Overview of Implementing Relational Operators�Query Evaluation

Chapter 12

Database Management Systems 3ed, R. Ramakrishnan and J. Gehrke

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Motivation: Evaluating Queries

• The same query can be evaluated in different ways.
• The evaluation strategy (plan) can make orders of magnitude of difference.
• Query efficiency is one of the main areas where DBMS systems compete with each other.
• Person-decades of development, secret details.

Database Management Systems 3ed, R. Ramakrishnan and J. Gehrke

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Overview of Query Evaluation

• Plan: 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.
• Much like cursor/iterator.
• Two main issues in query optimization:
• For a given query, what plans are considered?
• Algorithm to search 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 (IBM).

Database Management Systems 3ed, R. Ramakrishnan and J. Gehrke

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Some Common Techniques

• Algorithms for evaluating relational operators use some simple ideas extensively:
• Indexing: Can use WHERE conditions and indexes to retrieve small set of tuples (selections, joins)
• Iteration: Sometimes, faster to scan all tuples even if there is an index.
• Partitioning: By using sorting or hashing on a sort key, we can partition the input tuples and replace an expensive operation by similar operations on smaller inputs.

Database Management Systems 3ed, R. Ramakrishnan and J. Gehrke

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Examples

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Example Relations

Sailors

Reservations

Database Management Systems 3ed, R. Ramakrishnan and J. Gehrke

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Query Plan Example

• RA Tree: expression tree.
• Each leaf is a schema table.
• Internal nodes: relational algebra operator applied to children.
• Full plan labels each internal node with implementation strategy.

SELECT S.sname

FROM Reserves R, Sailors S

WHERE R.sid=S.sid AND

R.bid=100 AND S.rating>5

RA Tree:

Database Management Systems 3ed, R. Ramakrishnan and J. Gehrke

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Alternative Plan

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• Goal of optimization: To find efficient plans that compute the same answer.

Database Management Systems 3ed, R. Ramakrishnan and J. Gehrke

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Indexes and Query Plans

Database Management Systems 3ed, R. Ramakrishnan and J. Gehrke

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Access Paths

• An access path is a method of retrieving tuples:
• File scan, or index that matches a selection (in the query)
• A tree index matches (a conjunction of) terms that involve only attributes in a prefix of the search key.
• E.g., Tree index on <a, b, c> matches the selection a=5 AND b=3, and a=5 AND b>6, but not b=3.
• A hash index matches (a conjunction of) terms that has a term attribute = value for every attribute in the search key of the index.
• E.g., Hash index on <a, b, c> matches a=5 AND b=3 AND c=5; but it does not match b=3, or a=5 AND b=3, or a>5 AND b=3 AND c=5.

Database Management Systems 3ed, R. Ramakrishnan and J. Gehrke

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Exercise 12.4

Consider the following schema with the Sailors relation:

Sailors(sid: integer, sname: string, rating: integer, age: real) 

• For each of the following indexes, list whether the index matches the given selection conditions.
1. A hash index on the search key <Sailors.sid> 
1. σ_sid<50,000 (Sailors)
2. σ_sid=50,000 (Sailors)
2. A B+-tree on the search key <Sailors.sid>
• σ_sid<50,000 (Sailors)
• σ_sid=50,000 (Sailors)

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Database Management Systems 3ed, R. Ramakrishnan and J. Gehrke

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Selecting Indexes

Database Management Systems 3ed, R. Ramakrishnan and J. Gehrke

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Create Indexes in SQL-Server

• A DBMS supports many options for creating indices (more than we can cover).
• Sample Syntax:

use aworks;

create index IX_Product_Color

on SalesLT.Product (Color);

• More Examples�

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Database Management Systems 3ed, R. Ramakrishnan and J. Gehrke

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Understanding the Workload

• For each query in the workload:
• Which relations does it access?
• Which attributes are retrieved?
• Which attributes are involved in selection/join conditions? How selective are these conditions likely to be?
• For each update in the workload:
• Which attributes are involved in selection/join conditions? How selective are these conditions likely to be?
• The type of update (INSERT/DELETE/UPDATE), and the attributes that are affected.

Database Management Systems 3ed, R. Ramakrishnan and J. Gehrke

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Statistics and Catalogs

• Need 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 only periodically.
• More detailed information (e.g., histograms of the values in some field) are sometimes stored.

