diff --git a/src/teaching/cse-562/2019sp/slide/2019-02-11-Algorithms.html b/src/teaching/cse-562/2019sp/slide/2019-02-11-Algorithms.html index ac421d8b..b0dd3653 100644 --- a/src/teaching/cse-562/2019sp/slide/2019-02-11-Algorithms.html +++ b/src/teaching/cse-562/2019sp/slide/2019-02-11-Algorithms.html @@ -4,6 +4,21 @@ title: "Query Evaluation" date: February 11, 2019 textbook: "Ch. 15.1-15.5, 16.7" --- + + +

Query Evaluation Styles

@@ -130,19 +145,19 @@ textbook: "Ch. 15.1-15.5, 16.7"
Constant!
IOs added?
-
$|S| \cdot \texttt{cost}(R)$ tuples read
-
(or $|R| \cdot \texttt{cost}(S)$)
+
$(|R|-1) \cdot \texttt{cost}(S)$ tuples read
+
(or $(|S|-1) \cdot \texttt{cost}(R)$)
-

If $R$ is a query, this can be very expensive

+

If $S$ is a query, this can get very expensive

Cross ($R \times S$)

-

Optimization 1: Cache $R$ in memory

+

Optimization 1: Cache $S$ in memory

Memory Required?
-
$O(|R|)$
+
$O(|S|)$
IOs added?
None!
@@ -151,15 +166,15 @@ textbook: "Ch. 15.1-15.5, 16.7"

Cross ($R \times S$)

-

Optimization 2: Cache $R$ on disk

+

Optimization 2: Cache $S$ on disk

Memory Required?
Constant
IOs added?
-
$|R|$ tuples written.
-
$(|S| - 1) \cdot |R|$ tuples read.
+
$|S|$ tuples written.
+
$(|R| - 1) \cdot |R|$ tuples read.
@@ -207,15 +222,16 @@ textbook: "Ch. 15.1-15.5, 16.7"

Block-Nested Loop ($R \times S$)

-

(with $\mathcal B$ as the block size for $S$)

+

(with $\mathcal B$ as the block size for $R$)

+

(and with caching $S$ to disk)

Memory Required?
$O(\mathcal B)$
IOs added?
-
$|R|$ tuples written.
-
$(\frac{|S|}{\mathcal B} - 1) \cdot |R|$ tuples read.
+
$|S|$ tuples written.
+
$(\frac{|R|}{\mathcal B} - 1) \cdot |R|$ tuples read.

In-memory caching is a special case of block-nested loop with $\mathcal B = |S|$

Does the block size for $R$ matter?

diff --git a/src/teaching/cse-562/2019sp/slide/2019-02-13-ExtRA.html b/src/teaching/cse-562/2019sp/slide/2019-02-13-ExtRA.html index 9005ee0d..925c23f2 100644 --- a/src/teaching/cse-562/2019sp/slide/2019-02-13-ExtRA.html +++ b/src/teaching/cse-562/2019sp/slide/2019-02-13-ExtRA.html @@ -1,362 +1,512 @@ - - - - - - - CSE 4/562 - Spring 2018 - - - - - - - - - - - - - - - - - - - - - - - - - -
- - -
- - CSE 4/562 - Database Systems -
- -
- -
-

Extended RA

-

CSE 4/562 – Database Systems

-
February 12, 2018
-
- -
-
-

Extended Relational Algebra

- -
-
Set/Bag Operations
-
Select ($\sigma$), Project ($\pi$), Join ($\bowtie$), Union ($\cup$)
- -
Bag Operations
-
Distinct ($\delta$), Outer Joins (⟗)
- -
List Operations
-
Sort ($\tau$), Limit
- -
Arithmetic Operations
-
Extended Projection ($\pi$), Aggregation ($\sigma$), Grouping ($\gamma$)
-
- -
- -
-
-
-

Extended Projection

- -

Like normal projection, but can create new columns

- - $\pi_{M \leftarrow A+B*C,\; N \leftarrow 2}(R)$ -

produces 1 row for every row of R, with 2 columns: M and N

-
-
- -
-
-

Outer Join

-

... but first

-
- -
-

NULL Values

- -
    -
  • Field values can be unknown or inapplicable.
      -
    • A tree with an unknown species.
      • -
    • The street of a tree in a park.
      • -
    • The '.' on many of your ID cards
      • -
    • -
  • SQL provides a special NULL value for these cases
    • -
-

NULL makes things more complicated.

