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)
When the base data changes,
the view needs to be updated too!
Our view starts off initialized
+Idea: Recompute the view from scratch when data changes.
+Not quite facepalm-worthy, but not ideal.
+| $\Delta Q$ | +(ideally) Small & fast query | +
| $+$ | +(ideally) Fast "merge" operation | +
Intuition
+Intuition
+$+$ 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
+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})$$ +
+... but what if $\mathcal R$ and $\mathcal S$ both change
+ + +Multisets
+$$\{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?
++ $\pi_{\text{1st attr}}\{ + \left< A,X \right> \rightarrow 1, + \left< A,Y \right> \rightarrow 2, + \left< B,Z \right> \rightarrow 5, + \}$ +
++ $= \{$ + $A \rightarrow 1, A \rightarrow 2,$ + $B \rightarrow 5\}$ +
++ $= \{A \rightarrow 3, B \rightarrow 5\}$ +
+Multiset Deltas
+ +What does Selection Do?
++ $\sigma_{A}\{ + A \rightarrow 1, + B \rightarrow 5, + C \rightarrow 3 + \}$ +
++ $= \{ + A \rightarrow 1, + B \rightarrow 0, + C \rightarrow 0 \}$ +
++ $= \{ A \rightarrow 1\}$ +
+