the binding tuples
Overview of Query Optimization
A query plan: algebraic tree of operators, with choice of algorithm for each op
Two main issues in optimization: For a given query, which possible 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!
Relational Algebra Equivalences
Allow us to choose different join orders and to `push’ selections and projections ahead of joins.
Selections: (Commute)
Projections:
(Cascade)
Joins: R ⋈ (S ⋈ T) (R ⋈ S) ⋈ T (Associative)
(R ⋈ S) (S ⋈ R) (Commute)
R ⋈ (S ⋈ T) (T ⋈ R) ⋈ S Show that:
a1(R) ´ a1(…(an(R))))
c1(c2(R)) ´ c2(c1(R))c1^…^cn(R) ´ c1(… cn(R))
More Equivalences
A projection commutes with a selection that only uses attributes retained by the projection
Selection between attributes of the two arguments of a cross-product converts cross-product to a join
A selection on ONLY attributes of R commutes with R ⋈ S: (R ⋈ S) (R) ⋈ S
If a projection follows a join R ⋈ S, we can “push” it by retaining only attributes of R (and S) that are needed for the join or are kept by the projection
The System-R Optimizer: Establishing the Basic Model
Most widely used model; 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 Examples
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)
Query Blocks: Units of Optimization
An 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.
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 reln in FROM clause.
– All left-deep join trees (i.e., all ways to join the relations one-at-a-time, with the inner reln in the FROM clause, considering all reln permutations and join methods.)
Enumeration of Alternative Plans
There are two main cases: Single-relation plans Multiple-relation plans
For queries over a single relation, queries consist of a combination of selects, projects, and aggregate ops: Each available access path (file scan / index) is considered,
and the one with the least estimated cost is chosen. The different operations are essentially carried out
together (e.g., if an index is used for a selection, projection is done for each retrieved tuple, and the resulting tuples are pipelined into the aggregate computation).
Cost Estimation
For each plan considered, must estimate cost: Must estimate cost of each operation in plan
tree. Depends on input cardinalities.
Must also estimate size of result for each operation in tree! Use information about the input relations. For selections and joins, assume independence of
predicates.
Cost Estimates for Single-Relation Plans
Index I on primary key matches selection: Cost is Height(I)+1 for a B+ tree, about 1.2 for hash
index.
Clustered index I matching one or more selects: (NPages(I)+NPages(R)) * product of RF’s of matching
selects.
Non-clustered index I matching one or more selects: (NPages(I)+NTuples(R)) * product of RF’s of matching
selects.
Sequential scan of file: NPages(R).
Example
Given an index on rating: (1/NKeys(I)) * NTuples(R) = (1/10) * 40000 tuples
retrieved Clustered index: (1/NKeys(I)) * (NPages(I)+NPages(R)) =
(1/10) * (50+500) pages are retrieved Unclustered index: (1/NKeys(I)) * (NPages(I)+NTuples(R))
= (1/10) * (50+40000) pages are retrieved
Given an index on sid: Would have to retrieve all tuples/pages. With a clustered
index, the cost is 50+500, with unclustered index, 50+40000
A simple sequential scan: We retrieve all file pages (500)
SELECT S.sidFROM Sailors SWHERE S.rating=8
Queries Over Multiple Relations Fundamental decision in System R: only left-deep
join trees are considered As the number of joins increases, the number of
alternative plans grows rapidly; we need to restrict the search space
Left-deep trees allow us to generate all fully pipelined plans. Intermediate results not written to temporary files Not all left-deep trees are fully pipelined (e.g., SM join)
BA
C
D
BA
C
D
C DBA
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Costs of Joins
Nested loops join Disk accesses = b(R) + t(R) b(S)
Merge join b(R) + b(S) plus sort costs, if necessary
In practice, approximately linear, 3 (b(R) + b(S))
Hash join About 3 * (b(R) + b(S)) in the larger-than-
memory case