diff --git a/src/teaching/cse-562/2021sp/slide/2021-05-04-Review1.erb b/src/teaching/cse-562/2021sp/slide/2021-05-04-Review1.erb index e92d2f77..645b4b77 100644 --- a/src/teaching/cse-562/2021sp/slide/2021-05-04-Review1.erb +++ b/src/teaching/cse-562/2021sp/slide/2021-05-04-Review1.erb @@ -686,97 +686,3 @@ dependencies: - -
-
-
- $$\texttt{WHEN } \mathcal D \leftarrow \mathcal{D}+\Delta\mathcal D \texttt{ DO:}~~~~\\ - \texttt{VIEW} \leftarrow \texttt{VIEW} + \Delta Q(\mathcal D,\Delta\mathcal D)$$ -
- - - - - - - - - -
$\Delta Q$(ideally) Small & fast query
$+$(ideally) Fast "merge" operation
-
- -
-

Intuition

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

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

-

- $ \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 $ - $\Delta \mathcal R_1 \uplus \Delta \mathcal R_2$ -

-
-

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

-

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

-
-
- -
-
- $$(\mathcal R_1 \uplus \Delta \mathcal R_1) \times (\mathcal R_2 \uplus \Delta \mathcal R_2)$$ -
-
- $$\left(\mathcal R_1 \times (\mathcal R_2 \uplus \Delta \mathcal R_2)\right) \uplus \left(\Delta \mathcal R_1 \times (\mathcal R_2 \uplus \Delta \mathcal R_2)\right)$$ -
-
- $$\left(\mathcal R_1 \times \mathcal R_2\right) \uplus \left(\mathcal R_1 \times \Delta \mathcal R_2\right) \uplus \left(\Delta \mathcal R_1 \times (\mathcal R_2 \uplus \Delta \mathcal R_2)\right)$$ -
-
- $$\left(\mathcal R_1 \times \mathcal R_2\right) \uplus \left(\mathcal R_1 \times \Delta \mathcal R_2\right) \uplus \left(\Delta \mathcal R_1 \times \mathcal R_2\right) \uplus \left(\Delta \mathcal R_1 \times \Delta \mathcal R_2\right)$$ -
-
-
diff --git a/src/teaching/cse-562/2021sp/slide/2021-05-06-Review2.erb b/src/teaching/cse-562/2021sp/slide/2021-05-06-Review2.erb index ed914415..345631a2 100644 --- a/src/teaching/cse-562/2021sp/slide/2021-05-06-Review2.erb +++ b/src/teaching/cse-562/2021sp/slide/2021-05-06-Review2.erb @@ -9,6 +9,101 @@ dependencies: require "slide_utils.rb" %> +
+
+
+ $$\texttt{WHEN } \mathcal D \leftarrow \mathcal{D}+\Delta\mathcal D \texttt{ DO:}~~~~\\ + \texttt{VIEW} \leftarrow \texttt{VIEW} + \Delta Q(\mathcal D,\Delta\mathcal D)$$ +
+ + + + + + + + + +
$\Delta Q$(ideally) Small & fast query
$+$(ideally) Fast "merge" operation
+
+ +
+

Intuition

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

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

+

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

+
+

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

+

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

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