From 5543e26330d2d8c2de878c0465d39e3edeecc51a Mon Sep 17 00:00:00 2001 From: Oliver Date: Sat, 3 Apr 2021 13:52:51 -0400 Subject: [PATCH] Materialized Views --- src/teaching/cse-562/2021sp/index.erb | 4 +- .../slide/2021-03-30-StreamingQueries.erb | 16 + .../slide/2021-04-01-MaterializedViews.erb | 483 ++++++++ .../CustomerOrderLineitemExample.svg | 394 +++++++ .../cse-562/2021sp/slide/2021-04-01/DBToQ.svg | 1024 +++++++++++++++++ .../cse-562/2021sp/slide/2021-04-01/morbo.png | Bin 0 -> 240135 bytes 6 files changed, 1920 insertions(+), 1 deletion(-) create mode 100644 src/teaching/cse-562/2021sp/slide/2021-04-01-MaterializedViews.erb create mode 100644 src/teaching/cse-562/2021sp/slide/2021-04-01/CustomerOrderLineitemExample.svg create mode 100644 src/teaching/cse-562/2021sp/slide/2021-04-01/DBToQ.svg create mode 100644 src/teaching/cse-562/2021sp/slide/2021-04-01/morbo.png diff --git a/src/teaching/cse-562/2021sp/index.erb b/src/teaching/cse-562/2021sp/index.erb index da43edce..d0a6b3fd 100644 --- a/src/teaching/cse-562/2021sp/index.erb +++ b/src/teaching/cse-562/2021sp/index.erb @@ -96,10 +96,12 @@ schedule: slides: slide/2021-03-30-StreamingQueries.html - date: "Apr. 1" topic: "Data Updates + Incremental View Maintenance" - due: "Checkpoint 2" + materials: + slides: slide/2021-04-01-MaterializedViews.html - date: "Apr. 6" topic: "Aggregation + Checkpoint 3" - date: "Apr. 8" + due: "Checkpoint 2" topic: "Transactions: Intro + Concepts" - date: "Apr. 13" topic: "Transactions: Pessimistic" diff --git a/src/teaching/cse-562/2021sp/slide/2021-03-30-StreamingQueries.erb b/src/teaching/cse-562/2021sp/slide/2021-03-30-StreamingQueries.erb index 93b8ce2d..b1d7e828 100644 --- a/src/teaching/cse-562/2021sp/slide/2021-03-30-StreamingQueries.erb +++ b/src/teaching/cse-562/2021sp/slide/2021-03-30-StreamingQueries.erb @@ -5,6 +5,22 @@ date: March 30, 2021 textbook: --- + + + +
+
+

Checkpoint 2

+
    +
  • Deadline moved to April 7
  • +
  • Extra office hours Wed April 7
  • +
+
+
+

Sequential Data

diff --git a/src/teaching/cse-562/2021sp/slide/2021-04-01-MaterializedViews.erb b/src/teaching/cse-562/2021sp/slide/2021-04-01-MaterializedViews.erb new file mode 100644 index 00000000..478eecb3 --- /dev/null +++ b/src/teaching/cse-562/2021sp/slide/2021-04-01-MaterializedViews.erb @@ -0,0 +1,483 @@ +--- +template: templates/cse4562_2021_slides.erb +title: Materialized Views +date: April 1, 1921 +textbook: Ch. 8.5 +--- + + + +
+
+

+      CREATE VIEW salesSinceLastMonth AS
+        SELECT l.*
+        FROM lineitem l, orders o
+        WHERE l.orderkey = o.orderkey
+        AND o.orderdate > DATE(NOW() - '1 Month')
+    
+
+

+      SELECT partkey FROM salesSinceLastMonth
+      ORDER BY shipdate DESC LIMIT 10;
+    
+

+      SELECT suppkey, COUNT(*)
+      FROM salesSinceLastMonth
+      GROUP BY suppkey;
+    
+

+      SELECT partkey, COUNT(*)
+      FROM salesSinceLastMonth
+      GROUP BY partkey;
+    
+
+
+ +
+

Opportunity: Views exist to be queried frequently

+

Idea: Pre-compute and save the view’s contents!
+(like an index)

+
+
+ +
+
+ + openclipart.org +
+ +
+

When the base data changes,
the view needs to be updated too!

+
+ +
+
+ $$\texttt{VIEW} \leftarrow Q(\mathcal D)$$ +
+

Our view starts off initialized

+
+ +
+

Idea: Recompute the view from scratch when data changes.

+
+ +
+
+ $$\texttt{WHEN } \mathcal D \leftarrow \mathcal D+\Delta\mathcal D \texttt{ DO: }\\ + \texttt{VIEW} \leftarrow Q(\mathcal{D}+\Delta\mathcal{D})$$ +
+
+ +
+

Not quite facepalm-worthy, but not ideal.

