Topic 4: Query Optimization

Chapters 12 and 15 of Cow Book

Arun Kumar

1

CSE 232A Graduate Database Systems

Slide ACKs: Jignesh Patel, Paris Koutris

2

Query

Query Result

Database Server

Select R.text from Report R, Weather W where W.image.rain()

and W.city = R.city and W.date = R.date

and R.text.

matches(“insurance claims”)

QuerySyntax Tree and

Logical Query Plan

Parser

Physical Query Plan

Optimizer

Segments

Query Scheduler |…|……|………..|………..|

|…|……|………..|………..| |…|……|………..|………..| |…|……|………..|………..| |…|……|………..|………..| |…|……|………..|………..| |…|……|………..|………..| |…|……|………..|………..| |…|……|………..|………..| |…|……|………..|………..| |…|……|………..|………..|

Query Result

Execute Operators

Lifecycle of a Query

3

Recall the Netflix Schema

RatingID Stars RateDate UID MID1 3.5 08/27/15 79 20… … … … …

UID Name Age JoinDate79 Alice 23 01/10/1380 Bob 41 05/10/13

MID Name Year Director20 Inception 2010 Christopher Nolan16 Avatar 2009 Jim Cameron

Ratings

Users

Movies

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Example SQL Query

RatingID Stars RateDate UID MIDUID Name Age JoinDateMID Name Year Director

SELECT M.Year, COUNT(*) AS NumBest FROM Ratings R, Movies M WHERE R.MID = M.MID AND R.Stars = 5 GROUP BY M.Year ORDER BY NumBest DESC

Suppose, we also have a B+Tree Index on Ratings (Stars)

Logical Query Plan

5

SELECT R.stars = 5

Ratings Table

SELECT No predicate

Movies Table

JOIN R.MID = M.MID

GROUP BY AGGREGATE M.Year, COUNT(*)

SORT On NumBest

Result Table

Called “Logical” Operators

From extended RA

Each one has alternate “physical” implementations

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Indexed Access Use Index on Stars

Ratings Table

File Scan Read heapfile

Movies Table

Index-Nested Loop Join

Sort-based Aggregate

External Merge-Sort In-mem quicksort; B=50

Result Table Physical Query Plan

Called “Physical” Operators

Specifies exact algorithm/code to run for each logical operator, with all parameters (if any)

Aka “Query Evaluation Plan”

7

File Scan Read Index leaf pages

Ratings Table

File Scan Read heapfile

Movies Table

Hash Join

Hash-based Aggregate

External Merge-Sort In-mem quicksort; B=50

Result Table Physical Query Plan

This is also a correct PQP for the given LQP!

Q: Which PQP is faster?

This is a key job of the RDBMS Query Optimizer!

So, what is query optimization and how

does it work?

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9

Meet Query Optimization

A given LQP could have several possible PQPs with very different runtime performanceBasic Idea:

Get the optimal (fastest) PQP for a given LQPGoal (Ideal):

Goal (Realistic): Fine, just avoid the “clearly awful” PQPs!

Query optimization is a metaphor for life itself! It is often hard to even know what an optimal plan would be, but it is feasible to avoid many obviously bad plans!Jeff Naughton

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Query Optimization

❖ Overview of Query Optimizer ❖ Physical Query Plan (PQP) Concept: Pipelining Mechanism: Iterator Interface ❖ Enumerating Alternative PQPs Logical: Algebraic Rewrites Physical: Choosing Phy. Op. Impl. ❖ Costing PQPs ❖ Materialized Views

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Overview of Query Optimizer

SQL Query

Logical Query Plan

Physical Query Plan (Optimized)

Parser

Plan Enumerator

Plan Cost Estimator

Optimizer

To Scheduler/Executor

Catalog

System Catalog

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❖ Set of pre-defined relations for metadata about DB (schema) ❖ For each Relation: Relation name, File name File structure (heap file vs. clustered B+ tree, etc.) Attribute names and types; Integrity constraints; Indexes ❖ For each Index: Index name, Structure (B+ tree vs. hash, etc.); Index key

❖ For each View: View name, and View definition

Statistics in the System Catalog

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❖ RDBMS periodically collects stats about DB (instance) ❖ For each Table R: Cardinality, i.e., number of tuples, NTuples (R) Size, i.e., number of pages, NPages (R), or just NR ❖ For each Index X: Cardinality, i.e., number of distinct keys IKeys (X)

Size, i.e., number of pages IPages (X) (for a B+ tree, this is the number of leaf pages only)

Height (for tree indexes) IHeight (X) Min and max keys in index ILow (X), IHigh (X)

14

Query Optimization

❖ Overview of Query Optimizer ❖ Physical Query Plan (PQP) Concept: Pipelining Mechanism: Iterator Interface ❖ Enumerating Alternative PQPs Logical: Algebraic Rewrites Physical: Choosing Phy. Op. Impl. ❖ Costing PQPs ❖ Materialized Views

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File Scan Read Index leaf pages

Movies Table

File Scan Read heapfile

RatingsTable

Hash Join

Hash-based Aggregate

External Merge-Sort In-mem quicksort; B=50

Result Table Concept: Pipelining

Q: Does the hash-based aggregate have to wait till the entire output of the “upstream” hash join is available?

No! We can “pipeline” the output of the join – pass on a join output tuple as soon as it is obtained!

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Concept: Pipelining

Do not force “downstream” physical operators to wait till the entire output is availableBasic Idea:

Display output to the user incrementally CPU Parallelism in multi-core systems!Benefits:

Tuples

File Scan

Hash Join

Hash-based Aggregate

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Concept: Pipelining

❖ Crucial for PQPs with workflow of many phy. ops. ❖ Common feature of almost all RDBMSs ❖ Works for many operators: SCAN, HASH JOIN, etc.

Q: Are all physical operators amenable to pipelining?

No! Some may “stall” the pipeline: “Blocking Op”

Usually, any phy. op. involving sorting is blocking!

A blocking op. requires its output to be Materialized as a temporary table

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File Scan Read heapfile

Movies Table

File Scan Read heapfile

RatingsTable

Sort-Merge Join

Hash-based Aggregate

External Merge-Sort In-mem quicksort; B=50

Result Table Blocking Op

This phy. op. is blocking because we need to sort Movies and sort Ratings (materialize the output) before we can start any aggregate computations!

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Query Optimization

❖ Overview of Query Optimizer ❖ Physical Query Plan (PQP) Concept: Pipelining Mechanism: Iterator Interface ❖ Enumerating Alternative PQPs Logical: Algebraic Rewrites Physical: Choosing Phy. Op. Impl. ❖ Costing PQPs ❖ Materialized Views

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Mechanism: Iterator Interface

❖ Software API to process PQP; makes pipelining easy to impl. ❖ Enables us to abstract away individual phy. op. impl. details ❖ Three main functions in usage interface of each phy. op.: Open(): Initialize the phy. op. “state”, get arguments Allocate input and output buffers GetNext(): Ask the phy. op. impl. to “deliver” next

output tuple; pass it on; if blocking, wait Close(): Clear phy. op. state, free up space

21

Query Optimization

❖ Overview of Query Optimizer ❖ Physical Query Plan (PQP) Concept: Pipelining Mechanism: Iterator Interface ❖ Enumerating Alternative PQPs Logical: Algebraic Rewrites Physical: Choosing Phy. Op. Impl. ❖ Costing PQPs ❖ Materialized Views

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Overview of Query Optimizer

SQL Query

Logical Query Plan

Physical Query Plan (Optimized)

Parser

Plan Enumerator

Plan Cost Estimator

Optimizer

To Scheduler/Executor

Catalog

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Enumerating Alternative PQPs

❖ Plan Enumerator explores various PQPs for a given LQP ❖ Challenge: Space of plans is huge! How to make it feasible? ❖ RDBMS Plan Enumerator has Rules to help determine what

plans to enumerate, and also consults Cost models

❖ Two main sources of Rules for enumerating plans: Logical: Algebraic Rewrites: Use relational algebra equivalence to rewrite LQP itself!

Physical: Choosing Phy. Op. Impl.: Use different phy. op. impl. for a given log. op. in LQP

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Query Optimization

❖ Overview of Query Optimizer ❖ Physical Query Plan (PQP) Concept: Pipelining Mechanism: Iterator Interface ❖ Enumerating Alternative PQPs Logical: Algebraic Rewrites Physical: Choosing Phy. Op. Impl. ❖ Costing PQPs ❖ Materialized Views

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Algebraic Rewrite Rules

❖ Rewrite a given RA query in to another that is equivalent (a

logical property) but might be faster (a physical property) ❖ RA operators have some formal properties we can exploit ❖ We will cover only a few rewrite rules: Single-operator Rewrites Unary operators Binary operators Cross-operator Rewrites

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Unary Operator Rewrites

Q: Why are cascading rewrites beneficial?

�p1(�p2(R)) = �p2(�p1(R))

❖ Key unary operators in RA:

❖ Commutativity of

❖ Cascading of

❖ Cascading of

��

�

⇡

⇡

�p1(�p2(. . .�pn(R) . . . )) = �p1^p2^···^pn(R)

⇡A1(⇡A2(. . .⇡An(R) . . . )) = ⇡A1(R)

Ai ✓ Ai+18i = 1 . . . (n� 1)

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Binary Operator Rewrites

Q: Why are these properties beneficial?

Q: What other binary operators in RA satisfy these?

❖ Key binary operator in RA:

❖ Associativity of

❖ Commutativity of R ./ S = S ./ R

./

./

./ (R ./ S) ./ T = R ./ (S ./ T )

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Cross-Operator Rewrites

❖ Commuting and � ⇡ A ✓ B�p(A)(⇡B(R)) = ⇡B(�p(A)(R))

❖ Combining and � ⇥

❖ “Pushing the select”

❖ Commuting with and

A ✓ R.⇤

⇥⇡ ./

�p(R⇥ S) = R ./p S

�p(A)(R ./ S) = �p(A)(R) ./ S

�p(A)(R⇥ S) = �p(A)(R)⇥ S

⇡A(R⇥ S) = ⇡A\R.⇤(R)⇥ ⇡A\S.⇤(S)

⇡A(R ./p(B) S) = ⇡A\R.⇤(R) ./p(B) ⇡A\S.⇤(S)B ✓ A

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Review Question 

 

 

 

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Query Optimization

❖ Overview of Query Optimizer ❖ Physical Query Plan (PQP) Concept: Pipelining Mechanism: Iterator Interface ❖ Enumerating Alternative PQPs Logical: Algebraic Rewrites Physical: Choosing Phy. Op. Impl. ❖ Costing PQPs ❖ Materialized Views

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Choosing Phy. Op. Impl.

 

3 options 3 options 4 options = 36 PQPs!

Q: With algebraic rewrites?!

❖ Given a (rewritten) LQP, pick phy. op. impl. for each log. op.

❖ Recall various RA op. impl. with their I/O (and CPU costs)

File scan vs Indexed (B+ Tree vs Hash)

Hashing-based vs Sorting-based vs Indexed

BNLJ vs INLJ vs SMJ vs HJ

etc.

�⇡./

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Phy. Op. Impl.: Other Factors

❖ Are the indexes clustered or unclustered? ❖ Are there multiple matching indexes? Use multiple? ❖ Are index-only access paths possible for some ops? ❖ Are there “interesting orderings” among the inputs? ❖ Would sorted outputs benefit downstream ops? ❖ Estimation of cardinality of intermediate results! ❖ How best to reorder multi-table joins?

Still a hard, open research problem!Query optimizers are complex beasts!

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Phy. Op. Impl.: Join Orderings❖ Since joins are associative, exponential number of orderings!

 

 

 

 

   

 

 

 

 

 

 

 

   

  

 

       

Left Deep tree Right Deep tree“Bushy” tree

❖ Almost all RDBMSs consider only left deep join trees Enables easy pipelining! Why?

