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