Database Management Systems 3ed, R. Ramakrishnan and J. Gehrke

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Choice of Indexes

• What indexes should we create?
• Which relations should have indexes?
• What field(s) should be the search key?
• Should we build several indexes?
• For each index, what kind of an index should it be?
• Clustered? Hash/tree?
• Trade-off: Indexes can make queries go faster, updates slower. Require disk space, too.

Database Management Systems 3ed, R. Ramakrishnan and J. Gehrke

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Choice of Index, One Approach

1. Consider the most important queries in turn.
2. Consider the best query plan using the current indexes.
3. If a better plan is possible with an additional index, create it.
• Obviously, this implies that we must understand how a DBMS evaluates queries and creates query evaluation plans!
1. For now, we discuss simple 1-table queries.

Database Management Systems 3ed, R. Ramakrishnan and J. Gehrke

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Examples of Clustered Indexes

• B+ tree index on E.age can be used to get qualifying tuples.
• How selective is the condition?
• Is the index clustered?
• Consider the GROUP BY query.
• If many tuples have E.age > 10, using E.age index and sorting the retrieved tuples may be costly.
• Clustered E.dno index may be better!
• Equality queries and duplicates:
• Clustering on E.hobby helps!

SELECT E.dno

FROM Emp E

WHERE E.age>40

SELECT E.dno, COUNT (*)

FROM Emp E

WHERE E.age>10

GROUP BY E.dno

SELECT E.dno

FROM Emp E

WHERE E.hobby=Stamps

Database Management Systems 3ed, R. Ramakrishnan and J. Gehrke

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Index-Only Plans

• A number of queries can be answered without retrieving any tuples from one or more of the relations involved if a suitable index is available.

SELECT D.mgr

FROM Dept D, Emp E

WHERE D.dno=E.dno

SELECT D.mgr, E.eid

FROM Dept D, Emp E

WHERE D.dno=E.dno

SELECT E.dno, COUNT(*)

FROM Emp E

GROUP BY E.dno

SELECT E.dno, MIN(E.sal)

FROM Emp E

GROUP BY E.dno

SELECT AVG(E.sal)

FROM Emp E

WHERE E.age=25 AND

E.sal BETWEEN 3000 AND 5000

<E.dno>

<E.dno,E.eid>

Tree index!

<E.dno>

<E.dno,E.sal>

Tree index!

<E. age,E.sal>

or

<E.sal, E.age>

Tree!

Database Management Systems 3ed, R. Ramakrishnan and J. Gehrke

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Index Selection Guidelines

• Attributes in WHERE clause are candidates for index keys.
• Exact match condition suggests hash index.
• Range query suggests tree index.
• Clustering is especially useful for range queries.
• Multi-attribute search keys should be considered when a WHERE clause contains several conditions.
• Order of attributes is important for range queries.
• Such indexes can sometimes enable index-only strategies for important queries.
• For index-only strategies, clustering is not important!
• Try to choose indexes that benefit as many queries as possible. MS Index Tuning Wizard

Database Management Systems 3ed, R. Ramakrishnan and J. Gehrke

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Computing Relational Operators

Database Management Systems 3ed, R. Ramakrishnan and J. Gehrke

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Selection and Projection

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One Approach to Selections

• Estimate the most selective access path, retrieve tuples using it, and apply any remaining terms that don’t match the index:
• Most selective access path: An index or file scan that requires the fewest page I/Os.
• Terms that match this index reduce the number of tuples retrieved.
• Other terms affect the query result, but not the number of tuples/pages fetched.

Database Management Systems 3ed, R. Ramakrishnan and J. Gehrke

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Selectivity Example

• Consider day<8/9/94 AND bid=5 AND sid=3.
• A B+ tree index on day can be used; then, bid=5 and sid=3 must be checked for each retrieved tuple.
• A hash index on <bid, sid> could be used; day<8/9/94 must then be checked.

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Database Management Systems 3ed, R. Ramakrishnan and J. Gehrke

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Using an Index for Selections

• Cost depends on #qualifying tuples, and clustering.
• Cost of finding qualifying data entries (typically small) plus cost of retrieving records (could be large w/o clustering).
• In example, assume that about 10% of tuples qualify (100 pages, 10000 tuples).
• With a clustered index, cost is little more than 100 I/Os.
• if unclustered, up to 10,000 I/Os!