❖ “Interesting orderings” idea from System R optimizer paper ❖ Dynamic program to combine enumeration and costing“Access Path Selection in a Relational Database Management System” SIGMOD’79

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Query Optimization

❖ Overview of Query Optimizer ❖ Physical Query Plan (PQP) Concept: Pipelining Mechanism: Iterator Interface ❖ Enumerating Alternative PQPs Logical: Algebraic Rewrites Physical: Choosing Phy. Op. Impl. ❖ Costing PQPs ❖ Materialized Views

35

Overview of Query Optimizer

SQL Query

Logical Query Plan

Physical Query Plan (Optimized)

Parser

Plan Enumerator

Plan Cost Estimator

Optimizer

To Scheduler/Executor

Catalog

36

Costing PQPs

❖ For each PQP considered by the Plan Enumerator, the Plan

Cost Estimator computes “Cost” of the PQP Weighted sum of I/O cost and CPU cost (Distributed RDBMSs also include Network cost) ❖ Challenge: Given a PQP, compute overall cost ❖ Issues to consider: Pipelining vs. blocking ops; cannot simply add costs! Cardinality estimation for intermediate tables! Q: What statistics does the catalog have to help?

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Costing PQPs

❖ Most RDBMSs use various heuristics to make costing tractable; so, it is approximate!

❖ Example: Complex predicates

  

 Not enough info!

But, most RDBMSs use the independence heuristic!

Selectivity of conjunction = Product of selectivities

Thus, ≈ 0.05 * 0.1 = 0.005, i.e., 0.5%

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Query Optimization: Summary

❖ Plan Enumerator and Cost Estimator work in lock step: Rules determine what PQPs are enumerated Logical: Algebraic rewrites of LQP Physical: Op. Impl. and ordering alternatives Cost models and heuristics help cost the PQPs ❖ Still an active research area! Parametric Q.O., Multi-objective Q.O.,

Multi-objective parametric Q.O., Multiple Q.O., Online/Adaptive Q.O., Dynamic re-optimization, etc.

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Review Question

RatingID Stars RateDate UID MID

SELECT COUNT(DISTINCT UID) FROM Ratings

Page size 8KB; Buffer memory 4GB; 8B for each field

Propose an efficient physical plan and compute its I/O cost.

10m pages

Q: What if there was an unclustered B+ tree index on UID? (RecordID pointers can be assumed to be 8B too)

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Review Question

RatingID Stars RateDate UID MID

MID Name Year Director

SELECT AVG(Stars) FROM Ratings R, Movies M WHERE R.MID = M.MID AND

M.Director = “Christopher Nolan” AND R.UID = 1234;

10m pages

100k pages

Page size 8KB; Buffer memory 4GB

Propose an efficient physical plan that does not materialize any intermediate data (fully pipelined) and compute its I/O cost.

41

Query Optimization

❖ Overview of Query Optimizer ❖ Physical Query Plan (PQP) Concept: Pipelining Mechanism: Iterator Interface ❖ Enumerating Alternative PQPs Logical: Algebraic Rewrites Physical: Choosing Phy. Op. Impl. ❖ Costing PQPs ❖ Materialized Views

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Introducing Materialized Views

❖ A View is a “virtual table” created with an SQL query

❖ A Materialized View is a physically instantiated/stored view

RatingID Stars RateDate UID MIDUID Name Age JoinDate MID Name Year DirectorExample:

SELECT AVG(Stars) FROM Ratings R, Movies M, Users U WHERE R.MID = M.MID AND R.UID = U.UID

M.Director = “Christopher Nolan” AND U.Age >= 20 AND U.Age < 30;

�AVG(Stars)(R ./ �Director=“Christopher Nolan”(M) ./ �20Age<30(U))<latexit sha1_base64="4hc4knyHFKtKx2FU4HrZUrW2DfY=">AAACeXicbVFNbxMxEPUuXyV8NIUjHEyjog2HardFKgeQCkWCC6h8JK2UjdJZZ7Kxaq9X9iwoWi2/gd/GjT/ChQtOmkjQMJKl5zdvPOM3Wamkozj+GYRXrl67fmPjZuvW7Tt3N9tb9/rOVFZgTxhl7GkGDpUssEeSFJ6WFkFnCk+y86N5/uQLWidN8ZlmJQ415IWcSAHkqVH7e5qD1jBKNdBUUv2y/yb6RGBdt+HRR55m5itJ5KmTuVfVK9lraVGQsc2Ls7MVdzS1fl5TTtF+e28UFM12E73rrr2xF/NU+euqY44Nf873Y9+w1+2O2p14N14EXwfJEnTYMo5H7R/p2IhKY0FCgXODJC5pWIMlKRQ2rbRyWII4hxwHHhag0Q3rhXMN3/HMmE+M9acgvmD/rqhBOzfTmVfOx3WXc3Pyf7lBRZNnw1oWZUVYiItGk0pxMny+Bj5eGKhmHoCw0s/KxRQsCPLLankTkstfXgf9vd3E4w9PO4evlnZssAdsm0UsYQfskL1lx6zHBPsVPAx2gsfB7/BRGIVPLqRhsKy5z/6JcP8PbkK/yg==</latexit><latexit sha1_base64="4hc4knyHFKtKx2FU4HrZUrW2DfY=">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</latexit><latexit sha1_base64="4hc4knyHFKtKx2FU4HrZUrW2DfY=">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</latexit><latexit sha1_base64="4hc4knyHFKtKx2FU4HrZUrW2DfY=">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</latexit>

Requires file scans of R, M, and U and, say, hash joins

43

Materialized Views Example

CREATE MATERIALIZED VIEW NolanRatings AS SELECT RatingID, Stars, UID, MID FROM Ratings R, Movies M WHERE R.MID = M.MID AND

M.Director = “Christopher Nolan”;

�AVG(Stars)(R ./ �Director=“Christopher Nolan”(M) ./ �20Age<30(U))<latexit sha1_base64="4hc4knyHFKtKx2FU4HrZUrW2DfY=">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</latexit><latexit sha1_base64="4hc4knyHFKtKx2FU4HrZUrW2DfY=">AAACeXicbVFNbxMxEPUuXyV8NIUjHEyjog2HardFKgeQCkWCC6h8JK2UjdJZZ7Kxaq9X9iwoWi2/gd/GjT/ChQtOmkjQMJKl5zdvPOM3Wamkozj+GYRXrl67fmPjZuvW7Tt3N9tb9/rOVFZgTxhl7GkGDpUssEeSFJ6WFkFnCk+y86N5/uQLWidN8ZlmJQ415IWcSAHkqVH7e5qD1jBKNdBUUv2y/yb6RGBdt+HRR55m5itJ5KmTuVfVK9lraVGQsc2Ls7MVdzS1fl5TTtF+e28UFM12E73rrr2xF/NU+euqY44Nf873Y9+w1+2O2p14N14EXwfJEnTYMo5H7R/p2IhKY0FCgXODJC5pWIMlKRQ2rbRyWII4hxwHHhag0Q3rhXMN3/HMmE+M9acgvmD/rqhBOzfTmVfOx3WXc3Pyf7lBRZNnw1oWZUVYiItGk0pxMny+Bj5eGKhmHoCw0s/KxRQsCPLLankTkstfXgf9vd3E4w9PO4evlnZssAdsm0UsYQfskL1lx6zHBPsVPAx2gsfB7/BRGIVPLqRhsKy5z/6JcP8PbkK/yg==</latexit><latexit sha1_base64="4hc4knyHFKtKx2FU4HrZUrW2DfY=">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</latexit><latexit sha1_base64="4hc4knyHFKtKx2FU4HrZUrW2DfY=">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</latexit>

RatingID Stars RateDate UID MIDUID Name Age JoinDate MID Name Year Director

Example:

Creates a subset of R with ratings for only Nolan’s moviesV ⇡RatingID,Stars,UID,MID(R ./ �Director=“Christopher Nolan”(M))

<latexit sha1_base64="g7FJnXzvcMJEoRqMazKC0TO5kSk=">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</latexit><latexit sha1_base64="g7FJnXzvcMJEoRqMazKC0TO5kSk=">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</latexit><latexit sha1_base64="g7FJnXzvcMJEoRqMazKC0TO5kSk=">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</latexit><latexit sha1_base64="g7FJnXzvcMJEoRqMazKC0TO5kSk=">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</latexit>

44

�AVG(Stars)(R ./ �Director=“Christopher Nolan”(M) ./ �20Age<30(U))<latexit sha1_base64="4hc4knyHFKtKx2FU4HrZUrW2DfY=">AAACeXicbVFNbxMxEPUuXyV8NIUjHEyjog2HardFKgeQCkWCC6h8JK2UjdJZZ7Kxaq9X9iwoWi2/gd/GjT/ChQtOmkjQMJKl5zdvPOM3Wamkozj+GYRXrl67fmPjZuvW7Tt3N9tb9/rOVFZgTxhl7GkGDpUssEeSFJ6WFkFnCk+y86N5/uQLWidN8ZlmJQ415IWcSAHkqVH7e5qD1jBKNdBUUv2y/yb6RGBdt+HRR55m5itJ5KmTuVfVK9lraVGQsc2Ls7MVdzS1fl5TTtF+e28UFM12E73rrr2xF/NU+euqY44Nf873Y9+w1+2O2p14N14EXwfJEnTYMo5H7R/p2IhKY0FCgXODJC5pWIMlKRQ2rbRyWII4hxwHHhag0Q3rhXMN3/HMmE+M9acgvmD/rqhBOzfTmVfOx3WXc3Pyf7lBRZNnw1oWZUVYiItGk0pxMny+Bj5eGKhmHoCw0s/KxRQsCPLLankTkstfXgf9vd3E4w9PO4evlnZssAdsm0UsYQfskL1lx6zHBPsVPAx2gsfB7/BRGIVPLqRhsKy5z/6JcP8PbkK/yg==</latexit><latexit sha1_base64="4hc4knyHFKtKx2FU4HrZUrW2DfY=">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</latexit><latexit sha1_base64="4hc4knyHFKtKx2FU4HrZUrW2DfY=">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</latexit><latexit sha1_base64="4hc4knyHFKtKx2FU4HrZUrW2DfY=">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</latexit>

RatingID Stars RateDate UID MIDUID Name Age JoinDate MID Name Year Director

Example:

Given the materialized view V, RDBMS optimizer can automatically rewrite to use V to avoid scans of R and M

V ⇡RatingID,Stars,UID,MID(R ./ �Director=“Christopher Nolan”(M))<latexit sha1_base64="g7FJnXzvcMJEoRqMazKC0TO5kSk=">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</latexit><latexit sha1_base64="g7FJnXzvcMJEoRqMazKC0TO5kSk=">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</latexit><latexit sha1_base64="g7FJnXzvcMJEoRqMazKC0TO5kSk=">AAACZnicbZHBaxNBFMZn16pt1Da2iIdehgYhhVJ2RdCLUNoc7KFSq0kL2ZC+nbxNhs7OLDNvW8Ky/pHePHvxz3A2jaitDwZ+fN97zJtv0kJJR1H0PQgfrDx89Hh1rfXk6bP1jfbzzYEzpRXYF0YZe5GCQyU19kmSwovCIuSpwvP06qjxz6/ROmn0F5oXOMphqmUmBZCXxu16wBOFGYG15oYnhRxXSQ40k1Sd+RY9Pe7t8c/ednu83/DJca+uefeMJ6m5IYk8cXKaw5+xnrQoyNj6/eXlb+1oZv1TTDFD+/WjUaDrnbp7srs7bnei/WhR/D7ES+iwZZ2O29+SiRFljpqEAueGcVTQqAJLUiisW0npsABxBVMcetSQoxtVi5hq/sorE54Z648mvlD/nqggd26ep76z2dvd9Rrxf96wpOzdqJK6KAm1uL0oKxUnw5vM+WQRiZp7AGGl35WLGVgQ5H+m5UOI7z75Pgxe78eeP73pHBwu41hl22yHdVnM3rID9oGdsj4T7EewFmwGW8HPcD18Eb68bQ2D5cwW+6dC/gvzI7i/</latexit><latexit sha1_base64="g7FJnXzvcMJEoRqMazKC0TO5kSk=">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</latexit>

�AVG(Stars)(V ./ �20Age<30(U))<latexit sha1_base64="ZkjpKjWfAz7r6dTMfiAbaesJTz0=">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</latexit><latexit sha1_base64="ZkjpKjWfAz7r6dTMfiAbaesJTz0=">AAACNXicbVA9TxtBEN0jfJovJylpVlhIdmPdAVJSUDhJkRQUILBB8lnW3Hp8Xnn37rQ7l8g6+U+lyf+ggoIiCNHyF1gbI/H1pJXevnmjmXlRpqQl37/y5j7MLywuLa+UVtfWNzbLHz+1bJobgU2RqtScR2BRyQSbJEnheWYQdKTwLBr+mNTPfqOxMk1OaZRhR0OcyL4UQE7qlg/DGLSGbqiBBpKKb62f1RMCY2tjXm3xMEr/kEQeWhk7V7Hr81C575M7xjE/4Hu+MzdrtW654tf9KfhbEsxIhc1w1C1fhL1U5BoTEgqsbQd+Rp0CDEmhcFwKc4sZiCHE2HY0AY22U0yvHvMdp/R4PzXuJcSn6vOOArS1Ix0552Rd+7o2Ed+rtXPqf+0UMslywkQ8DurnilPKJxHynjQoSI0cAWGk25WLARgQ5IIuuRCC1ye/Ja3deuD48X6l8X0WxzLbYtusygL2hTXYL3bEmkywv+yS/Wc33j/v2rv17h6tc96s5zN7Ae/+AdQxqYU=</latexit><latexit sha1_base64="ZkjpKjWfAz7r6dTMfiAbaesJTz0=">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</latexit><latexit sha1_base64="ZkjpKjWfAz7r6dTMfiAbaesJTz0=">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</latexit>

Likely much faster since V is likely much smaller than R, but this depends on data statistics; leave it to optimizer!

