mid-labeled partial digest student: 蕭禕廷 advisor: 傅恆霖 教授 1
TRANSCRIPT
![Page 1: Mid-labeled Partial Digest Student: 蕭禕廷 Advisor: 傅恆霖 教授 1](https://reader036.vdocuments.mx/reader036/viewer/2022062304/56649f0e5503460f94c222a1/html5/thumbnails/1.jpg)
Mid-labeled Partial Digest
Student: 蕭禕廷Advisor: 傅恆霖 教授
1
![Page 2: Mid-labeled Partial Digest Student: 蕭禕廷 Advisor: 傅恆霖 教授 1](https://reader036.vdocuments.mx/reader036/viewer/2022062304/56649f0e5503460f94c222a1/html5/thumbnails/2.jpg)
Contents
2
1. Introduction 2. Partial Digest 3. Mid-labeled Partial Digest
![Page 3: Mid-labeled Partial Digest Student: 蕭禕廷 Advisor: 傅恆霖 教授 1](https://reader036.vdocuments.mx/reader036/viewer/2022062304/56649f0e5503460f94c222a1/html5/thumbnails/3.jpg)
1. Introduction
3
![Page 4: Mid-labeled Partial Digest Student: 蕭禕廷 Advisor: 傅恆霖 教授 1](https://reader036.vdocuments.mx/reader036/viewer/2022062304/56649f0e5503460f94c222a1/html5/thumbnails/4.jpg)
DNA
T C A G G T C A C A
A G T C C A G T G T
. . .
. . .. . .. . .
4
![Page 5: Mid-labeled Partial Digest Student: 蕭禕廷 Advisor: 傅恆霖 教授 1](https://reader036.vdocuments.mx/reader036/viewer/2022062304/56649f0e5503460f94c222a1/html5/thumbnails/5.jpg)
Restriction Enzyme (限制內切酶 )
G A A T T CC T T A A G
EcoRI
5
![Page 6: Mid-labeled Partial Digest Student: 蕭禕廷 Advisor: 傅恆霖 教授 1](https://reader036.vdocuments.mx/reader036/viewer/2022062304/56649f0e5503460f94c222a1/html5/thumbnails/6.jpg)
Restriction Sites (切位 )
EcoRI
G A A T T CC T T A A G
G A A T T CC T T A A G
G A A T T CC T T A A G
Restriction Sites
6
![Page 7: Mid-labeled Partial Digest Student: 蕭禕廷 Advisor: 傅恆霖 教授 1](https://reader036.vdocuments.mx/reader036/viewer/2022062304/56649f0e5503460f94c222a1/html5/thumbnails/7.jpg)
2. Partial Digest
7
![Page 8: Mid-labeled Partial Digest Student: 蕭禕廷 Advisor: 傅恆霖 教授 1](https://reader036.vdocuments.mx/reader036/viewer/2022062304/56649f0e5503460f94c222a1/html5/thumbnails/8.jpg)
Partial Digest Problem
Partial digest problem is to find , by knowing .
𝑥1 𝑥2 𝑥𝑛. . .. . .8
![Page 9: Mid-labeled Partial Digest Student: 蕭禕廷 Advisor: 傅恆霖 教授 1](https://reader036.vdocuments.mx/reader036/viewer/2022062304/56649f0e5503460f94c222a1/html5/thumbnails/9.jpg)
Partial Digest Problem Example
0 2 104 72
345
67
810
9
![Page 10: Mid-labeled Partial Digest Student: 蕭禕廷 Advisor: 傅恆霖 教授 1](https://reader036.vdocuments.mx/reader036/viewer/2022062304/56649f0e5503460f94c222a1/html5/thumbnails/10.jpg)
Partial Digest Problem Algorithm
Skiena et al. gave an algorithm
10
max ∆ 𝑋
![Page 11: Mid-labeled Partial Digest Student: 蕭禕廷 Advisor: 傅恆霖 教授 1](https://reader036.vdocuments.mx/reader036/viewer/2022062304/56649f0e5503460f94c222a1/html5/thumbnails/11.jpg)
11
22334567810
8
0 10
![Page 12: Mid-labeled Partial Digest Student: 蕭禕廷 Advisor: 傅恆霖 教授 1](https://reader036.vdocuments.mx/reader036/viewer/2022062304/56649f0e5503460f94c222a1/html5/thumbnails/12.jpg)
12
0 10
223345678
8?