SELECT *

FROM Reserves R

WHERE R.rname < ‘C%’

Database Management Systems 3ed, R. Ramakrishnan and J. Gehrke

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Projection

• The expensive part is removing duplicates.
• SQL systems don’t remove duplicates unless the keyword DISTINCT is specified in a query.
• Sorting Approach: Sort on <sid, bid> and remove duplicates.
• Hashing Approach:
• Hash on <sid, bid> to create partitions.
• Load partitions into memory one at a time.
• Build in-memory hash structure, and eliminate duplicates.
• If there is an index with both R.sid and R.bid in the search key, may be cheaper to sort data entries!

SELECT DISTINCT

R.sid, R.bid

FROM Reserves R

Database Management Systems 3ed, R. Ramakrishnan and J. Gehrke

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The Biggie: Join

Nested Loops: Scan and Match

Sort and Merge

Database Management Systems 3ed, R. Ramakrishnan and J. Gehrke

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Join: Sort-Merge (R S)

• Sort R and S on the join column, then scan them to do a ``merge’’ (on join col.), and output result tuples.
• Advance scan of R until current R-tuple >= current S tuple.
• Advance scan of S until current S-tuple >= current R tuple.
• Repeat until match: current R tuple = current S tuple.
• At this point, all R tuples with same value in Ri (current R group) and all S tuples with same value in Sj (current S group) match; output <r, s> for all pairs of such tuples.
• Then resume scanning R and S.
• R is scanned once; each S group is scanned once per matching R tuple.

i=j

Database Management Systems 3ed, R. Ramakrishnan and J. Gehrke

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Example of Sort-Merge Join

• Cost: sort + scan =
• sort cost + (M+N) [sid is key]
• The cost of scanning, M+N, could be M*N (very unlikely!)

Database Management Systems 3ed, R. Ramakrishnan and J. Gehrke

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Sorting

• Sorting is strongly optimized in DBMS.
• Common method: merge-sort.
• I/O Cost for merge sort using B buffer pages�is O(N * log_B-1 N/B)
• See Ch.13.
• Example: With enough buffer pages, both Reserves and Sailors can be sorted in 2 passes. total join cost: 7500.

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Database Management Systems 3ed, R. Ramakrishnan and J. Gehrke

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Example of Sort-Merge Join

• Cost: sort + scan =�4* (500+1000) + (500+1000) =�7,500 I/Os

Database Management Systems 3ed, R. Ramakrishnan and J. Gehrke

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Exercise 14.4.3

• Consider the join R.A with S.b given the following information. The cost measure is the number of page i/Os, ignoring the cost of writing out the result.
• Relation R contains 10,000 tuples and has 10 tuples per page.
• Relation S contains 2000 tuples, also 10 tuples per page.
• Attribute b is the primary key for S.
• Both relations are stored as heap files. No indexes are available.
• What is the cost of joining R and S using a sort-merge join? Assume that the number of I/Os for sorting a table T is 4 *pages_in_T .

Database Management Systems 3ed, R. Ramakrishnan and J. Gehrke

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Nested Loops: Flowchart

From http://www.dbsophic.com/physical-join-operators-in-sql-server-nested-loops/.

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Database Management Systems 3ed, R. Ramakrishnan and J. Gehrke

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Join: Index Nested Loops

• If there is an index on the join column of one relation (say S), can make it the inner and exploit the index.
• Cost: Pages_in_r * �( 1 + tup_per_page* cost of finding matching S tuples)
• For each R tuple, cost of probing S index is about 1.2 for hash index, 2-4 for B+ tree.
• Cost of then finding S tuples (assuming alt. (2) or (3) for data entries) depends on clustering.
• Clustered index on S: 1 I/O (typical) for each R tuple, �unclustered: up to 1 I/O per matching S tuple.

foreach tuple r in R do

foreach tuple s in S where r_i == s_j do

add <r, s> to result

Database Management Systems 3ed, R. Ramakrishnan and J. Gehrke

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Examples: Scan and Match

• Hash-index (Alt. 2) on sid of Sailors (as inner):
• Scan Reserves: 1000 page I/Os, 100*1000 tuples.
• For each Reserves tuple:
• 1.2 I/Os to get data entry in index.
• 1 I/O to get (the exactly one) matching Sailors tuple.
• Total: 220,000 I/Os for finding matches.
• Hash-index (Alt. 2) on sid of Reserves (as inner):
• Scan Sailors: 500 page I/Os, 80*500 tuples.
• For each Sailors tuple:
• 1.2 I/Os to get data entry in index.
• plus cost of retrieving matching Reserves tuples. Assuming uniform distribution, 2.5 reservations per sailor (100,000 R/ 40,000 S). Cost of retrieving them is 1 or 2.5 I/Os depending on whether the index is clustered.