Q: How did DBA know to materialize a view for Nolan ratings?

Materialized Views Example

45

RatingID Stars RateDate UID MIDUID Name Age JoinDate MID Name Year Director

Example:

We are given this materialized view V over R and M

V ⇡RatingID,Stars,UID,MID(R ./ �Director=“Christopher Nolan”(M))<latexit sha1_base64="g7FJnXzvcMJEoRqMazKC0TO5kSk=">AAACZnicbZHBaxNBFMZn16pt1Da2iIdehgYhhVJ2RdCLUNoc7KFSq0kL2ZC+nbxNhs7OLDNvW8Ky/pHePHvxz3A2jaitDwZ+fN97zJtv0kJJR1H0PQgfrDx89Hh1rfXk6bP1jfbzzYEzpRXYF0YZe5GCQyU19kmSwovCIuSpwvP06qjxz6/ROmn0F5oXOMphqmUmBZCXxu16wBOFGYG15oYnhRxXSQ40k1Sd+RY9Pe7t8c/ednu83/DJca+uefeMJ6m5IYk8cXKaw5+xnrQoyNj6/eXlb+1oZv1TTDFD+/WjUaDrnbp7srs7bnei/WhR/D7ES+iwZZ2O29+SiRFljpqEAueGcVTQqAJLUiisW0npsABxBVMcetSQoxtVi5hq/sorE54Z648mvlD/nqggd26ep76z2dvd9Rrxf96wpOzdqJK6KAm1uL0oKxUnw5vM+WQRiZp7AGGl35WLGVgQ5H+m5UOI7z75Pgxe78eeP73pHBwu41hl22yHdVnM3rID9oGdsj4T7EewFmwGW8HPcD18Eb68bQ2D5cwW+6dC/gvzI7i/</latexit><latexit sha1_base64="g7FJnXzvcMJEoRqMazKC0TO5kSk=">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</latexit><latexit sha1_base64="g7FJnXzvcMJEoRqMazKC0TO5kSk=">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</latexit><latexit sha1_base64="g7FJnXzvcMJEoRqMazKC0TO5kSk=">AAACZnicbZHBaxNBFMZn16pt1Da2iIdehgYhhVJ2RdCLUNoc7KFSq0kL2ZC+nbxNhs7OLDNvW8Ky/pHePHvxz3A2jaitDwZ+fN97zJtv0kJJR1H0PQgfrDx89Hh1rfXk6bP1jfbzzYEzpRXYF0YZe5GCQyU19kmSwovCIuSpwvP06qjxz6/ROmn0F5oXOMphqmUmBZCXxu16wBOFGYG15oYnhRxXSQ40k1Sd+RY9Pe7t8c/ednu83/DJca+uefeMJ6m5IYk8cXKaw5+xnrQoyNj6/eXlb+1oZv1TTDFD+/WjUaDrnbp7srs7bnei/WhR/D7ES+iwZZ2O29+SiRFljpqEAueGcVTQqAJLUiisW0npsABxBVMcetSQoxtVi5hq/sorE54Z648mvlD/nqggd26ep76z2dvd9Rrxf96wpOzdqJK6KAm1uL0oKxUnw5vM+WQRiZp7AGGl35WLGVgQ5H+m5UOI7z75Pgxe78eeP73pHBwu41hl22yHdVnM3rID9oGdsj4T7EewFmwGW8HPcD18Eb68bQ2D5cwW+6dC/gvzI7i/</latexit>

Q: What if new ratings are inserted to R for Nolan’s movies?

Materialized View Maintenance

❖ RDBMS will automatically “trigger” updates to V ❖ Such updates are called Materialized View Maintenance ❖ 2 alternatives: Recompute whole view from scratch vs

Incremental View Maintenance (IVM)

46

Recomputing V from scratch may be an overkill Try to incrementally update parts that change

Incremental View Maintenance (IVM)

Basic Idea:

V 0 = Q(D0)<latexit sha1_base64="V/tJ7TUF+7HCIRyXbkTldE8r42w=">AAAB8XicbZDLSgMxFIZPvNZ6q7p0EyzSuikzIuhGKOrCZQv2gu1QMmmmDc1khiQjlKFv4caFIm59G3e+jWk7C239IfDxn3PIOb8fC66N43yjldW19Y3N3FZ+e2d3b79wcNjUUaIoa9BIRKrtE80El6xhuBGsHStGQl+wlj+6ndZbT0xpHskHM46ZF5KB5AGnxFjrsVnC17heviud9QpFp+LMhJfBzaAImWq9wle3H9EkZNJQQbTuuE5svJQow6lgk3w30SwmdEQGrGNRkpBpL51tPMGn1unjIFL2SYNn7u+JlIRaj0PfdobEDPVibWr+V+skJrjyUi7jxDBJ5x8FicAmwtPzcZ8rRo0YWyBUcbsrpkOiCDU2pLwNwV08eRma5xXXcv2iWL3J4sjBMZxAGVy4hCrcQw0aQEHCM7zCG9LoBb2jj3nrCspmjuCP0OcPmRaO5Q==</latexit><latexit sha1_base64="V/tJ7TUF+7HCIRyXbkTldE8r42w=">AAAB8XicbZDLSgMxFIZPvNZ6q7p0EyzSuikzIuhGKOrCZQv2gu1QMmmmDc1khiQjlKFv4caFIm59G3e+jWk7C239IfDxn3PIOb8fC66N43yjldW19Y3N3FZ+e2d3b79wcNjUUaIoa9BIRKrtE80El6xhuBGsHStGQl+wlj+6ndZbT0xpHskHM46ZF5KB5AGnxFjrsVnC17heviud9QpFp+LMhJfBzaAImWq9wle3H9EkZNJQQbTuuE5svJQow6lgk3w30SwmdEQGrGNRkpBpL51tPMGn1unjIFL2SYNn7u+JlIRaj0PfdobEDPVibWr+V+skJrjyUi7jxDBJ5x8FicAmwtPzcZ8rRo0YWyBUcbsrpkOiCDU2pLwNwV08eRma5xXXcv2iWL3J4sjBMZxAGVy4hCrcQw0aQEHCM7zCG9LoBb2jj3nrCspmjuCP0OcPmRaO5Q==</latexit><latexit sha1_base64="V/tJ7TUF+7HCIRyXbkTldE8r42w=">AAAB8XicbZDLSgMxFIZPvNZ6q7p0EyzSuikzIuhGKOrCZQv2gu1QMmmmDc1khiQjlKFv4caFIm59G3e+jWk7C239IfDxn3PIOb8fC66N43yjldW19Y3N3FZ+e2d3b79wcNjUUaIoa9BIRKrtE80El6xhuBGsHStGQl+wlj+6ndZbT0xpHskHM46ZF5KB5AGnxFjrsVnC17heviud9QpFp+LMhJfBzaAImWq9wle3H9EkZNJQQbTuuE5svJQow6lgk3w30SwmdEQGrGNRkpBpL51tPMGn1unjIFL2SYNn7u+JlIRaj0PfdobEDPVibWr+V+skJrjyUi7jxDBJ5x8FicAmwtPzcZ8rRo0YWyBUcbsrpkOiCDU2pLwNwV08eRma5xXXcv2iWL3J4sjBMZxAGVy4hCrcQw0aQEHCM7zCG9LoBb2jj3nrCspmjuCP0OcPmRaO5Q==</latexit><latexit sha1_base64="V/tJ7TUF+7HCIRyXbkTldE8r42w=">AAAB8XicbZDLSgMxFIZPvNZ6q7p0EyzSuikzIuhGKOrCZQv2gu1QMmmmDc1khiQjlKFv4caFIm59G3e+jWk7C239IfDxn3PIOb8fC66N43yjldW19Y3N3FZ+e2d3b79wcNjUUaIoa9BIRKrtE80El6xhuBGsHStGQl+wlj+6ndZbT0xpHskHM46ZF5KB5AGnxFjrsVnC17heviud9QpFp+LMhJfBzaAImWq9wle3H9EkZNJQQbTuuE5svJQow6lgk3w30SwmdEQGrGNRkpBpL51tPMGn1unjIFL2SYNn7u+JlIRaj0PfdobEDPVibWr+V+skJrjyUi7jxDBJ5x8FicAmwtPzcZ8rRo0YWyBUcbsrpkOiCDU2pLwNwV08eRma5xXXcv2iWL3J4sjBMZxAGVy4hCrcQw0aQEHCM7zCG9LoBb2jj3nrCspmjuCP0OcPmRaO5Q==</latexit>

V = Q(D)<latexit sha1_base64="MDDam1hJPkCdqHSi1aGPF+ZdvfA=">AAAB73icbZBNSwMxEIZn/az1q+rRS7AI9VJ2RdCLUNSDxxbsB7RLyabZNjSbXZNZoZT+CS8eFPHq3/HmvzFt96CtLwQe3pkhM2+QSGHQdb+dldW19Y3N3FZ+e2d3b79wcNgwcaoZr7NYxroVUMOlULyOAiVvJZrTKJC8GQxvp/XmE9dGxOoBRwn3I9pXIhSMorVaDXJNaqW7s26h6JbdmcgyeBkUIVO1W/jq9GKWRlwhk9SYtucm6I+pRsEkn+Q7qeEJZUPa522Likbc+OPZvhNyap0eCWNtn0Iyc39PjGlkzCgKbGdEcWAWa1Pzv1o7xfDKHwuVpMgVm38UppJgTKbHk57QnKEcWaBMC7srYQOqKUMbUd6G4C2evAyN87JnuXZRrNxkceTgGE6gBB5cQgXuoQp1YCDhGV7hzXl0Xpx352PeuuJkM0fwR87nD9WkjoM=</latexit><latexit sha1_base64="MDDam1hJPkCdqHSi1aGPF+ZdvfA=">AAAB73icbZBNSwMxEIZn/az1q+rRS7AI9VJ2RdCLUNSDxxbsB7RLyabZNjSbXZNZoZT+CS8eFPHq3/HmvzFt96CtLwQe3pkhM2+QSGHQdb+dldW19Y3N3FZ+e2d3b79wcNgwcaoZr7NYxroVUMOlULyOAiVvJZrTKJC8GQxvp/XmE9dGxOoBRwn3I9pXIhSMorVaDXJNaqW7s26h6JbdmcgyeBkUIVO1W/jq9GKWRlwhk9SYtucm6I+pRsEkn+Q7qeEJZUPa522Likbc+OPZvhNyap0eCWNtn0Iyc39PjGlkzCgKbGdEcWAWa1Pzv1o7xfDKHwuVpMgVm38UppJgTKbHk57QnKEcWaBMC7srYQOqKUMbUd6G4C2evAyN87JnuXZRrNxkceTgGE6gBB5cQgXuoQp1YCDhGV7hzXl0Xpx352PeuuJkM0fwR87nD9WkjoM=</latexit><latexit sha1_base64="MDDam1hJPkCdqHSi1aGPF+ZdvfA=">AAAB73icbZBNSwMxEIZn/az1q+rRS7AI9VJ2RdCLUNSDxxbsB7RLyabZNjSbXZNZoZT+CS8eFPHq3/HmvzFt96CtLwQe3pkhM2+QSGHQdb+dldW19Y3N3FZ+e2d3b79wcNgwcaoZr7NYxroVUMOlULyOAiVvJZrTKJC8GQxvp/XmE9dGxOoBRwn3I9pXIhSMorVaDXJNaqW7s26h6JbdmcgyeBkUIVO1W/jq9GKWRlwhk9SYtucm6I+pRsEkn+Q7qeEJZUPa522Likbc+OPZvhNyap0eCWNtn0Iyc39PjGlkzCgKbGdEcWAWa1Pzv1o7xfDKHwuVpMgVm38UppJgTKbHk57QnKEcWaBMC7srYQOqKUMbUd6G4C2evAyN87JnuXZRrNxkceTgGE6gBB5cQgXuoQp1YCDhGV7hzXl0Xpx352PeuuJkM0fwR87nD9WkjoM=</latexit><latexit sha1_base64="MDDam1hJPkCdqHSi1aGPF+ZdvfA=">AAAB73icbZBNSwMxEIZn/az1q+rRS7AI9VJ2RdCLUNSDxxbsB7RLyabZNjSbXZNZoZT+CS8eFPHq3/HmvzFt96CtLwQe3pkhM2+QSGHQdb+dldW19Y3N3FZ+e2d3b79wcNgwcaoZr7NYxroVUMOlULyOAiVvJZrTKJC8GQxvp/XmE9dGxOoBRwn3I9pXIhSMorVaDXJNaqW7s26h6JbdmcgyeBkUIVO1W/jq9GKWRlwhk9SYtucm6I+pRsEkn+Q7qeEJZUPa522Likbc+OPZvhNyap0eCWNtn0Iyc39PjGlkzCgKbGdEcWAWa1Pzv1o7xfDKHwuVpMgVm38UppJgTKbHk57QnKEcWaBMC7srYQOqKUMbUd6G4C2evAyN87JnuXZRrNxkceTgGE6gBB5cQgXuoQp1YCDhGV7hzXl0Xpx352PeuuJkM0fwR87nD9WkjoM=</latexit>