![Page 13: Mid-labeled Partial Digest Student: 蕭禕廷 Advisor: 傅恆霖 教授 1](https://reader036.vdocuments.mx/reader036/viewer/2022062304/56649f0e5503460f94c222a1/html5/thumbnails/13.jpg)
13
0 10
223345678
88
82
![Page 14: Mid-labeled Partial Digest Student: 蕭禕廷 Advisor: 傅恆霖 教授 1](https://reader036.vdocuments.mx/reader036/viewer/2022062304/56649f0e5503460f94c222a1/html5/thumbnails/14.jpg)
14
0 10
2334567
87
73
1 ?
![Page 15: Mid-labeled Partial Digest Student: 蕭禕廷 Advisor: 傅恆霖 教授 1](https://reader036.vdocuments.mx/reader036/viewer/2022062304/56649f0e5503460f94c222a1/html5/thumbnails/15.jpg)
15
0 10
2334567
83
37
5
![Page 16: Mid-labeled Partial Digest Student: 蕭禕廷 Advisor: 傅恆霖 教授 1](https://reader036.vdocuments.mx/reader036/viewer/2022062304/56649f0e5503460f94c222a1/html5/thumbnails/16.jpg)
16
⨉ o
![Page 17: Mid-labeled Partial Digest Student: 蕭禕廷 Advisor: 傅恆霖 教授 1](https://reader036.vdocuments.mx/reader036/viewer/2022062304/56649f0e5503460f94c222a1/html5/thumbnails/17.jpg)
17
. . . . .
. ..
. . .
. . . 𝑛
124
2𝑛− 1
2𝑛 (+
2𝑛+1−1
...
![Page 18: Mid-labeled Partial Digest Student: 蕭禕廷 Advisor: 傅恆霖 教授 1](https://reader036.vdocuments.mx/reader036/viewer/2022062304/56649f0e5503460f94c222a1/html5/thumbnails/18.jpg)
Partial Digest ProblemAlgorithm
18
∆ 𝑋
?
𝑛
Each node needs time.
The total cost is .
![Page 19: Mid-labeled Partial Digest Student: 蕭禕廷 Advisor: 傅恆霖 教授 1](https://reader036.vdocuments.mx/reader036/viewer/2022062304/56649f0e5503460f94c222a1/html5/thumbnails/19.jpg)
3. Mid-labeled Partial Digest
19
![Page 20: Mid-labeled Partial Digest Student: 蕭禕廷 Advisor: 傅恆霖 教授 1](https://reader036.vdocuments.mx/reader036/viewer/2022062304/56649f0e5503460f94c222a1/html5/thumbnails/20.jpg)
Mid-Labeled Partial Digest
𝑥1 𝑥2 𝑥𝑛. . .. . .
partial digest
20
![Page 21: Mid-labeled Partial Digest Student: 蕭禕廷 Advisor: 傅恆霖 教授 1](https://reader036.vdocuments.mx/reader036/viewer/2022062304/56649f0e5503460f94c222a1/html5/thumbnails/21.jpg)
Mid-Labeled Partial Digest
,
contains exactly labels
𝑥1 𝑥2 𝑥𝑛. . .. . .
𝑙1 𝑙2 𝑙𝑘. . .
21
![Page 22: Mid-labeled Partial Digest Student: 蕭禕廷 Advisor: 傅恆霖 教授 1](https://reader036.vdocuments.mx/reader036/viewer/2022062304/56649f0e5503460f94c222a1/html5/thumbnails/22.jpg)
Mid-Labeled Partial Digest
𝑥1 𝑥2 𝑥6
𝑙1 𝑙2 𝑙3
𝑥3 𝑥4𝑥5𝑙1
∆ 𝑋 𝑙 1, 𝑙1 ∆ 𝑋 𝜙
𝑙1 𝑙2 𝑙3∆ 𝑋 𝑙 1, 𝑙3
22
![Page 23: Mid-labeled Partial Digest Student: 蕭禕廷 Advisor: 傅恆霖 教授 1](https://reader036.vdocuments.mx/reader036/viewer/2022062304/56649f0e5503460f94c222a1/html5/thumbnails/23.jpg)
Mid-Labeled Partial Digest Example
𝑙1
0 2 104 7
23
![Page 24: Mid-labeled Partial Digest Student: 蕭禕廷 Advisor: 傅恆霖 教授 1](https://reader036.vdocuments.mx/reader036/viewer/2022062304/56649f0e5503460f94c222a1/html5/thumbnails/24.jpg)
24
22343567810
𝑙1
𝑑1 𝑑2
¿ {𝑑1 ,𝑑2 }={2 ,3 }
*
$
$
![Page 25: Mid-labeled Partial Digest Student: 蕭禕廷 Advisor: 傅恆霖 教授 1](https://reader036.vdocuments.mx/reader036/viewer/2022062304/56649f0e5503460f94c222a1/html5/thumbnails/25.jpg)
25
22343567 10
𝑙1
*
0 104 7
$
4 33
6
7$
$ $
$
8
8
$
![Page 26: Mid-labeled Partial Digest Student: 蕭禕廷 Advisor: 傅恆霖 教授 1](https://reader036.vdocuments.mx/reader036/viewer/2022062304/56649f0e5503460f94c222a1/html5/thumbnails/26.jpg)
Mid-Labeled Partial Digest Algorithm
𝑙1
𝑑1 𝑑2
2𝑛(𝑑1+𝑑2𝑑1 )$
26
![Page 27: Mid-labeled Partial Digest Student: 蕭禕廷 Advisor: 傅恆霖 教授 1](https://reader036.vdocuments.mx/reader036/viewer/2022062304/56649f0e5503460f94c222a1/html5/thumbnails/27.jpg)
Mid-Labeled Partial Digest Algorithm
27
𝑑2 𝑑𝑖
𝑙1 𝑙2 𝑙𝑖 −1 𝑙𝑖
𝑑1. . .