+
+ +
+
+ $$\texttt{WHEN } \mathcal D \leftarrow \mathcal{D}+\Delta\mathcal D \texttt{ DO: }\\ + \texttt{VIEW} \leftarrow \texttt{VIEW} + \Delta Q(\mathcal D,\Delta\mathcal D)$$ +
+ + + + + + + + + +
$\Delta Q$(ideally) Small & fast query
$+$(ideally) Fast "merge" operation
+
+
+ +
+
+

Intuition

+
+ $$\mathcal{D} = \{\ 1,\ 2,\ 3,\ 4\ \} \hspace{1in} \Delta\mathcal{D} = \{\ 5\ \}$$ + $$Q(\mathcal D) = \texttt{SUM}(\mathcal D)$$ +
+
+
$$ 1 + 2 + 3 + 4 + 5 $$
+
$$Q(\mathcal D+\Delta\mathcal D) \sim O(|\mathcal D| + |\Delta\mathcal D|)$$
+
+
+
$$ 10 + 5 $$
+
$$\texttt{VIEW} + SUM(\Delta\mathcal D) \sim O(|\Delta\mathcal D|)$$
+
+
+ +
+

Intuition

+
+ $$\mathcal{R} = \{\ \textbf{A, B, C}\ \},\ \mathcal S = \{\ \textbf{X, Y}\ \} \hspace{1in} \Delta\mathcal{R} = \{\ \textbf{D}\ \}$$ + $$Q(\mathcal R, \mathcal S) = \texttt{COUNT}(\mathcal R \times \mathcal S)$$ +
+
+
$$ \texttt{COUNT}(\textbf{AX, AY, BX, BY, CX, CY, }\underline{\textbf{DX, DY}}) $$
+
$$Q(\mathcal R+\Delta\mathcal R, \mathcal S) \sim O( (|\mathcal R| + |\Delta\mathcal D|) \cdot |\mathcal S|)$$
+
+
+
$$ 6 + \texttt{COUNT}(\underline{\textbf{DX, DY}}) $$
+
$$\texttt{VIEW} + \texttt{COUNT}(\Delta\mathcal R \times \mathcal S) \sim O(|\Delta\mathcal R| \cdot |\mathcal S|)$$
+
+
+
+ +
+
+

$+$ is like $\uplus$

+

$\bowtie$ is like $\times$

+ +

Are these types of patterns common?

+
+ +
+

Rings/Semirings

+ +

Semiring: $\left< \mathbb S, +, \times, \mathbb 0, \mathbb 1\right>$

+ +

Any set of 'things' $\mathbb S$ such that...

+ + + + + + + + + +
+

"Closed"

+ $$S_i + S_j = S_k$$ + $$S_i \times S_j = S_k$$ +
+

Additive, Multiplicative Identities

+ $$S_i + 0 = S_i$$ + $$S_i \times 1 = S_i$$ + $$S_i \times 0 = 0$$ +
+ $$S_i \times (S_j + S_k) = (S_i \times S_j) + (S_j \times S_k)$$ +

Addition distributes over multiplication

+
+
+ +
+

Rings/Semirings

+ +

Ring: $\left< \mathbb S, +, \times, \mathbb 0, \mathbb 1, -\right>$

+ +

Any semiring with an additive inverse....

+ + $$S_i + (-S_i) = 0$$ +
+ +
+ + +

THIS TANGENT ENDS NOW

+ Futurama is © 20th Century Fox Television +
+ +
+ +
+
+
+ $$\texttt{WHEN } \mathcal D \leftarrow \mathcal{D}+\Delta\mathcal D \texttt{ DO: }\\ + \texttt{VIEW} \leftarrow \texttt{VIEW} + \Delta Q(\mathcal D,\Delta\mathcal D)$$ +
+
+ +
+

Basic Questions

+
    +
  • What does $\Delta \mathcal R$ mean?
  • +
  • What is $\mathcal R + \Delta \mathcal R$?
  • +
  • How do we derive $\Delta Q$?
  • +
+
+
+ +
+
+

What is $\Delta \mathcal R$?

+
+

Insertions

+

Deletions

+

Updates

+
+
+ +
+

What is $\Delta \mathcal R$?

+

A Set/Bag of Insertions

+

+

+

A Set/Bag of Deletions

+
+
+ +
+
+

What is $\Delta \mathcal R$?