Database Management Systems 3ed, R. Ramakrishnan and J. Gehrke

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Exercise 14.4.1

• Consider the join R.A with S.b given the following information. The cost measure is the number of page I/Os, ignoring the cost of writing out the result.
• Relation R contains 10,000 tuples and has 10 tuples per page.
• Relation S contains 2000 tuples, also 10 tuples per page.
• Attribute b is the primary key for S.
• Both relations are stored as heap files. No indexes are available.
• What is the cost of joining R and S using nested loop join? R is the outer relation.
• How many tuples does the join of R and S produce, at most, and how many pages are required to store the result of the join back on disk?

Database Management Systems 3ed, R. Ramakrishnan and J. Gehrke

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Query Planning

Database Management Systems 3ed, R. Ramakrishnan and J. Gehrke

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Highlights of System R Optimizer

• Impact:
• Most widely used currently; works well for < 10 joins.
• Cost estimation: NP-hard, 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. (see text)
• Cartesian products avoided.

Database Management Systems 3ed, R. Ramakrishnan and J. Gehrke

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Cost Estimation

• For 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 also estimate size of result for each operation in tree!
• Use information about the input relations.
• For selections and joins, assume independence of predicates.

Database Management Systems 3ed, R. Ramakrishnan and J. Gehrke

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Size Estimation and Reduction Factors

• Consider 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 list

FROM relation list

WHERE term1 AND ... AND termk

Database Management Systems 3ed, R. Ramakrishnan and J. Gehrke

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Schema for Examples

• Similar 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)

Database Management Systems 3ed, R. Ramakrishnan and J. Gehrke

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Motivating Example

• Cost: 1000+1000*500 I/Os
• By 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.sname

FROM Reserves R, Sailors S

WHERE R.sid=S.sid AND

R.bid=100 AND S.rating>5

RA Tree:

Plan:

Database Management Systems 3ed, R. Ramakrishnan and J. Gehrke

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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: 3560 page I/Os.

Database Management Systems 3ed, R. Ramakrishnan and J. Gehrke

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Alternative Plan 2�With Indexes

• With clustered index on bid of Reserves, we get 100,000/100 = 1000 tuples on 1000/100 = 10 pages for selection.
• INL with pipelining (outer is not materialized).

• Join column sid is a key for Sailors.
• At most one matching tuple, unclustered index on sid OK.
• Decision not to push rating>5 before the join:
• there is an index on sid of Sailors, don’t want to compute selection
• Cost: Selection of Reserves tuples (10 I/Os).
• For each, must get matching Sailors tuple (1000*(1.2+1)).
• Total 2210 page I/Os.

​

Reserves

Sailors

sid=sid

bid=100

sname

(On-the-fly)

rating > 5

(Use hash

index; do

not write

result to

temp)

(Index Nested Loops,

with pipelining )

(On-the-fly)

Database Management Systems 3ed, R. Ramakrishnan and J. Gehrke

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Summary

• There are several alternative evaluation algorithms for each relational operator.
• A query is evaluated by converting it to a tree of operators and evaluating the operators in the tree.
• Must understand query optimization in order to fully understand the performance impact of a given database design (relations, indexes) on a workload (set of queries).
• Two parts to optimizing a query:
• Consider a set of alternative plans.
• Must prune search space; typically, left-deep plans only.
• Must estimate cost of each plan that is considered.
• Must estimate size of result and cost for each plan node.
• Key issues: Statistics, indexes, operator implementations.

Database Management Systems 3ed, R. Ramakrishnan and J. Gehrke

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Choosing Indexes

• Understanding the nature of the workload for the application, and the performance goals, is essential to developing a good design.
• What are the important queries and updates? What attributes/relations are involved?
• Indexes must be chosen to speed up important queries (and perhaps some updates!).
• Index maintenance overhead on updates to key fields.
• Choose indexes that can help many queries, if possible.
• Build indexes to support index-only strategies.
• Clustering is an important decision, demanding on DBMS but potentially high payoff.

Database Management Systems 3ed, R. Ramakrishnan and J. Gehrke

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