-
- -
- $$\textbf{Trees.SPC_COMMON} = \texttt{'Brooklyn'}$$ - -

- What happens if Trees.SPC_COMMON is NULL? -

- -
- $$\texttt{NULL} = \textbf{'Brooklyn'} \equiv \textbf{Unknown}$$ -
-
- -
- - - - - - - - - - -
UnknownANDUnknown$\equiv$Unknown
UnknownANDTrue$\equiv$Unknown
UnknownANDFalse$\equiv$False
UnknownORUnknown$\equiv$Unknown
UnknownORTrue$\equiv$True
UnknownORFalse$\equiv$Unknown
NOTUnknown$\equiv$Unknown
- -

WHERE clauses eliminate all non-True rows

-
- -
- $$Streets \bowtie_{StreetName} Trees$$ - -

What happens if some streets have no trees?

-
- -
-

Outer Join (⟗, ⟕, ⟖)

- -
    -
  1. Include all results from the normal (inner) join.
    2. -
  2. Also include rows that don't get joined.
    3. -
-
- -
-

Outer Join

- -
-
Inner Join
-
Normal, plain, simple join
- -
Left Outer Join (⟕)
-
Include un-joined rows from the left hand side
- -
Right Outer Join (⟖)
-
Include un-joined rows from the right hand side
- -
[Full] Outer Join (⟗)
-
Include un-joined rows from either side
-
-
-
- -
-
-

Sort / Limit

- -

- $$\tau_{A}(R)$$ - The tuples of $R$ in ascending order according to 'A' -

- -

- $$\textbf{L}_{n}(R)$$ - The first $n$ tuples of R -

(Typically combined with sort. If not, pick arbitrarily.)
-

-
- -
-

Sort

- -

- Pick your favorite sort algorithm. -

- -

What happens if you don't have enough memory?

-
- -
-

Key Idea: Merging 2 sorted lists requires $O(1)$ memory.

-
- -
-

2-Way Sort

-
-
Pass 1
-
Create lots of (small) sorted lists.
- -
Pass 2+
-
Merge sorted lists of size $N$ into sorted lists of size $2N$
-
-
- -
-

Pass 1: Create Sorted Runs

- -
- -
-

Pass 2: Merge Sorted Runs

- -
- -
-

Repeat Pass 2 As Needed.

-
- -
-

What's the bottleneck?

- -

IO Cost: $O(N \cdot \lceil\log_2(N)\rceil)$
(with $N$ blocks)

-
- -
- -
- -
-

Using More Memory

- -
-
Pass 1
-
Sort Bigger Buffers
-
Re-Use Memory When Done
- -
Pass 2
-
Merge $K$ Runs Simultaneously: $O(N \cdot \lceil\log_K(N)\rceil)$ IO
-
-
- -
-

Replacement Sort

- -
- -
-

Replacement Sort

- -
- -
-

Replacement Sort

- -
- -
-

Replacement Sort

- -
- -
-

Replacement Sort

- -
- -
-

Replacement Sort

- -
- -
-

Replacement Sort

- -
- -
-

Replacement Sort

- -
- -
-

On average, we'll get runs of size $2 \cdot |WS|$

-
-
- -
- - - - - - - +--- +template: templates/cse4562_2019_slides.erb +title: "Extended Relational Algebra" +date: February 13, 2019 +textbook: "Ch. 5.2, 15.4" +--- +
+
+

Extended Relational Algebra

+ +
+
Set/Bag Operations
+
Select ($\sigma$), Project ($\pi$), Join ($\bowtie$), Union ($\cup$)
+ +
Bag Operations
+
Distinct ($\delta$), Outer Joins (⟗)
+ +
List Operations
+
Sort ($\tau$), Limit (L)
+ +
Arithmetic Operations
+
Extended Projection ($\pi$), Aggregation ($\sigma$), Grouping ($\gamma$)
+
+ +
+ +
+
+
+

Extended Projection

+ +

Like normal projection, but can create new columns

+ + $\pi_{M \leftarrow A+B*C,\; N \leftarrow 2}(R)$ +

produces 1 row for every row of R, with 2 columns: M and N

+
+
+ +
+
+

Outer Join

+

... but first

+
+ +
+

NULL Values

+ +
    +
  • Field values can be unknown or inapplicable.
      +
    • A tree with an unknown species.
      • +
    • The street of a tree in a park.
      • +
    • The '.' on many of your ID cards
      • +
    • +
  • SQL provides a special NULL value for these cases
    • +
+

NULL makes things more complicated.