❖ D’ can be the outcome of inserts and/or deletes to D ❖ Q can be a unary query or involve multiple tables ❖ Computing V’ may require inserts and/or deletes to V;

realized as algebraic rewrite rules at LQP level ❖ Whether or not IVM of V is feasible and/or efficient depends

on form of Q, nature of updates to D, data statistics, etc. ❖ We will focus only on inserts to D triggering inserts to V

47

Incremental View Maintenance (IVM)

Unary IVM for insertions:

Newly inserted tuplesR0 = R [�R<latexit sha1_base64="1XeBHzMtXPv7C0W2mlvBbLlFEA8=">AAAB/XicbZDLSsNAFIYnXmu9xcvOzWARXZVEBN0IRV24rMVeoAllMj1ph04mYWYi1FB8FTcuFHHre7jzbZy2WWjrDwMf/zmHc+YPEs6Udpxva2FxaXlltbBWXN/Y3Nq2d3YbKk4lhTqNeSxbAVHAmYC6ZppDK5FAooBDMxhcj+vNB5CKxeJeDxPwI9ITLGSUaGN17P3aMb7ENezRNMHeDXBNcK1jl5yyMxGeBzeHEspV7dhfXjemaQRCU06UartOov2MSM0oh1HRSxUkhA5ID9oGBYlA+dnk+hE+Mk4Xh7E0T2g8cX9PZCRSahgFpjMiuq9ma2Pzv1o71eGFnzGRpBoEnS4KU451jMdR4C6TQDUfGiBUMnMrpn0iCdUmsKIJwZ398jw0Tsuu4buzUuUqj6OADtAhOkEuOkcVdIuqqI4oekTP6BW9WU/Wi/VufUxbF6x8Zg/9kfX5A4gHk1c=</latexit><latexit sha1_base64="1XeBHzMtXPv7C0W2mlvBbLlFEA8=">AAAB/XicbZDLSsNAFIYnXmu9xcvOzWARXZVEBN0IRV24rMVeoAllMj1ph04mYWYi1FB8FTcuFHHre7jzbZy2WWjrDwMf/zmHc+YPEs6Udpxva2FxaXlltbBWXN/Y3Nq2d3YbKk4lhTqNeSxbAVHAmYC6ZppDK5FAooBDMxhcj+vNB5CKxeJeDxPwI9ITLGSUaGN17P3aMb7ENezRNMHeDXBNcK1jl5yyMxGeBzeHEspV7dhfXjemaQRCU06UartOov2MSM0oh1HRSxUkhA5ID9oGBYlA+dnk+hE+Mk4Xh7E0T2g8cX9PZCRSahgFpjMiuq9ma2Pzv1o71eGFnzGRpBoEnS4KU451jMdR4C6TQDUfGiBUMnMrpn0iCdUmsKIJwZ398jw0Tsuu4buzUuUqj6OADtAhOkEuOkcVdIuqqI4oekTP6BW9WU/Wi/VufUxbF6x8Zg/9kfX5A4gHk1c=</latexit><latexit sha1_base64="1XeBHzMtXPv7C0W2mlvBbLlFEA8=">AAAB/XicbZDLSsNAFIYnXmu9xcvOzWARXZVEBN0IRV24rMVeoAllMj1ph04mYWYi1FB8FTcuFHHre7jzbZy2WWjrDwMf/zmHc+YPEs6Udpxva2FxaXlltbBWXN/Y3Nq2d3YbKk4lhTqNeSxbAVHAmYC6ZppDK5FAooBDMxhcj+vNB5CKxeJeDxPwI9ITLGSUaGN17P3aMb7ENezRNMHeDXBNcK1jl5yyMxGeBzeHEspV7dhfXjemaQRCU06UartOov2MSM0oh1HRSxUkhA5ID9oGBYlA+dnk+hE+Mk4Xh7E0T2g8cX9PZCRSahgFpjMiuq9ma2Pzv1o71eGFnzGRpBoEnS4KU451jMdR4C6TQDUfGiBUMnMrpn0iCdUmsKIJwZ398jw0Tsuu4buzUuUqj6OADtAhOkEuOkcVdIuqqI4oekTP6BW9WU/Wi/VufUxbF6x8Zg/9kfX5A4gHk1c=</latexit><latexit sha1_base64="1XeBHzMtXPv7C0W2mlvBbLlFEA8=">AAAB/XicbZDLSsNAFIYnXmu9xcvOzWARXZVEBN0IRV24rMVeoAllMj1ph04mYWYi1FB8FTcuFHHre7jzbZy2WWjrDwMf/zmHc+YPEs6Udpxva2FxaXlltbBWXN/Y3Nq2d3YbKk4lhTqNeSxbAVHAmYC6ZppDK5FAooBDMxhcj+vNB5CKxeJeDxPwI9ITLGSUaGN17P3aMb7ENezRNMHeDXBNcK1jl5yyMxGeBzeHEspV7dhfXjemaQRCU06UartOov2MSM0oh1HRSxUkhA5ID9oGBYlA+dnk+hE+Mk4Xh7E0T2g8cX9PZCRSahgFpjMiuq9ma2Pzv1o71eGFnzGRpBoEnS4KU451jMdR4C6TQDUfGiBUMnMrpn0iCdUmsKIJwZ398jw0Tsuu4buzUuUqj6OADtAhOkEuOkcVdIuqqI4oekTP6BW9WU/Wi/VufUxbF6x8Zg/9kfX5A4gHk1c=</latexit>

Select:

Project:

V �SelectCondition(R)<latexit sha1_base64="eXj9dgW6EeNzOHOTIiPjAgtJIKM=">AAACGHicbVDLSgMxFM34rPVVdekmWATd6IwIuix249JXq9ApJZPeqcFMMiR3lDL0M9z4K25cKOLWnX9jpu1CqwcCh3Pu5eacKJXCou9/eVPTM7Nz86WF8uLS8spqZW29aXVmODS4ltrcRMyCFAoaKFDCTWqAJZGE6+iuXvjX92Cs0OoK+ym0E9ZTIhacoZM6lf0mDSXEyIzRDzS0opewTpgwvBWYX4IEjnWtuqKYHuxc7HYqVX/PH4L+JcGYVMkYZ53KZ9jVPEtAIZfM2lbgp9jOmUHBJQzKYWYhZfyO9aDlqGIJ2HY+DDag207p0lgb9xTSofpzI2eJtf0kcpPFl+2kV4j/ea0M4+N2LlSaISg+OhRnkqKmRUu0K4xLLvuOMG5cek75LTOMo+uy7EoIJiP/Jc2DvcDx88Nq7WRcR4lski2yQwJyRGrklJyRBuHkkTyTV/LmPXkv3rv3MRqd8sY7G+QXvM9vZb2gmg==</latexit><latexit sha1_base64="eXj9dgW6EeNzOHOTIiPjAgtJIKM=">AAACGHicbVDLSgMxFM34rPVVdekmWATd6IwIuix249JXq9ApJZPeqcFMMiR3lDL0M9z4K25cKOLWnX9jpu1CqwcCh3Pu5eacKJXCou9/eVPTM7Nz86WF8uLS8spqZW29aXVmODS4ltrcRMyCFAoaKFDCTWqAJZGE6+iuXvjX92Cs0OoK+ym0E9ZTIhacoZM6lf0mDSXEyIzRDzS0opewTpgwvBWYX4IEjnWtuqKYHuxc7HYqVX/PH4L+JcGYVMkYZ53KZ9jVPEtAIZfM2lbgp9jOmUHBJQzKYWYhZfyO9aDlqGIJ2HY+DDag207p0lgb9xTSofpzI2eJtf0kcpPFl+2kV4j/ea0M4+N2LlSaISg+OhRnkqKmRUu0K4xLLvuOMG5cek75LTOMo+uy7EoIJiP/Jc2DvcDx88Nq7WRcR4lski2yQwJyRGrklJyRBuHkkTyTV/LmPXkv3rv3MRqd8sY7G+QXvM9vZb2gmg==</latexit><latexit sha1_base64="eXj9dgW6EeNzOHOTIiPjAgtJIKM=">AAACGHicbVDLSgMxFM34rPVVdekmWATd6IwIuix249JXq9ApJZPeqcFMMiR3lDL0M9z4K25cKOLWnX9jpu1CqwcCh3Pu5eacKJXCou9/eVPTM7Nz86WF8uLS8spqZW29aXVmODS4ltrcRMyCFAoaKFDCTWqAJZGE6+iuXvjX92Cs0OoK+ym0E9ZTIhacoZM6lf0mDSXEyIzRDzS0opewTpgwvBWYX4IEjnWtuqKYHuxc7HYqVX/PH4L+JcGYVMkYZ53KZ9jVPEtAIZfM2lbgp9jOmUHBJQzKYWYhZfyO9aDlqGIJ2HY+DDag207p0lgb9xTSofpzI2eJtf0kcpPFl+2kV4j/ea0M4+N2LlSaISg+OhRnkqKmRUu0K4xLLvuOMG5cek75LTOMo+uy7EoIJiP/Jc2DvcDx88Nq7WRcR4lski2yQwJyRGrklJyRBuHkkTyTV/LmPXkv3rv3MRqd8sY7G+QXvM9vZb2gmg==</latexit><latexit sha1_base64="eXj9dgW6EeNzOHOTIiPjAgtJIKM=">AAACGHicbVDLSgMxFM34rPVVdekmWATd6IwIuix249JXq9ApJZPeqcFMMiR3lDL0M9z4K25cKOLWnX9jpu1CqwcCh3Pu5eacKJXCou9/eVPTM7Nz86WF8uLS8spqZW29aXVmODS4ltrcRMyCFAoaKFDCTWqAJZGE6+iuXvjX92Cs0OoK+ym0E9ZTIhacoZM6lf0mDSXEyIzRDzS0opewTpgwvBWYX4IEjnWtuqKYHuxc7HYqVX/PH4L+JcGYVMkYZ53KZ9jVPEtAIZfM2lbgp9jOmUHBJQzKYWYhZfyO9aDlqGIJ2HY+DDag207p0lgb9xTSofpzI2eJtf0kcpPFl+2kV4j/ea0M4+N2LlSaISg+OhRnkqKmRUu0K4xLLvuOMG5cek75LTOMo+uy7EoIJiP/Jc2DvcDx88Nq7WRcR4lski2yQwJyRGrklJyRBuHkkTyTV/LmPXkv3rv3MRqd8sY7G+QXvM9vZb2gmg==</latexit>