+ + + + + + + + + + + + + + + + +
$\mathcal R$$+$$\Delta \mathcal R$
A Set/Bag"+"A Set/Bag of Insertions
+ A Set/Bag of Deletions
$\mathcal R$
$\cup$/$\uplus$
+
$-$
+
$\Delta \mathcal R_{ins}$
+
$\Delta \mathcal R_{del}$
+

... this feels a bit wrong

+
+
+ +
+
+

+ $\texttt{VIEW} \leftarrow \texttt{VIEW} + $$\Delta Q(\mathcal D, \Delta \mathcal D)$ +

+
+

Given $Q(\mathcal R, \mathcal S, \ldots)$

+

Construct $\Delta Q(\mathcal R, \Delta \mathcal R, \mathcal S, \Delta \mathcal S, \ldots)$

+
+
+ +
+

$\sigma(\mathcal R) \rightarrow \sigma(\mathcal R \uplus \Delta \mathcal R)$

+

+ $ \equiv $ + $\sigma(\mathcal R)$ + $ \uplus $ + $\sigma(\Delta \mathcal R)$ +

+
+

$Q(\mathcal D) = \sigma(\mathcal R)$

+

$\Delta Q(\mathcal D, \Delta \mathcal D) = \sigma(\Delta \mathcal R)$

+
+

Set/Bag difference also commutes through selection

+
+ +
+

$\pi(\mathcal R) \rightarrow \pi(\mathcal R \uplus \Delta \mathcal R)$

+

+ $ \equiv $ + $\pi(\mathcal R)$ + $ \uplus $ + $\pi(\Delta \mathcal R)$ +

+
+

$Q(\mathcal D) = \pi(\mathcal R)$

+

$\Delta Q(\mathcal D, \Delta \mathcal D) = \pi(\Delta \mathcal R)$

+
+

Does this work under set semantics?

+
+ +
+

$\mathcal R_1 \uplus \mathcal R_2 \rightarrow \mathcal R_1 \uplus \Delta \mathcal R_1 \uplus \mathcal R_2 \uplus \Delta \mathcal R_2$

+

+ $ \equiv $ + $\mathcal R_1 \uplus \mathcal R_2$ + $ \uplus $ + $\Delta \mathcal R_1 \uplus \Delta \mathcal R_2$ +

+
+

$Q(\mathcal D) = \mathcal R_1 \uplus \mathcal R_2$

+

$\Delta Q(\mathcal D, \Delta \mathcal D) = \Delta \mathcal R_1 \uplus \Delta \mathcal R_2$

+
+
+ +
+

How do we derive $\Delta Q$?

+

So far: + $$\Delta Q_{ins}(\mathcal D, \Delta \mathcal D) = Q(\Delta \mathcal Q_{ins})$$ + $$\Delta Q_{del}(\mathcal D, \Delta \mathcal D) = Q(\Delta \mathcal Q_{del})$$ +

+
+
+ +
+
+ $$\mathcal R \times \mathcal S\ \rightarrow\ (\mathcal R \uplus \Delta \mathcal R) \times \mathcal S$$ +
+ +
+
+ $$\mathcal{R} = \{\ \textbf{A, B, C}\ \},\ \mathcal S = \{\ \textbf{X, Y}\ \}$$ + $$Q(\mathcal R, \mathcal S) = \texttt{COUNT}(\mathcal R \times \mathcal S)$$ +
+
+ $$\mathcal R \times \mathcal S = \{\ \textbf{AX, AY, BX, BY, CX, CY}\ \}$$ +
+
+ $$\Delta\mathcal{R} = \{\ \textbf{D}\ \}$$ +
+
+ $$(\mathcal R \uplus \Delta\mathcal R) \times \mathcal S =\\ \{\ \textbf{AX, AY, BX, BY, CX, CY, }\underline{\textbf{DX, DY}}\ \}$$ +
$\equiv $ + $\mathcal R \times \mathcal S$ + $\uplus$ + $\Delta \mathcal R \times \mathcal S$ +
+

... but what if $\mathcal R$ and $\mathcal S$ both change

+
+ +
+
+ $$(\mathcal R_1 \uplus \Delta \mathcal R_1) \times (\mathcal R_2 \uplus \Delta \mathcal R_2)$$ +
+
+ $$\left(\mathcal R_1 \times (\mathcal R_2 \uplus \Delta \mathcal R_2)\right) \uplus \left(\Delta \mathcal R_1 \times (\mathcal R_2 \uplus \Delta \mathcal R_2)\right)$$ +
+
+ $$\left(\mathcal R_1 \times \mathcal R_2\right) \uplus \left(\mathcal R_1 \times \Delta \mathcal R_2\right) \uplus \left(\Delta \mathcal R_1 \times (\mathcal R_2 \uplus \Delta \mathcal R_2)\right)$$ +
+
+ $\left(\mathcal R_1 \times \mathcal R_2\right)$ $\uplus$   + $\left(\mathcal R_1 \times \Delta \mathcal R_2\right) \uplus \left(\Delta \mathcal R_1 \times \mathcal R_2\right) \uplus \left(\Delta \mathcal R_1 \times \Delta \mathcal R_2\right)$ +
+
+
+
+ +
+
+ +
+
+ +
+
+