+
+ +
+ $$\textbf{Trees.SPC_COMMON} = \texttt{'Brooklyn'}$$ + +

+ What happens if Trees.SPC_COMMON is NULL? +

+ +
+ $$\texttt{NULL} = \textbf{'Brooklyn'} \equiv \textbf{Unknown}$$ +
+
+ +
+ + + + + + + + + + +
UnknownANDUnknown$\equiv$Unknown
UnknownANDTrue$\equiv$Unknown
UnknownANDFalse$\equiv$False
UnknownORUnknown$\equiv$Unknown
UnknownORTrue$\equiv$True
UnknownORFalse$\equiv$Unknown
NOTUnknown$\equiv$Unknown
+ +

WHERE clauses eliminate all non-True rows

+
+
+ +
+
+ $$Streets \bowtie_{StreetName} Trees$$ + +

What happens if some streets have no trees?

+
+ +
+

Outer Join (⟗, ⟕, ⟖)

+ +
    +
  1. Include all results from the normal (inner) join.
    2. +
  2. Also include rows that don't get joined.
    3. +
+
+ +
+

Outer Join

+ +
+
Inner Join
+
Normal, plain, simple join
+ +
Left Outer Join (⟕)
+
Include un-joined rows from the left hand side
+ +
Right Outer Join (⟖)
+
Include un-joined rows from the right hand side
+ +
[Full] Outer Join (⟗)
+
Include un-joined rows from either side
+
+
+
+
+

Streets

+ + + + + + +
DistrictStreetName
AApple St.
BBorder St.
CCoventry St.
DDurham St.
+
+
+

Trees

+ + + + + + +
TreeIdStreetName
1Apple St.
2Border St.
3Durham St.
4Elicott St.
+
+
+
+

Streets ⟗ Trees

+ + + + + + + +
DistrictStreetName TreeIdStreetName
A Apple St. 1 Apple St.
B Border St. 2 Border St.
C Coventry St.NULL NULL
D Durham St. 3 Durham St.
NULL NULL 4 Elicott St.
+

Only LEFT outer join

+

Only RIGHT outer join

+
+
+ +
+
+

Sort / Limit

+ +

+ $$\tau_{A}(R)$$ + The tuples of $R$ in ascending order according to 'A' +

+ +

+ $$\textbf{L}_{n}(R)$$ + The first $n$ tuples of R +

(Typically combined with sort. If not, pick arbitrarily.)
+

+
+ +
+

Sort

+ +

+ Pick your favorite sort algorithm. +

+ +

What happens if you don't have enough memory?

+
+ +
+

Key Idea: Merging 2 sorted lists requires $O(1)$ memory.

+
+ +
+

2-Way Sort

+
+
Pass 1
+
Create lots of (small) sorted lists.
+ +
Pass 2+
+
Merge sorted lists of size $N$ into sorted lists of size $2N$
+
+
+ +
+

Pass 1: Create Sorted Runs

+ +
+ +
+

Pass 2: Merge Sorted Runs

+ +
+ +
+

Repeat Pass 2 As Needed.

+
+ +
+

What's the bottleneck?

+ +

IO Cost: $O(N \cdot \lceil\log_2(N)\rceil)$
(with $N$ blocks)

+
+ +
+ +
+ +
+

Using More Memory

+ +
+
Pass 1
+
Sort Bigger Buffers
+
Re-Use Memory When Done
+ +
Pass 2
+
Merge $K$ Runs Simultaneously: $O(N \cdot \lceil\log_K(N)\rceil)$ IO
+
+
+ +
+