V 0 = V [ �SelectCondition(�R)<latexit sha1_base64="si5+RCDuBX9i9nVd6eTKQZT6Obs=">AAACHnicbVDLSgMxFM3UV62vUZdugkXUjcyIohuhWBcufbUKnVIy6W0bmskMyR2hDP0SN/6KGxeKCK70b8zULnwdCBzOOZebe8JECoOe9+EUJianpmeKs6W5+YXFJXd5pW7iVHOo8VjG+iZkBqRQUEOBEm4SDSwKJVyH/WruX9+CNiJWVzhIoBmxrhIdwRlaqeXu1zfpEa3TgKcJDYzoRqwVRAx7ArNLkMCxGqu2yMPDreAEJDJ6sd1yy96ONwL9S/wxKZMxzlruW9COeRqBQi6ZMQ3fS7CZMY2CSxiWgtRAwnifdaFhqWIRmGY2Om9IN6zSpp1Y26eQjtTvExmLjBlEoU3mPze/vVz8z2uk2DlsZkIlKYLiX4s6qaQY07wr2hbaFiAHljCubQmc8h7TjKNttGRL8H+f/JfUd3d8y8/3ypXjcR1FskbWyRbxyQGpkFNyRmqEkzvyQJ7Is3PvPDovzutXtOCMZ1bJDzjvn79roag=</latexit><latexit sha1_base64="si5+RCDuBX9i9nVd6eTKQZT6Obs=">AAACHnicbVDLSgMxFM3UV62vUZdugkXUjcyIohuhWBcufbUKnVIy6W0bmskMyR2hDP0SN/6KGxeKCK70b8zULnwdCBzOOZebe8JECoOe9+EUJianpmeKs6W5+YXFJXd5pW7iVHOo8VjG+iZkBqRQUEOBEm4SDSwKJVyH/WruX9+CNiJWVzhIoBmxrhIdwRlaqeXu1zfpEa3TgKcJDYzoRqwVRAx7ArNLkMCxGqu2yMPDreAEJDJ6sd1yy96ONwL9S/wxKZMxzlruW9COeRqBQi6ZMQ3fS7CZMY2CSxiWgtRAwnifdaFhqWIRmGY2Om9IN6zSpp1Y26eQjtTvExmLjBlEoU3mPze/vVz8z2uk2DlsZkIlKYLiX4s6qaQY07wr2hbaFiAHljCubQmc8h7TjKNttGRL8H+f/JfUd3d8y8/3ypXjcR1FskbWyRbxyQGpkFNyRmqEkzvyQJ7Is3PvPDovzutXtOCMZ1bJDzjvn79roag=</latexit><latexit sha1_base64="si5+RCDuBX9i9nVd6eTKQZT6Obs=">AAACHnicbVDLSgMxFM3UV62vUZdugkXUjcyIohuhWBcufbUKnVIy6W0bmskMyR2hDP0SN/6KGxeKCK70b8zULnwdCBzOOZebe8JECoOe9+EUJianpmeKs6W5+YXFJXd5pW7iVHOo8VjG+iZkBqRQUEOBEm4SDSwKJVyH/WruX9+CNiJWVzhIoBmxrhIdwRlaqeXu1zfpEa3TgKcJDYzoRqwVRAx7ArNLkMCxGqu2yMPDreAEJDJ6sd1yy96ONwL9S/wxKZMxzlruW9COeRqBQi6ZMQ3fS7CZMY2CSxiWgtRAwnifdaFhqWIRmGY2Om9IN6zSpp1Y26eQjtTvExmLjBlEoU3mPze/vVz8z2uk2DlsZkIlKYLiX4s6qaQY07wr2hbaFiAHljCubQmc8h7TjKNttGRL8H+f/JfUd3d8y8/3ypXjcR1FskbWyRbxyQGpkFNyRmqEkzvyQJ7Is3PvPDovzutXtOCMZ1bJDzjvn79roag=</latexit><latexit sha1_base64="si5+RCDuBX9i9nVd6eTKQZT6Obs=">AAACHnicbVDLSgMxFM3UV62vUZdugkXUjcyIohuhWBcufbUKnVIy6W0bmskMyR2hDP0SN/6KGxeKCK70b8zULnwdCBzOOZebe8JECoOe9+EUJianpmeKs6W5+YXFJXd5pW7iVHOo8VjG+iZkBqRQUEOBEm4SDSwKJVyH/WruX9+CNiJWVzhIoBmxrhIdwRlaqeXu1zfpEa3TgKcJDYzoRqwVRAx7ArNLkMCxGqu2yMPDreAEJDJ6sd1yy96ONwL9S/wxKZMxzlruW9COeRqBQi6ZMQ3fS7CZMY2CSxiWgtRAwnifdaFhqWIRmGY2Om9IN6zSpp1Y26eQjtTvExmLjBlEoU3mPze/vVz8z2uk2DlsZkIlKYLiX4s6qaQY07wr2hbaFiAHljCubQmc8h7TjKNttGRL8H+f/JfUd3d8y8/3ypXjcR1FskbWyRbxyQGpkFNyRmqEkzvyQJ7Is3PvPDovzutXtOCMZ1bJDzjvn79roag=</latexit>

V ⇡ProjectionList(R)<latexit sha1_base64="jB2Y+HCtJvNE1r3cZvsnXR5nbnU=">AAACFHicbVDLSgMxFM3UV62vUZdugkWoCGVGBF0W3bhwUcU+oDMMmTTTxmaSIckoZehHuPFX3LhQxK0Ld/6NmbYLbT0QOJxzL7nnhAmjSjvOt1VYWFxaXimultbWNza37O2dphKpxKSBBROyHSJFGOWkoalmpJ1IguKQkVY4uMj91j2Rigp+q4cJ8WPU4zSiGGkjBfZRE3qMRBpJKR6gl9DAi5HuU53VpbgjOJ+6MmeMKjeHgV12qs4YcJ64U1IGU9QD+8vrCpzGhGvMkFId10m0nyGpKWZkVPJSRRKEB6hHOoZyFBPlZ+NQI3hglC6MhDSPazhWf29kKFZqGIdmMr9YzXq5+J/XSXV05meUJ6kmHE8+ilIGtYB5Q7BLpcnNhoYgLKm5FeI+kghr02PJlODORp4nzeOqa/j1Sbl2Pq2jCPbAPqgAF5yCGrgEddAAGDyCZ/AK3qwn68V6tz4mowVrurML/sD6/AE8dp7s</latexit><latexit sha1_base64="jB2Y+HCtJvNE1r3cZvsnXR5nbnU=">AAACFHicbVDLSgMxFM3UV62vUZdugkWoCGVGBF0W3bhwUcU+oDMMmTTTxmaSIckoZehHuPFX3LhQxK0Ld/6NmbYLbT0QOJxzL7nnhAmjSjvOt1VYWFxaXimultbWNza37O2dphKpxKSBBROyHSJFGOWkoalmpJ1IguKQkVY4uMj91j2Rigp+q4cJ8WPU4zSiGGkjBfZRE3qMRBpJKR6gl9DAi5HuU53VpbgjOJ+6MmeMKjeHgV12qs4YcJ64U1IGU9QD+8vrCpzGhGvMkFId10m0nyGpKWZkVPJSRRKEB6hHOoZyFBPlZ+NQI3hglC6MhDSPazhWf29kKFZqGIdmMr9YzXq5+J/XSXV05meUJ6kmHE8+ilIGtYB5Q7BLpcnNhoYgLKm5FeI+kghr02PJlODORp4nzeOqa/j1Sbl2Pq2jCPbAPqgAF5yCGrgEddAAGDyCZ/AK3qwn68V6tz4mowVrurML/sD6/AE8dp7s</latexit><latexit sha1_base64="jB2Y+HCtJvNE1r3cZvsnXR5nbnU=">AAACFHicbVDLSgMxFM3UV62vUZdugkWoCGVGBF0W3bhwUcU+oDMMmTTTxmaSIckoZehHuPFX3LhQxK0Ld/6NmbYLbT0QOJxzL7nnhAmjSjvOt1VYWFxaXimultbWNza37O2dphKpxKSBBROyHSJFGOWkoalmpJ1IguKQkVY4uMj91j2Rigp+q4cJ8WPU4zSiGGkjBfZRE3qMRBpJKR6gl9DAi5HuU53VpbgjOJ+6MmeMKjeHgV12qs4YcJ64U1IGU9QD+8vrCpzGhGvMkFId10m0nyGpKWZkVPJSRRKEB6hHOoZyFBPlZ+NQI3hglC6MhDSPazhWf29kKFZqGIdmMr9YzXq5+J/XSXV05meUJ6kmHE8+ilIGtYB5Q7BLpcnNhoYgLKm5FeI+kghr02PJlODORp4nzeOqa/j1Sbl2Pq2jCPbAPqgAF5yCGrgEddAAGDyCZ/AK3qwn68V6tz4mowVrurML/sD6/AE8dp7s</latexit><latexit sha1_base64="jB2Y+HCtJvNE1r3cZvsnXR5nbnU=">AAACFHicbVDLSgMxFM3UV62vUZdugkWoCGVGBF0W3bhwUcU+oDMMmTTTxmaSIckoZehHuPFX3LhQxK0Ld/6NmbYLbT0QOJxzL7nnhAmjSjvOt1VYWFxaXimultbWNza37O2dphKpxKSBBROyHSJFGOWkoalmpJ1IguKQkVY4uMj91j2Rigp+q4cJ8WPU4zSiGGkjBfZRE3qMRBpJKR6gl9DAi5HuU53VpbgjOJ+6MmeMKjeHgV12qs4YcJ64U1IGU9QD+8vrCpzGhGvMkFId10m0nyGpKWZkVPJSRRKEB6hHOoZyFBPlZ+NQI3hglC6MhDSPazhWf29kKFZqGIdmMr9YzXq5+J/XSXV05meUJ6kmHE8+ilIGtYB5Q7BLpcnNhoYgLKm5FeI+kghr02PJlODORp4nzeOqa/j1Sbl2Pq2jCPbAPqgAF5yCGrgEddAAGDyCZ/AK3qwn68V6tz4mowVrurML/sD6/AE8dp7s</latexit>