Multisets

+

$$\{1, 1, 1, 2, 2, 2, 2, 2, 3, 3, 4, 4, 4, 4, 4, 4, 5\}$$

+

(not compact)

+ +

+ $$\{1 \rightarrow \times 3; 2 \rightarrow \times 5; 3 \rightarrow \times 2; 4 \rightarrow \times 6; 5 \rightarrow \times 1\}$$ +

+

Multiset representation: Tuple $\rightarrow$ # of occurrences

+

multiplicity

+
+ +
+

Multiset Deltas

+ +

Insertions = Positive Multiplicity

+

Deletions = Negative Multiplicity

+

+ = Bag/Multiset Union

+
+ +
+

Multiset Deltas

+ +

What does Union Do?

+

+ $\{ A \rightarrow 1, B \rightarrow 2 \} \uplus \{ B \rightarrow 2, C \rightarrow 4 \} = $ +

+

+ $=\{$ + $A \rightarrow 1,$ + $B \rightarrow 5,$ + $C \rightarrow 4$ + $\}$ +

+

+ $\{ A \rightarrow 1 \} \uplus \{ A \rightarrow -1 \}$ + $= \{A \rightarrow 0\}$ + $ = \{\}$ +

+
+ +
+

Multiset Deltas

+ +

What does Cross-Product Do?

+

+ $\{ A \rightarrow 1, B \rightarrow 3 \} \times \{ C \rightarrow 4 \} $ +

+

+ + $= \{ \left< A,C \right> \rightarrow$ + $4$ + $\left< B,C \right> \rightarrow$ + $12$ + $\}$ +

+
+ +
+

Multiset Deltas

+ +

What does Projection Do?

+

+ $\pi_{\text{1st attr}}\{ + \left< A,X \right> \rightarrow 1, + \left< A,Y \right> \rightarrow 2, + \left< B,Z \right> \rightarrow 5, + \}$ +

+

+ $= \{$ + $A \rightarrow 1, A \rightarrow 2,$ + $B \rightarrow 5\}$ +

+

+ $= \{A \rightarrow 3, B \rightarrow 5\}$ +

+
+ +
+ $$\bowtie\; \equiv \times$$ + $$\pi, \uplus \equiv +$$ + + Rings strike again! +
+ +
+

Multiset Deltas

+ +

What does Selection Do?

+

+ $\sigma_{A}\{ + A \rightarrow 1, + B \rightarrow 5, + C \rightarrow 3 + \}$ +

+

+ $= \{ + A \rightarrow 1, + B \rightarrow 0, + C \rightarrow 0 \}$ +

+

+ $= \{ A \rightarrow 1\}$ +

+
+ +
+ +
+ Next class: Updates +
\ No newline at end of file diff --git a/src/teaching/cse-562/2021sp/slide/2021-04-01/CustomerOrderLineitemExample.svg b/src/teaching/cse-562/2021sp/slide/2021-04-01/CustomerOrderLineitemExample.svg new file mode 100644 index 00000000..838ee803 --- /dev/null +++ b/src/teaching/cse-562/2021sp/slide/2021-04-01/CustomerOrderLineitemExample.svg @@ -0,0 +1,394 @@ + + + + + + + + image/svg+xml + + + + + + + CUSTOMER + ORDERS + LINEITEM + σmktsegment + σorderdate + σshipdate + + + + + + + + + + + + + Δ + Δ[ (σ(C) ⋈ σ(O)) ⋈ σ(L) ] + + + + Δ + Δ[ (σ(C) ⋈ σ(O)) ] ⋈ σ(L) + + + + Δ + Δ[ (σ(C) ⋈ σ(O)) ] ⋈ σ(L) + = ∅ + = ∅ + + + + Δ + (σ(C) ⋈ σ(O)) ⋈ Δ[ σ(L) ] + + + + Δ + (σ(C) ⋈ σ(O)) ⋈ σ( Δ[L] ) + + diff --git a/src/teaching/cse-562/2021sp/slide/2021-04-01/DBToQ.svg b/src/teaching/cse-562/2021sp/slide/2021-04-01/DBToQ.svg new file mode 100644 index 00000000..c61902ec --- /dev/null +++ b/src/teaching/cse-562/2021sp/slide/2021-04-01/DBToQ.svg @@ -0,0 +1,1024 @@ + + + + + + + + + + + + + + + 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