Replacement Sort

+ +
+ +
+

Replacement Sort

+ +
+ +
+

Replacement Sort

+ +
+ +
+

Replacement Sort

+ +
+ +
+

Replacement Sort

+ +
+ +
+

Replacement Sort

+ +
+ +
+

Replacement Sort

+ +
+ +
+

Replacement Sort

+ +
+ +
+

On average, we'll get runs of size $2 \cdot |WS|$

+
+
+ +
+
+

Aggregation

+ +
+
+
Normal Aggregates
+
SELECT COUNT(*) FROM R
+
SELECT SUM(A) FROM R
+
+ +
+
Group-By Aggregates
+
SELECT A, SUM(B) FROM R GROUP BY A
+
+ +
+
Distinct
+
SELECT DISTINCT A FROM R
+
SELECT A FROM R GROUP BY A
+
+
+
+ +
+

Normal Aggregates

+ + + + + + + + + +
TREE_IDSPC_COMMONBORONAMETREE_DBH
180683'red maple''Queens'3
315986'pin oak''Queens'21
204026'honeylocust''Brooklyn'3
204337'honeylocust''Brooklyn'10
189565'American linden''Brooklyn'21
... and 683783 more
+ +
+ SELECT COUNT(*) FROM TREES +
+
+ +
+ + + + + + + + + + + + + + + +
TREE_IDSPC_COMMONBORONAMETREE_DBH
COUNT = 0
180683'red maple''Queens'3
COUNT = 1
315986'pin oak''Queens'21
COUNT = 2
204026'honeylocust''Brooklyn'3
COUNT = 3
204337'honeylocust''Brooklyn'10
COUNT = 4
189565'American linden''Brooklyn'21
COUNT = 5
... and 683783 more
COUNT = 683788
+
+ +
+
+ SELECT SUM(TREE_DBH) FROM TREES +
+ + + + + + + + + + + + + + +
TREE_IDSPC_COMMONBORONAMETREE_DBH
SUM = 0
180683'red maple''Queens'3
SUM = 3
315986'pin oak''Queens'21
SUM = 24
204026'honeylocust''Brooklyn'3
SUM = 27
204337'honeylocust''Brooklyn'10
SUM = 37
189565'American linden''Brooklyn'21
SUM = 58
... and 683783 more
+
+ +
+

Basic Aggregate Pattern

+

This is also sometimes called a "fold"

+
+
Init
+
Define a starting value for the accumulator
+
Fold(Accum, New)
+
Merge a new value into the accumulator
+
+
+ +
+

COUNT(*)

+
+
Init
+
$0$
+
Fold(Accum, New)
+
$Accum + 1$
+
+
+ +
+

SUM(A)

+
+
Init
+
$0$
+
Fold(Accum, New)
+
$Accum + New$
+
+
+ +
+

AVG(A)

+
+
Init
+
$\{ sum = 0, count = 0 \}$
+
Fold(Accum, New)
+
$\{ sum = Accum.sum + New, \\\;count = Accum.count + 1\}$
+
Finalize(Accum)
+
$\frac{Accum.sum}{Accum.count}$
+
+
+ +
+

Basic Aggregate Pattern

+
+
Init
+
Define a starting value for the accumulator
+
Fold(Accum, New)
+
Merge a new value into the accumulator
+
Finalize(Accum)
+
Extract the aggregate from the accumulator.
+
+
+ +
+

Basic Aggregate Types

+

Grey et. al. "Data Cube: A Relational Aggregation Operator Generalizing Group-By, Cross-Tab, and Sub-Totals

+ +
+
Distributive
+
Finite-sized accumulator and doesn't need a finalize (COUNT, SUM)
+
Algebraic
+
Finite-sized accumulator but needs a finalize (AVG)
+
Holistic
+
Unbounded accumulator (MEDIAN)
+
+
+
+ +
+
+

Group-By Aggregates

+
+ SELECT SPC_COMMON, COUNT(*) FROM TREES GROUP BY SPC_COMMON +
+
+ +
+

Naive Idea: Keep a separate accumulator for each group

+
+ +
+ + + + + + + + + + + +
TREE_IDSPC_COMMONBORONAMETREE_DBH
{}
180683'red maple''Queens'3
{ 'red maple' = 1 }
204337'honeylocust''Brooklyn'10
{ 'red maple' = 1, 'honeylocust' = 1 }
315986'pin oak''Queens'21
{ 'red maple' = 1, 'honeylocust' = 1, 'pin oak' = 1 }
204026'honeylocust''Brooklyn'3
{ 'red maple' = 1, 'honeylocust' = 2, 'pin oak' = 1 }
+
+ +
+

What could go wrong?