V 0 = V [ ⇡ProjectionList(�R)<latexit sha1_base64="grYid+FzWJ3Q7FIqbHmFF6psNZ8=">AAACGnicbVDNSsNAGNz4W+tf1KOXxSLWS0lE0ItQ1IMHD1VsWmhC2Gw37dpNNuxuhBL6HF58FS8eFPEmXnwbN20O2jqwMMx8H/vNBAmjUlnWtzE3v7C4tFxaKa+urW9smlvbjuSpwKSJOeOiHSBJGI1JU1HFSDsRBEUBI61gcJH7rQciJOXxnRomxItQL6YhxUhpyTdt5wCeQQe6OE2gm1DfjZDqU5U1BL8nOB+61leMqu4lYQrB20PfrFg1aww4S+yCVECBhm9+ul2O04jECjMkZce2EuVlSCiKGRmV3VSSBOEB6pGOpjGKiPSycbQR3NdKF4Zc6BcrOFZ/b2QoknIYBXoyP1xOe7n4n9dJVXjqZTROUkViPPkoTBlUHOY9wS4VOj4baoKwoPpWiPtIIKx0m2Vdgj0deZY4RzVb85vjSv28qKMEdsEeqAIbnIA6uAIN0AQYPIJn8ArejCfjxXg3Piajc0axswP+wPj6AZGan/o=</latexit><latexit sha1_base64="grYid+FzWJ3Q7FIqbHmFF6psNZ8=">AAACGnicbVDNSsNAGNz4W+tf1KOXxSLWS0lE0ItQ1IMHD1VsWmhC2Gw37dpNNuxuhBL6HF58FS8eFPEmXnwbN20O2jqwMMx8H/vNBAmjUlnWtzE3v7C4tFxaKa+urW9smlvbjuSpwKSJOeOiHSBJGI1JU1HFSDsRBEUBI61gcJH7rQciJOXxnRomxItQL6YhxUhpyTdt5wCeQQe6OE2gm1DfjZDqU5U1BL8nOB+61leMqu4lYQrB20PfrFg1aww4S+yCVECBhm9+ul2O04jECjMkZce2EuVlSCiKGRmV3VSSBOEB6pGOpjGKiPSycbQR3NdKF4Zc6BcrOFZ/b2QoknIYBXoyP1xOe7n4n9dJVXjqZTROUkViPPkoTBlUHOY9wS4VOj4baoKwoPpWiPtIIKx0m2Vdgj0deZY4RzVb85vjSv28qKMEdsEeqAIbnIA6uAIN0AQYPIJn8ArejCfjxXg3Piajc0axswP+wPj6AZGan/o=</latexit><latexit sha1_base64="grYid+FzWJ3Q7FIqbHmFF6psNZ8=">AAACGnicbVDNSsNAGNz4W+tf1KOXxSLWS0lE0ItQ1IMHD1VsWmhC2Gw37dpNNuxuhBL6HF58FS8eFPEmXnwbN20O2jqwMMx8H/vNBAmjUlnWtzE3v7C4tFxaKa+urW9smlvbjuSpwKSJOeOiHSBJGI1JU1HFSDsRBEUBI61gcJH7rQciJOXxnRomxItQL6YhxUhpyTdt5wCeQQe6OE2gm1DfjZDqU5U1BL8nOB+61leMqu4lYQrB20PfrFg1aww4S+yCVECBhm9+ul2O04jECjMkZce2EuVlSCiKGRmV3VSSBOEB6pGOpjGKiPSycbQR3NdKF4Zc6BcrOFZ/b2QoknIYBXoyP1xOe7n4n9dJVXjqZTROUkViPPkoTBlUHOY9wS4VOj4baoKwoPpWiPtIIKx0m2Vdgj0deZY4RzVb85vjSv28qKMEdsEeqAIbnIA6uAIN0AQYPIJn8ArejCfjxXg3Piajc0axswP+wPj6AZGan/o=</latexit><latexit sha1_base64="grYid+FzWJ3Q7FIqbHmFF6psNZ8=">AAACGnicbVDNSsNAGNz4W+tf1KOXxSLWS0lE0ItQ1IMHD1VsWmhC2Gw37dpNNuxuhBL6HF58FS8eFPEmXnwbN20O2jqwMMx8H/vNBAmjUlnWtzE3v7C4tFxaKa+urW9smlvbjuSpwKSJOeOiHSBJGI1JU1HFSDsRBEUBI61gcJH7rQciJOXxnRomxItQL6YhxUhpyTdt5wCeQQe6OE2gm1DfjZDqU5U1BL8nOB+61leMqu4lYQrB20PfrFg1aww4S+yCVECBhm9+ul2O04jECjMkZce2EuVlSCiKGRmV3VSSBOEB6pGOpjGKiPSycbQR3NdKF4Zc6BcrOFZ/b2QoknIYBXoyP1xOe7n4n9dJVXjqZTROUkViPPkoTBlUHOY9wS4VOj4baoKwoPpWiPtIIKx0m2Vdgj0deZY4RzVb85vjSv28qKMEdsEeqAIbnIA6uAIN0AQYPIJn8ArejCfjxXg3Piajc0axswP+wPj6AZGan/o=</latexit>

Select and Project can be composed and reordered as before

Can be just an append (union with “bag” semantics)

Requires full set union with V for deduplication

48

Incremental View Maintenance (IVM)

Unary IVM for insertions:

Newly inserted tuplesR0 = R [�R<latexit sha1_base64="1XeBHzMtXPv7C0W2mlvBbLlFEA8=">AAAB/XicbZDLSsNAFIYnXmu9xcvOzWARXZVEBN0IRV24rMVeoAllMj1ph04mYWYi1FB8FTcuFHHre7jzbZy2WWjrDwMf/zmHc+YPEs6Udpxva2FxaXlltbBWXN/Y3Nq2d3YbKk4lhTqNeSxbAVHAmYC6ZppDK5FAooBDMxhcj+vNB5CKxeJeDxPwI9ITLGSUaGN17P3aMb7ENezRNMHeDXBNcK1jl5yyMxGeBzeHEspV7dhfXjemaQRCU06UartOov2MSM0oh1HRSxUkhA5ID9oGBYlA+dnk+hE+Mk4Xh7E0T2g8cX9PZCRSahgFpjMiuq9ma2Pzv1o71eGFnzGRpBoEnS4KU451jMdR4C6TQDUfGiBUMnMrpn0iCdUmsKIJwZ398jw0Tsuu4buzUuUqj6OADtAhOkEuOkcVdIuqqI4oekTP6BW9WU/Wi/VufUxbF6x8Zg/9kfX5A4gHk1c=</latexit><latexit sha1_base64="1XeBHzMtXPv7C0W2mlvBbLlFEA8=">AAAB/XicbZDLSsNAFIYnXmu9xcvOzWARXZVEBN0IRV24rMVeoAllMj1ph04mYWYi1FB8FTcuFHHre7jzbZy2WWjrDwMf/zmHc+YPEs6Udpxva2FxaXlltbBWXN/Y3Nq2d3YbKk4lhTqNeSxbAVHAmYC6ZppDK5FAooBDMxhcj+vNB5CKxeJeDxPwI9ITLGSUaGN17P3aMb7ENezRNMHeDXBNcK1jl5yyMxGeBzeHEspV7dhfXjemaQRCU06UartOov2MSM0oh1HRSxUkhA5ID9oGBYlA+dnk+hE+Mk4Xh7E0T2g8cX9PZCRSahgFpjMiuq9ma2Pzv1o71eGFnzGRpBoEnS4KU451jMdR4C6TQDUfGiBUMnMrpn0iCdUmsKIJwZ398jw0Tsuu4buzUuUqj6OADtAhOkEuOkcVdIuqqI4oekTP6BW9WU/Wi/VufUxbF6x8Zg/9kfX5A4gHk1c=</latexit><latexit sha1_base64="1XeBHzMtXPv7C0W2mlvBbLlFEA8=">AAAB/XicbZDLSsNAFIYnXmu9xcvOzWARXZVEBN0IRV24rMVeoAllMj1ph04mYWYi1FB8FTcuFHHre7jzbZy2WWjrDwMf/zmHc+YPEs6Udpxva2FxaXlltbBWXN/Y3Nq2d3YbKk4lhTqNeSxbAVHAmYC6ZppDK5FAooBDMxhcj+vNB5CKxeJeDxPwI9ITLGSUaGN17P3aMb7ENezRNMHeDXBNcK1jl5yyMxGeBzeHEspV7dhfXjemaQRCU06UartOov2MSM0oh1HRSxUkhA5ID9oGBYlA+dnk+hE+Mk4Xh7E0T2g8cX9PZCRSahgFpjMiuq9ma2Pzv1o71eGFnzGRpBoEnS4KU451jMdR4C6TQDUfGiBUMnMrpn0iCdUmsKIJwZ398jw0Tsuu4buzUuUqj6OADtAhOkEuOkcVdIuqqI4oekTP6BW9WU/Wi/VufUxbF6x8Zg/9kfX5A4gHk1c=</latexit><latexit sha1_base64="1XeBHzMtXPv7C0W2mlvBbLlFEA8=">AAAB/XicbZDLSsNAFIYnXmu9xcvOzWARXZVEBN0IRV24rMVeoAllMj1ph04mYWYi1FB8FTcuFHHre7jzbZy2WWjrDwMf/zmHc+YPEs6Udpxva2FxaXlltbBWXN/Y3Nq2d3YbKk4lhTqNeSxbAVHAmYC6ZppDK5FAooBDMxhcj+vNB5CKxeJeDxPwI9ITLGSUaGN17P3aMb7ENezRNMHeDXBNcK1jl5yyMxGeBzeHEspV7dhfXjemaQRCU06UartOov2MSM0oh1HRSxUkhA5ID9oGBYlA+dnk+hE+Mk4Xh7E0T2g8cX9PZCRSahgFpjMiuq9ma2Pzv1o71eGFnzGRpBoEnS4KU451jMdR4C6TQDUfGiBUMnMrpn0iCdUmsKIJwZ398jw0Tsuu4buzUuUqj6OADtAhOkEuOkcVdIuqqI4oekTP6BW9WU/Wi/VufUxbF6x8Zg/9kfX5A4gHk1c=</latexit>

Group By Agg:

Feasibility of IVM Depends on Agg() function! Rewrite rules exist for SUM, COUNT, and MIN/MAX over bags AVG not possible in general; needs deeper system changes

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V 0 = �AggList,SUM (Y )(V [ �AggList,SUM (Y )�R)<latexit sha1_base64="J9JSZSiTeNi8meg8CJ4WaxvATmo=">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</latexit><latexit sha1_base64="J9JSZSiTeNi8meg8CJ4WaxvATmo=">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</latexit><latexit sha1_base64="J9JSZSiTeNi8meg8CJ4WaxvATmo=">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</latexit><latexit sha1_base64="J9JSZSiTeNi8meg8CJ4WaxvATmo=">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</latexit>

V 0 = �AggList,SUM (Y )(V [ �AggList,COUNT(Y )�R)<latexit sha1_base64="Po07Uw9aYUnL5/uWsc6vj2c5HBE=">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</latexit><latexit sha1_base64="Po07Uw9aYUnL5/uWsc6vj2c5HBE=">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</latexit><latexit sha1_base64="Po07Uw9aYUnL5/uWsc6vj2c5HBE=">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</latexit><latexit sha1_base64="Po07Uw9aYUnL5/uWsc6vj2c5HBE=">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</latexit>

V 0 = �AggList,MIN (Y )(V [ �AggList,MIN (Y )�R)<latexit sha1_base64="qqwARVHKYintUVEhXD+XXp2gE2w=">AAACUnicjVLLSgMxFE3ru76qLt0Ei1hBZEYE3Qi+FgoqVWxVOqXcSdMxmMwMyR2hDPONgrjxQ9y4UNOH4GvhgcDhnHu5NyfxYykMOs5zLj80PDI6Nj5RmJyanpktzs3XTJRoxqsskpG+9sFwKUJeRYGSX8eag/Ilv/LvDrr+1T3XRkThJXZi3lAQhKItGKCVmkVRW6E71AtAKWimngK8FZjuBcGJnZ2tfQqnx2dZ+WY1K9eox5L4/w3UO+QSgV6sNoslZ93pgf4m7oCUyACVZvHRa0UsUTxEJsGYuuvE2EhBo2CSZwUvMTwGdgcBr1saguKmkfYiyeiyVVq0HWl7QqQ99WtHCsqYjvJtZXdj89Prin959QTb241UhHGCPGT9Qe1EUoxoN1/aEpozlB1LgGlhd6XsFjQwtK9QsCG4P6/8m9Q21l3LzzdLu/uDOMbJIlkiZeKSLbJLjkiFVAkjD+SFvJH33FPuNW9/Sb80nxv0LJBvyE99APIXs8c=</latexit><latexit sha1_base64="qqwARVHKYintUVEhXD+XXp2gE2w=">AAACUnicjVLLSgMxFE3ru76qLt0Ei1hBZEYE3Qi+FgoqVWxVOqXcSdMxmMwMyR2hDPONgrjxQ9y4UNOH4GvhgcDhnHu5NyfxYykMOs5zLj80PDI6Nj5RmJyanpktzs3XTJRoxqsskpG+9sFwKUJeRYGSX8eag/Ilv/LvDrr+1T3XRkThJXZi3lAQhKItGKCVmkVRW6E71AtAKWimngK8FZjuBcGJnZ2tfQqnx2dZ+WY1K9eox5L4/w3UO+QSgV6sNoslZ93pgf4m7oCUyACVZvHRa0UsUTxEJsGYuuvE2EhBo2CSZwUvMTwGdgcBr1saguKmkfYiyeiyVVq0HWl7QqQ99WtHCsqYjvJtZXdj89Prin959QTb241UhHGCPGT9Qe1EUoxoN1/aEpozlB1LgGlhd6XsFjQwtK9QsCG4P6/8m9Q21l3LzzdLu/uDOMbJIlkiZeKSLbJLjkiFVAkjD+SFvJH33FPuNW9/Sb80nxv0LJBvyE99APIXs8c=</latexit><latexit sha1_base64="qqwARVHKYintUVEhXD+XXp2gE2w=">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</latexit><latexit sha1_base64="qqwARVHKYintUVEhXD+XXp2gE2w=">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</latexit>

49

Incremental View Maintenance (IVM)

Join IVM for insertions:

V A ./ B<latexit sha1_base64="pw669SiEEFo9OAlJjiH5z7yop+s=">AAACAXicbZA9SwNBEIb34leMX1EbwWYxCFbhTgQtY2wsI5gPSELY28wlS/Zuj905Qwix8a/YWChi67+w89+4Sa7QxBcWHt6ZYXZeP5bCoOt+O5mV1bX1jexmbmt7Z3cvv39QMyrRHKpcSaUbPjMgRQRVFCihEWtgoS+h7g9upvX6A2gjVHSPoxjaIetFIhCcobU6+aMabUkIkGmthvSatnw1RAG03MkX3KI7E10GL4UCSVXp5L9aXcWTECLkkhnT9NwY22OmUXAJk1wrMRAzPmA9aFqMWAimPZ5dMKGn1unSQGn7IqQz9/fEmIXGjELfdoYM+2axNjX/qzUTDK7aYxHFCULE54uCRFJUdBoH7QoNHOXIAuNa2L9S3meacbSh5WwI3uLJy1A7L3qW7y4KpXIaR5YckxNyRjxySUrkllRIlXDySJ7JK3lznpwX5935mLdmnHTmkPyR8/kDKmCWDA==</latexit><latexit sha1_base64="pw669SiEEFo9OAlJjiH5z7yop+s=">AAACAXicbZA9SwNBEIb34leMX1EbwWYxCFbhTgQtY2wsI5gPSELY28wlS/Zuj905Qwix8a/YWChi67+w89+4Sa7QxBcWHt6ZYXZeP5bCoOt+O5mV1bX1jexmbmt7Z3cvv39QMyrRHKpcSaUbPjMgRQRVFCihEWtgoS+h7g9upvX6A2gjVHSPoxjaIetFIhCcobU6+aMabUkIkGmthvSatnw1RAG03MkX3KI7E10GL4UCSVXp5L9aXcWTECLkkhnT9NwY22OmUXAJk1wrMRAzPmA9aFqMWAimPZ5dMKGn1unSQGn7IqQz9/fEmIXGjELfdoYM+2axNjX/qzUTDK7aYxHFCULE54uCRFJUdBoH7QoNHOXIAuNa2L9S3meacbSh5WwI3uLJy1A7L3qW7y4KpXIaR5YckxNyRjxySUrkllRIlXDySJ7JK3lznpwX5935mLdmnHTmkPyR8/kDKmCWDA==</latexit><latexit sha1_base64="pw669SiEEFo9OAlJjiH5z7yop+s=">AAACAXicbZA9SwNBEIb34leMX1EbwWYxCFbhTgQtY2wsI5gPSELY28wlS/Zuj905Qwix8a/YWChi67+w89+4Sa7QxBcWHt6ZYXZeP5bCoOt+O5mV1bX1jexmbmt7Z3cvv39QMyrRHKpcSaUbPjMgRQRVFCihEWtgoS+h7g9upvX6A2gjVHSPoxjaIetFIhCcobU6+aMabUkIkGmthvSatnw1RAG03MkX3KI7E10GL4UCSVXp5L9aXcWTECLkkhnT9NwY22OmUXAJk1wrMRAzPmA9aFqMWAimPZ5dMKGn1unSQGn7IqQz9/fEmIXGjELfdoYM+2axNjX/qzUTDK7aYxHFCULE54uCRFJUdBoH7QoNHOXIAuNa2L9S3meacbSh5WwI3uLJy1A7L3qW7y4KpXIaR5YckxNyRjxySUrkllRIlXDySJ7JK3lznpwX5935mLdmnHTmkPyR8/kDKmCWDA==</latexit><latexit sha1_base64="pw669SiEEFo9OAlJjiH5z7yop+s=">AAACAXicbZA9SwNBEIb34leMX1EbwWYxCFbhTgQtY2wsI5gPSELY28wlS/Zuj905Qwix8a/YWChi67+w89+4Sa7QxBcWHt6ZYXZeP5bCoOt+O5mV1bX1jexmbmt7Z3cvv39QMyrRHKpcSaUbPjMgRQRVFCihEWtgoS+h7g9upvX6A2gjVHSPoxjaIetFIhCcobU6+aMabUkIkGmthvSatnw1RAG03MkX3KI7E10GL4UCSVXp5L9aXcWTECLkkhnT9NwY22OmUXAJk1wrMRAzPmA9aFqMWAimPZ5dMKGn1unSQGn7IqQz9/fEmIXGjELfdoYM+2axNjX/qzUTDK7aYxHFCULE54uCRFJUdBoH7QoNHOXIAuNa2L9S3meacbSh5WwI3uLJy1A7L3qW7y4KpXIaR5YckxNyRjxySUrkllRIlXDySJ7JK3lznpwX5935mLdmnHTmkPyR8/kDKmCWDA==</latexit>

A0 = A [�A<latexit sha1_base64="nLK99WSiKQwynE/Gnx6DiqAU79Q=">AAAB/XicbZDLSsNAFIZPvNZ6i5edm8EiuiqJCLoRWnXhsoK9QBPKZDpph04mYWYi1FB8FTcuFHHre7jzbZy2WWjrDwMf/zmHc+YPEs6Udpxva2FxaXlltbBWXN/Y3Nq2d3YbKk4loXUS81i2AqwoZ4LWNdOcthJJcRRw2gwG1+N684FKxWJxr4cJ9SPcEyxkBGtjdez96jG6RFXkkTRB3g3lGqNqxy45ZWciNA9uDiXIVevYX143JmlEhSYcK9V2nUT7GZaaEU5HRS9VNMFkgHu0bVDgiCo/m1w/QkfG6aIwluYJjSbu74kMR0oNo8B0Rlj31WxtbP5Xa6c6vPAzJpJUU0Gmi8KUIx2jcRSoyyQlmg8NYCKZuRWRPpaYaBNY0YTgzn55HhqnZdfw3VmpcpXHUYADOIQTcOEcKnALNagDgUd4hld4s56sF+vd+pi2Llj5zB78kfX5AziKkyQ=</latexit><latexit sha1_base64="nLK99WSiKQwynE/Gnx6DiqAU79Q=">AAAB/XicbZDLSsNAFIZPvNZ6i5edm8EiuiqJCLoRWnXhsoK9QBPKZDpph04mYWYi1FB8FTcuFHHre7jzbZy2WWjrDwMf/zmHc+YPEs6Udpxva2FxaXlltbBWXN/Y3Nq2d3YbKk4loXUS81i2AqwoZ4LWNdOcthJJcRRw2gwG1+N684FKxWJxr4cJ9SPcEyxkBGtjdez96jG6RFXkkTRB3g3lGqNqxy45ZWciNA9uDiXIVevYX143JmlEhSYcK9V2nUT7GZaaEU5HRS9VNMFkgHu0bVDgiCo/m1w/QkfG6aIwluYJjSbu74kMR0oNo8B0Rlj31WxtbP5Xa6c6vPAzJpJUU0Gmi8KUIx2jcRSoyyQlmg8NYCKZuRWRPpaYaBNY0YTgzn55HhqnZdfw3VmpcpXHUYADOIQTcOEcKnALNagDgUd4hld4s56sF+vd+pi2Llj5zB78kfX5AziKkyQ=</latexit><latexit sha1_base64="nLK99WSiKQwynE/Gnx6DiqAU79Q=">AAAB/XicbZDLSsNAFIZPvNZ6i5edm8EiuiqJCLoRWnXhsoK9QBPKZDpph04mYWYi1FB8FTcuFHHre7jzbZy2WWjrDwMf/zmHc+YPEs6Udpxva2FxaXlltbBWXN/Y3Nq2d3YbKk4loXUS81i2AqwoZ4LWNdOcthJJcRRw2gwG1+N684FKxWJxr4cJ9SPcEyxkBGtjdez96jG6RFXkkTRB3g3lGqNqxy45ZWciNA9uDiXIVevYX143JmlEhSYcK9V2nUT7GZaaEU5HRS9VNMFkgHu0bVDgiCo/m1w/QkfG6aIwluYJjSbu74kMR0oNo8B0Rlj31WxtbP5Xa6c6vPAzJpJUU0Gmi8KUIx2jcRSoyyQlmg8NYCKZuRWRPpaYaBNY0YTgzn55HhqnZdfw3VmpcpXHUYADOIQTcOEcKnALNagDgUd4hld4s56sF+vd+pi2Llj5zB78kfX5AziKkyQ=</latexit><latexit sha1_base64="nLK99WSiKQwynE/Gnx6DiqAU79Q=">AAAB/XicbZDLSsNAFIZPvNZ6i5edm8EiuiqJCLoRWnXhsoK9QBPKZDpph04mYWYi1FB8FTcuFHHre7jzbZy2WWjrDwMf/zmHc+YPEs6Udpxva2FxaXlltbBWXN/Y3Nq2d3YbKk4loXUS81i2AqwoZ4LWNdOcthJJcRRw2gwG1+N684FKxWJxr4cJ9SPcEyxkBGtjdez96jG6RFXkkTRB3g3lGqNqxy45ZWciNA9uDiXIVevYX143JmlEhSYcK9V2nUT7GZaaEU5HRS9VNMFkgHu0bVDgiCo/m1w/QkfG6aIwluYJjSbu74kMR0oNo8B0Rlj31WxtbP5Xa6c6vPAzJpJUU0Gmi8KUIx2jcRSoyyQlmg8NYCKZuRWRPpaYaBNY0YTgzn55HhqnZdfw3VmpcpXHUYADOIQTcOEcKnALNagDgUd4hld4s56sF+vd+pi2Llj5zB78kfX5AziKkyQ=</latexit>

B0 = B [�B<latexit sha1_base64="3rsI6ElVwi6Lfo3qZpJsR2daZOU=">AAAB/XicbZDLSsNAFIYn9VbrLV52bgaL6KokIuhGKNGFywr2Ak0ok+m0HTqZhJkToYbiq7hxoYhb38Odb+O0zUJbfxj4+M85nDN/mAiuwXG+rcLS8srqWnG9tLG5tb1j7+41dJwqyuo0FrFqhUQzwSWrAwfBWoliJAoFa4bD60m9+cCU5rG8h1HCgoj0Je9xSsBYHfvAO8FX2MM+TRPs3zABBHsdu+xUnKnwIrg5lFGuWsf+8rsxTSMmgQqiddt1EggyooBTwcYlP9UsIXRI+qxtUJKI6SCbXj/Gx8bp4l6szJOAp+7viYxEWo+i0HRGBAZ6vjYx/6u1U+hdBhmXSQpM0tmiXiowxHgSBe5yxSiIkQFCFTe3YjogilAwgZVMCO78lxehcVZxDd+dl6teHkcRHaIjdIpcdIGq6BbVUB1R9Iie0St6s56sF+vd+pi1Fqx8Zh/9kfX5Az03kyc=</latexit><latexit sha1_base64="3rsI6ElVwi6Lfo3qZpJsR2daZOU=">AAAB/XicbZDLSsNAFIYn9VbrLV52bgaL6KokIuhGKNGFywr2Ak0ok+m0HTqZhJkToYbiq7hxoYhb38Odb+O0zUJbfxj4+M85nDN/mAiuwXG+rcLS8srqWnG9tLG5tb1j7+41dJwqyuo0FrFqhUQzwSWrAwfBWoliJAoFa4bD60m9+cCU5rG8h1HCgoj0Je9xSsBYHfvAO8FX2MM+TRPs3zABBHsdu+xUnKnwIrg5lFGuWsf+8rsxTSMmgQqiddt1EggyooBTwcYlP9UsIXRI+qxtUJKI6SCbXj/Gx8bp4l6szJOAp+7viYxEWo+i0HRGBAZ6vjYx/6u1U+hdBhmXSQpM0tmiXiowxHgSBe5yxSiIkQFCFTe3YjogilAwgZVMCO78lxehcVZxDd+dl6teHkcRHaIjdIpcdIGq6BbVUB1R9Iie0St6s56sF+vd+pi1Fqx8Zh/9kfX5Az03kyc=</latexit><latexit sha1_base64="3rsI6ElVwi6Lfo3qZpJsR2daZOU=">AAAB/XicbZDLSsNAFIYn9VbrLV52bgaL6KokIuhGKNGFywr2Ak0ok+m0HTqZhJkToYbiq7hxoYhb38Odb+O0zUJbfxj4+M85nDN/mAiuwXG+rcLS8srqWnG9tLG5tb1j7+41dJwqyuo0FrFqhUQzwSWrAwfBWoliJAoFa4bD60m9+cCU5rG8h1HCgoj0Je9xSsBYHfvAO8FX2MM+TRPs3zABBHsdu+xUnKnwIrg5lFGuWsf+8rsxTSMmgQqiddt1EggyooBTwcYlP9UsIXRI+qxtUJKI6SCbXj/Gx8bp4l6szJOAp+7viYxEWo+i0HRGBAZ6vjYx/6u1U+hdBhmXSQpM0tmiXiowxHgSBe5yxSiIkQFCFTe3YjogilAwgZVMCO78lxehcVZxDd+dl6teHkcRHaIjdIpcdIGq6BbVUB1R9Iie0St6s56sF+vd+pi1Fqx8Zh/9kfX5Az03kyc=</latexit><latexit sha1_base64="3rsI6ElVwi6Lfo3qZpJsR2daZOU=">AAAB/XicbZDLSsNAFIYn9VbrLV52bgaL6KokIuhGKNGFywr2Ak0ok+m0HTqZhJkToYbiq7hxoYhb38Odb+O0zUJbfxj4+M85nDN/mAiuwXG+rcLS8srqWnG9tLG5tb1j7+41dJwqyuo0FrFqhUQzwSWrAwfBWoliJAoFa4bD60m9+cCU5rG8h1HCgoj0Je9xSsBYHfvAO8FX2MM+TRPs3zABBHsdu+xUnKnwIrg5lFGuWsf+8rsxTSMmgQqiddt1EggyooBTwcYlP9UsIXRI+qxtUJKI6SCbXj/Gx8bp4l6szJOAp+7viYxEWo+i0HRGBAZ6vjYx/6u1U+hdBhmXSQpM0tmiXiowxHgSBe5yxSiIkQFCFTe3YjogilAwgZVMCO78lxehcVZxDd+dl6teHkcRHaIjdIpcdIGq6BbVUB1R9Iie0St6s56sF+vd+pi1Fqx8Zh/9kfX5Az03kyc=</latexit>

