Struktur Data & Algoritme Objectives Outline Compression

Struktur Data & Algoritme ( Data Structures & Algorithms )

Denny (denny@cs.ui.ac.id) Suryana Setiawan (setiawan@cs.ui.ac.id)

Fakultas Ilmu Komputer Universitas Indonesia Semester Genap - 2004/2005

Version 2.0 - Internal Use Only

Tree: application

SDA/HUFF/V2.0/2

Objectives

„ understand one of file compression technique (Huffman)

SDA/HUFF/V2.0/3

Outline

„ Compression

„ Huffman compression

SDA/HUFF/V2.0/4

Compression

„ Process:

„Encoding: raw →compressed

„Decoding: compressed →raw

„ Types of compression

„Lossy : MPEG, JPEG

„Lossless

„ Compression Algorithm:

„RLE: Run Length Encoding

„Lempel-Zif

„Huffman Encoding

„ Performance of compression depends on file types.

SDA/HUFF/V2.0/5

Huffman Compression

„ If a woodchuck could chuck wood!

„ 32 char ×8 bit = 256 bits

„ 13 distinct characters →4 bit

„ Compressed code: 128 bits

„ Variable length string of bits to further improve compression.

„ Using prefix codes

SDA/HUFF/V2.0/6

Huffman Compression

„ Frequently occurring letters: short representation.

„ Infrequent letters: long representations.

SDA/HUFF/V2.0/7

i

a ^{8 5} u³ e³

Huffman Encoding: comparation

a = 00 →16 bits i = 01 →10 bits u = 10 →6 bits e = 11 →6 bits Total : 42 bits

SDA/HUFF/V2.0/8

Huffman Encoding: comparation

i

⁵

a

⁸

u

³

e

³ 6 11

19 a = 0 → 8 bits

i = 10 → 10 bits u = 110 → 9 bits e = 111 → 9 bits Total: 36 bits

SDA/HUFF/V2.0/9

0 0

0 0

0

0 0

0 0

0 0

0 1

1

1 1 1 1

1 1

1 1 1

1

! a l

u d

k w I f

h

c spaceo

Huffman Encoding

SDA/HUFF/V2.0/10

13

6 3

4 9

2 32

19 7 10

4

2

!:1 a:1 l:1

u:3 d:3

k:2 w:2 I:1 f:1

h:2

c:5 o:5

space:5

Huffman Encoding

SDA/HUFF/V2.0/11

Huffman Encoding (freq)

! = 0000 (1) I = 10000 (1) a = 00010 (1) f = 10001 (1) l = 00011 (1) h = 1001 (2) u = 001 (3) c = 101 (5) d = 010 (3) space= 110 (5) k = 0110 (2) o = 111 (5) w = 0111 (2)

Cost: ∑d_i* f_i= 111 bits = 44% ×256 bits

SDA/HUFF/V2.0/12

Huffman Encoding: steps

c

⁵

o

⁵ ₅

u

³

d

³

w

²

k

²

a

¹

l

¹

f

¹

I

¹

h

²

!

¹ 2

SDA/HUFF/V2.0/13

Huffman Encoding: steps

c

⁵

o

⁵ ₅

u

³

d

³

w

²

k

²

f

¹

I

¹

h

²

!

¹

a l

2 2

SDA/HUFF/V2.0/14

Huffman Encoding: steps

c

⁵

o

⁵ ₅

u

³

d

³

w

²

k

²

I

¹

h

²

a l

2

f !

2

3

SDA/HUFF/V2.0/15

c

⁵

o

⁵ ₅

u

³

d

³

w

²

k

²

h

²

a l

I

2

f !

3

4

Huffman Encoding: steps

SDA/HUFF/V2.0/16

c

⁵

o

⁵ ₅

u

³

d

³

k

²

a l I

2

f !

4 3

w h

4

Huffman Encoding: steps

SDA/HUFF/V2.0/17

Huffman Encoding: steps

c

⁵

o

⁵ ₅

u

³

d

³

I

f !

3 4

w h

k a l

4 6

SDA/HUFF/V2.0/18

Huffman Encoding: steps

c

⁵

o

⁵ ₅

f !

3 4

w

h k

a l

4

u d

6

I

SDA/HUFF/V2.0/19

c

⁵

o

⁵ ₅

f !

3 4

w

h k

a l

4

u d

6

I

7

Huffman Encoding: steps

SDA/HUFF/V2.0/20

Huffman Encoding: steps

c

⁵

o

^{5 5 4}

w h u d

6

f ! a l k

I

7

9

SDA/HUFF/V2.0/21

o

^{5 5}

u d

6

f !

a l k

I

7

c

w h

9

10

Huffman Encoding: steps

SDA/HUFF/V2.0/22

u d

6

f ! a l k

I c

7

w h o

9

10

13

Huffman Encoding: steps

SDA/HUFF/V2.0/23

c

w h

9

o

10

u d f !

k a l

I

13 19

Huffman Encoding: steps

SDA/HUFF/V2.0/24

u d f !

k a l

I

13

c

w h o

19

32

Huffman Encoding: steps

SDA/HUFF/V2.0/25

Huffman Encoding: steps

u d f !

a l k

I c

w h o

Total: 111 bits

SDA/HUFF/V2.0/26

Summary

„ Huffman encoding use frequency information to compress file.

„ The most frequent character get a shorter prefix code, and vice versa.

SDA/HUFF/V2.0/27

Further Reading

„ Chapter 12

SDA/HUFF/V2.0/28

What’s Next

„ Graph