+
+ +
+

Alternative Grouping Algorithms

+ +
+
2-pass Hash Aggregate
+
Like 2-pass Hash Join: Distribute groups across buckets, then do an in-memory aggregate for each bucket.
+ +
Sort-Aggregate
+
Like Sort-Merge Join: Sort data by groups, then group elements will be adjacent.
+
+
+ +
+ +
+ +
+ + + + + + + + + + + + + +
TREE_IDSPC_COMMONBORONAMETREE_DBH
{}
204337'honeylocust''Brooklyn'10
{ 'honeylocust' = 1 }
204026'honeylocust''Brooklyn'3
{ 'honeylocust' = 2 }
... and more
315986'pin oak''Queens'21
{ 'honeylocust' = 3206, 'pin oak' = 1 }
... and more
180683'red maple''Queens'3
{ 'pin oak' = 53814, 'red maple' = 1 }
+
+
+ +
+
+
Set/Bag Operations
+
Select ($\sigma$), Project ($\pi$), Join ($\bowtie$), Union ($\cup$)
+ +
Bag Operations
+
Distinct ($\delta$), Outer Joins (⟗)
+ +
List Operations
+
Sort ($\tau$), Limit (L)
+ +
Arithmetic Operations
+
Extended Projection ($\pi$), Aggregation ($\sigma$), Grouping ($\gamma$)
+
+
diff --git a/src/teaching/cse-562/2019sp/slide/graphics/2018-02-14-Merge-Run.svg b/src/teaching/cse-562/2019sp/slide/graphics/2018-02-14-Merge-Run.svg new file mode 100644 index 00000000..e9ecce4c --- /dev/null +++ b/src/teaching/cse-562/2019sp/slide/graphics/2018-02-14-Merge-Run.svg @@ -0,0 +1,806 @@ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + image/svg+xml + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + diff --git a/src/teaching/cse-562/2019sp/slide/graphics/2018-02-14-Merge-Tree.svg b/src/teaching/cse-562/2019sp/slide/graphics/2018-02-14-Merge-Tree.svg new file mode 100644 index 00000000..4bfcaa5c --- /dev/null +++ b/src/teaching/cse-562/2019sp/slide/graphics/2018-02-14-Merge-Tree.svg @@ -0,0 +1,679 @@ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + image/svg+xml + + + + + + + + + + + + + + 1 + 2 + 4 + + log2(N) + + + + + + + + + + + + + + + N + + + + + + + + + + + + + + + + + 1 + + diff --git a/src/teaching/cse-562/2019sp/slide/graphics/2018-02-14-ReplSort-1.svg b/src/teaching/cse-562/2019sp/slide/graphics/2018-02-14-ReplSort-1.svg new file mode 100644 index 00000000..5aa69c37 --- /dev/null +++ b/src/teaching/cse-562/2019sp/slide/graphics/2018-02-14-ReplSort-1.svg @@ -0,0 +1,194 @@ + + + + + + + + + + image/svg+xml + + + + + + + + 12 + 8 + 10 + ... + Working Set + Input + Output + 35 + 2 + 4 + ... + + diff --git a/src/teaching/cse-562/2019sp/slide/graphics/2018-02-14-ReplSort-2.svg b/src/teaching/cse-562/2019sp/slide/graphics/2018-02-14-ReplSort-2.svg new file mode 100644 index 00000000..f6b7e4c2 --- /dev/null +++ b/src/teaching/cse-562/2019sp/slide/graphics/2018-02-14-ReplSort-2.svg @@ -0,0 +1,194 @@ + + + + + + + + + + image/svg+xml + + + + + + + + 12 + 8 + 10 + ... + Working Set + Input + Output + 35 + 2 + 4 + ... + + diff --git a/src/teaching/cse-562/2019sp/slide/graphics/2018-02-14-ReplSort-3.svg b/src/teaching/cse-562/2019sp/slide/graphics/2018-02-14-ReplSort-3.svg new file mode 100644 index 00000000..2ea39b8a --- /dev/null +++ b/src/teaching/cse-562/2019sp/slide/graphics/2018-02-14-ReplSort-3.svg @@ -0,0 +1,172 @@ + + + + + + + + + + image/svg+xml + + + + + + + + 12 + 8 + 10 + ... + Working Set + Input + Output + 35 + 2 + + diff --git a/src/teaching/cse-562/2019sp/slide/graphics/2018-02-14-ReplSort-4.svg b/src/teaching/cse-562/2019sp/slide/graphics/2018-02-14-ReplSort-4.svg new file mode 100644 index 00000000..6e88c7bd --- /dev/null +++ b/src/teaching/cse-562/2019sp/slide/graphics/2018-02-14-ReplSort-4.svg @@ -0,0 +1,172 @@ + + + + + + + + + + image/svg+xml + + + + + + + + 10 + 8 + 12 + ... + Working Set + Input + Output + 35 + 2 + + diff --git a/src/teaching/cse-562/2019sp/slide/graphics/2018-02-14-ReplSort-5.svg b/src/teaching/cse-562/2019sp/slide/graphics/2018-02-14-ReplSort-5.svg new file mode 100644 index 00000000..e365a9e8 --- /dev/null +++ b/src/teaching/cse-562/2019sp/slide/graphics/2018-02-14-ReplSort-5.svg @@ -0,0 +1,194 @@ + + + + + + + + + + image/svg+xml + + + + + + + + 10 + 8 + 12 + ... + Working Set + Input + Output + 35 + 2 + 4 + ... + + diff --git a/src/teaching/cse-562/2019sp/slide/graphics/2018-02-14-ReplSort-6.svg b/src/teaching/cse-562/2019sp/slide/graphics/2018-02-14-ReplSort-6.svg new file mode 100644 index 00000000..02c49355 --- /dev/null +++ b/src/teaching/cse-562/2019sp/slide/graphics/2018-02-14-ReplSort-6.svg @@ -0,0 +1,194 @@ + + + + + + + + + + image/svg+xml + + + + + + + + 10 + 8 + 12 + ... + Working Set + Input + Output + 35 + 2 + 4 + ... + + diff --git a/src/teaching/cse-562/2019sp/slide/graphics/2018-02-14-ReplSort-7.svg b/src/teaching/cse-562/2019sp/slide/graphics/2018-02-14-ReplSort-7.svg new file mode 100644 index 00000000..2746c5fb --- /dev/null +++ b/src/teaching/cse-562/2019sp/slide/graphics/2018-02-14-ReplSort-7.svg @@ -0,0 +1,167 @@ + + + + + + + + + + image/svg+xml + + + + + + + + 12 + ... + Working Set + Input + Output + 2 + 4 + ... + max = 10 + + diff --git a/src/teaching/cse-562/2019sp/slide/graphics/2018-02-14-ReplSort-8.svg b/src/teaching/cse-562/2019sp/slide/graphics/2018-02-14-ReplSort-8.svg new file mode 100644 index 00000000..c88d6589 --- /dev/null +++ b/src/teaching/cse-562/2019sp/slide/graphics/2018-02-14-ReplSort-8.svg @@ -0,0 +1,167 @@ + + + + + + + + + + image/svg+xml + + + + + + + + 12 + ... + Working Set + Input + Output + 2 + 4 + ... + max = 10 + + diff --git a/src/teaching/cse-562/2019sp/slide/graphics/2018-02-14-Sort-Run.svg b/src/teaching/cse-562/2019sp/slide/graphics/2018-02-14-Sort-Run.svg new file mode 100644 index 00000000..f40228ee --- /dev/null +++ b/src/teaching/cse-562/2019sp/slide/graphics/2018-02-14-Sort-Run.svg @@ -0,0 +1,529 @@ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + image/svg+xml + + + + + + + + + σ/π/⋈ + + + τ + + + + + + + + + + + + + + + + + + + + + diff --git a/src/teaching/cse-562/2019sp/slide/graphics/2019-02-13-2PassHashAgg.svg b/src/teaching/cse-562/2019sp/slide/graphics/2019-02-13-2PassHashAgg.svg new file mode 100644 index 00000000..411f8578 --- /dev/null +++ b/src/teaching/cse-562/2019sp/slide/graphics/2019-02-13-2PassHashAgg.svg @@ -0,0 +1,359 @@ + + + + + + + + + + image/svg+xml + + + + + + + + + + h(A) = 0 + h(A) = 1 + + + + + 1 + + + + 1 + + + + 3 + + + + 3 + + + + 2 + + + + 2 + + + + 1 + + + + 1 + + ✔ + + + + 1: Count = 2 + + + + 2: Count = 1 + + + + 3: Count = 1 + + +