Alternatively, we can just append the output of the following query to V (union below is just append too):

IVM for complex queries compose such op-level rewrites

V 0 = V [ (�A ./ B0) [ (A0 ./ �B)<latexit sha1_base64="jeGTXlJ411dIE56XxZzP2PaRVE8=">AAACJXicbVBNS0JBFJ3Xp9mX1bLNkIS5kfciqEWBWouWBqmBT2TeeNXBeR/M3FeI+Gfa9FfatEgiaNVfadRHlHVg4HDOudy5x4uk0GjbH9bC4tLyympqLb2+sbm1ndnZrekwVhyqPJShuvOYBikCqKJACXeRAuZ7Eupe/3Li1+9BaREGtziIoOmzbiA6gjM0UitzXsvRC1qjLo8jeuRegURGS9T1wgcUQMu5fGKVct9ikirnW5msXbCnoH+Jk5AsSVBpZcZuO+SxDwFyybRuOHaEzSFTKLiEUdqNNUSM91kXGoYGzAfdHE6vHNFDo7RpJ1TmBUin6s+JIfO1HvieSfoMe3rem4j/eY0YO2fNoQiiGCHgs0WdWFIM6aQy2hYKOMqBIYwrYf5KeY8pxtEUmzYlOPMn/yW144Jj+M1JtlhO6kiRfXJAjohDTkmRXJMKqRJOHskzeSVj68l6sd6s91l0wUpm9sgvWJ9fyNShKQ==</latexit><latexit sha1_base64="jeGTXlJ411dIE56XxZzP2PaRVE8=">AAACJXicbVBNS0JBFJ3Xp9mX1bLNkIS5kfciqEWBWouWBqmBT2TeeNXBeR/M3FeI+Gfa9FfatEgiaNVfadRHlHVg4HDOudy5x4uk0GjbH9bC4tLyympqLb2+sbm1ndnZrekwVhyqPJShuvOYBikCqKJACXeRAuZ7Eupe/3Li1+9BaREGtziIoOmzbiA6gjM0UitzXsvRC1qjLo8jeuRegURGS9T1wgcUQMu5fGKVct9ikirnW5msXbCnoH+Jk5AsSVBpZcZuO+SxDwFyybRuOHaEzSFTKLiEUdqNNUSM91kXGoYGzAfdHE6vHNFDo7RpJ1TmBUin6s+JIfO1HvieSfoMe3rem4j/eY0YO2fNoQiiGCHgs0WdWFIM6aQy2hYKOMqBIYwrYf5KeY8pxtEUmzYlOPMn/yW144Jj+M1JtlhO6kiRfXJAjohDTkmRXJMKqRJOHskzeSVj68l6sd6s91l0wUpm9sgvWJ9fyNShKQ==</latexit><latexit sha1_base64="jeGTXlJ411dIE56XxZzP2PaRVE8=">AAACJXicbVBNS0JBFJ3Xp9mX1bLNkIS5kfciqEWBWouWBqmBT2TeeNXBeR/M3FeI+Gfa9FfatEgiaNVfadRHlHVg4HDOudy5x4uk0GjbH9bC4tLyympqLb2+sbm1ndnZrekwVhyqPJShuvOYBikCqKJACXeRAuZ7Eupe/3Li1+9BaREGtziIoOmzbiA6gjM0UitzXsvRC1qjLo8jeuRegURGS9T1wgcUQMu5fGKVct9ikirnW5msXbCnoH+Jk5AsSVBpZcZuO+SxDwFyybRuOHaEzSFTKLiEUdqNNUSM91kXGoYGzAfdHE6vHNFDo7RpJ1TmBUin6s+JIfO1HvieSfoMe3rem4j/eY0YO2fNoQiiGCHgs0WdWFIM6aQy2hYKOMqBIYwrYf5KeY8pxtEUmzYlOPMn/yW144Jj+M1JtlhO6kiRfXJAjohDTkmRXJMKqRJOHskzeSVj68l6sd6s91l0wUpm9sgvWJ9fyNShKQ==</latexit><latexit sha1_base64="jeGTXlJ411dIE56XxZzP2PaRVE8=">AAACJXicbVBNS0JBFJ3Xp9mX1bLNkIS5kfciqEWBWouWBqmBT2TeeNXBeR/M3FeI+Gfa9FfatEgiaNVfadRHlHVg4HDOudy5x4uk0GjbH9bC4tLyympqLb2+sbm1ndnZrekwVhyqPJShuvOYBikCqKJACXeRAuZ7Eupe/3Li1+9BaREGtziIoOmzbiA6gjM0UitzXsvRC1qjLo8jeuRegURGS9T1wgcUQMu5fGKVct9ikirnW5msXbCnoH+Jk5AsSVBpZcZuO+SxDwFyybRuOHaEzSFTKLiEUdqNNUSM91kXGoYGzAfdHE6vHNFDo7RpJ1TmBUin6s+JIfO1HvieSfoMe3rem4j/eY0YO2fNoQiiGCHgs0WdWFIM6aQy2hYKOMqBIYwrYf5KeY8pxtEUmzYlOPMn/yW144Jj+M1JtlhO6kiRfXJAjohDTkmRXJMKqRJOHskzeSVj68l6sd6s91l0wUpm9sgvWJ9fyNShKQ==</latexit>

(�A ./ B0) [ (A0 ./ �B)� (�A ./ �B)<latexit sha1_base64="F8+01gWVJT5H2At8fJlGkZcSFrU=">AAACN3icbVDLSgNBEJz1bXxFPXoZDJLkYNgVQY9J9OBJFIwGskuYnXSSIbMPZnqVsPhXXvwNb3rxoIhX/8BJXESNBQNFVTU9XX4shUbbfrSmpmdm5+YXFnNLyyura/n1jUsdJYpDg0cyUk2faZAihAYKlNCMFbDAl3DlD45G/tU1KC2i8AKHMXgB64WiKzhDI7XzpyX3GCQyWqOuH92gAFovlqnLk5iWasVvMUvVy3SXTo58u+18wa7YY9BJ4mSkQDKctfMPbifiSQAhcsm0bjl2jF7KFAou4TbnJhpixgesBy1DQxaA9tLx3bd0xygd2o2UeSHSsfpzImWB1sPAN8mAYV//9Ubif14rwe6hl4owThBC/rWom0iKER2VSDtCAUc5NIRxJcxfKe8zxTiaqnOmBOfvyZPkcq/iGH6+X6jWszoWyBbZJiXikANSJSfkjDQIJ3fkibyQV+veerberPev6JSVzWySX7A+PgEZ46fc</latexit><latexit sha1_base64="F8+01gWVJT5H2At8fJlGkZcSFrU=">AAACN3icbVDLSgNBEJz1bXxFPXoZDJLkYNgVQY9J9OBJFIwGskuYnXSSIbMPZnqVsPhXXvwNb3rxoIhX/8BJXESNBQNFVTU9XX4shUbbfrSmpmdm5+YXFnNLyyura/n1jUsdJYpDg0cyUk2faZAihAYKlNCMFbDAl3DlD45G/tU1KC2i8AKHMXgB64WiKzhDI7XzpyX3GCQyWqOuH92gAFovlqnLk5iWasVvMUvVy3SXTo58u+18wa7YY9BJ4mSkQDKctfMPbifiSQAhcsm0bjl2jF7KFAou4TbnJhpixgesBy1DQxaA9tLx3bd0xygd2o2UeSHSsfpzImWB1sPAN8mAYV//9Ubif14rwe6hl4owThBC/rWom0iKER2VSDtCAUc5NIRxJcxfKe8zxTiaqnOmBOfvyZPkcq/iGH6+X6jWszoWyBbZJiXikANSJSfkjDQIJ3fkibyQV+veerberPev6JSVzWySX7A+PgEZ46fc</latexit><latexit sha1_base64="F8+01gWVJT5H2At8fJlGkZcSFrU=">AAACN3icbVDLSgNBEJz1bXxFPXoZDJLkYNgVQY9J9OBJFIwGskuYnXSSIbMPZnqVsPhXXvwNb3rxoIhX/8BJXESNBQNFVTU9XX4shUbbfrSmpmdm5+YXFnNLyyura/n1jUsdJYpDg0cyUk2faZAihAYKlNCMFbDAl3DlD45G/tU1KC2i8AKHMXgB64WiKzhDI7XzpyX3GCQyWqOuH92gAFovlqnLk5iWasVvMUvVy3SXTo58u+18wa7YY9BJ4mSkQDKctfMPbifiSQAhcsm0bjl2jF7KFAou4TbnJhpixgesBy1DQxaA9tLx3bd0xygd2o2UeSHSsfpzImWB1sPAN8mAYV//9Ubif14rwe6hl4owThBC/rWom0iKER2VSDtCAUc5NIRxJcxfKe8zxTiaqnOmBOfvyZPkcq/iGH6+X6jWszoWyBbZJiXikANSJSfkjDQIJ3fkibyQV+veerberPev6JSVzWySX7A+PgEZ46fc</latexit><latexit sha1_base64="F8+01gWVJT5H2At8fJlGkZcSFrU=">AAACN3icbVDLSgNBEJz1bXxFPXoZDJLkYNgVQY9J9OBJFIwGskuYnXSSIbMPZnqVsPhXXvwNb3rxoIhX/8BJXESNBQNFVTU9XX4shUbbfrSmpmdm5+YXFnNLyyura/n1jUsdJYpDg0cyUk2faZAihAYKlNCMFbDAl3DlD45G/tU1KC2i8AKHMXgB64WiKzhDI7XzpyX3GCQyWqOuH92gAFovlqnLk5iWasVvMUvVy3SXTo58u+18wa7YY9BJ4mSkQDKctfMPbifiSQAhcsm0bjl2jF7KFAou4TbnJhpixgesBy1DQxaA9tLx3bd0xygd2o2UeSHSsfpzImWB1sPAN8mAYV//9Ubif14rwe6hl4owThBC/rWom0iKER2VSDtCAUc5NIRxJcxfKe8zxTiaqnOmBOfvyZPkcq/iGH6+X6jWszoWyBbZJiXikANSJSfkjDQIJ3fkibyQV+veerberPev6JSVzWySX7A+PgEZ46fc</latexit>

Assume no duplicate inserts

50

Query Optimization

❖ Overview of Query Optimizer ❖ Physical Query Plan (PQP) Concept: Pipelining Mechanism: Iterator Interface ❖ Enumerating Alternative PQPs Logical: Algebraic Rewrites Physical: Choosing Phy. Op. Impl. ❖ Costing PQPs ❖ Materialized Views