. . .
. . .
. . .𝑙𝑘
𝑑𝑘+1
![Page 28: Mid-labeled Partial Digest Student: 蕭禕廷 Advisor: 傅恆霖 教授 1](https://reader036.vdocuments.mx/reader036/viewer/2022062304/56649f0e5503460f94c222a1/html5/thumbnails/28.jpg)
Mid-Labeled Partial Digest Algorithm
. . .𝑙𝑖 −1 𝑙𝑖 𝑙 𝑗 𝑙 𝑗+1. . . . . .
𝑑𝑖 𝑑 𝑗+1
28
![Page 29: Mid-labeled Partial Digest Student: 蕭禕廷 Advisor: 傅恆霖 教授 1](https://reader036.vdocuments.mx/reader036/viewer/2022062304/56649f0e5503460f94c222a1/html5/thumbnails/29.jpg)
. . .
Mid-Labeled Partial Digest Algorithm
. . .𝑙𝑖 −1 𝑙 𝑗+1𝑙𝑖 𝑙 𝑗 . . .
𝑑𝑖 𝑑 𝑗+1
29
𝑙𝑖 , 𝑙𝑖+1 ,…, 𝑙 𝑗
𝑙1
𝑑1 𝑑2
∆ 𝑋 𝑙 1, 𝑙1
∆ 𝑋 𝑙 𝑖 ,𝑙 𝑗
![Page 30: Mid-labeled Partial Digest Student: 蕭禕廷 Advisor: 傅恆霖 教授 1](https://reader036.vdocuments.mx/reader036/viewer/2022062304/56649f0e5503460f94c222a1/html5/thumbnails/30.jpg)
Mid-Labeled Partial Digest Algorithm
𝑙1 𝑙𝑖𝑙𝑖 −1. . .. . .. . .
𝑚𝑎𝑥 ∆𝑋 𝑙 1, 𝑙𝑖 −1
$𝑚𝑎𝑥 ∆𝑋 𝑙 1, 𝑙𝑖 −1
30
done?
![Page 31: Mid-labeled Partial Digest Student: 蕭禕廷 Advisor: 傅恆霖 教授 1](https://reader036.vdocuments.mx/reader036/viewer/2022062304/56649f0e5503460f94c222a1/html5/thumbnails/31.jpg)
Mid-Labeled Partial Digest Algorithm. .
. . . .. . .
. . .
𝑛
(𝑑𝑚 1+𝑑𝑚2
𝑑𝑚1)
. . .
. . .
. . .
. . .
. . .
31
𝑙𝑚 1,…, 𝑙𝑚 2−1
𝑑𝑚1𝑑𝑚2
𝑚𝑎𝑥 ∆𝑋 𝑙 1, 𝑙𝑖 −1
𝑙1 𝑙𝑖𝑙𝑖 −1
![Page 32: Mid-labeled Partial Digest Student: 蕭禕廷 Advisor: 傅恆霖 教授 1](https://reader036.vdocuments.mx/reader036/viewer/2022062304/56649f0e5503460f94c222a1/html5/thumbnails/32.jpg)
Mid-Labeled Partial Digest Algorithm. .
. . . .. . .
. . .
𝑛
(𝑑𝑚 1+𝑑𝑚2
𝑑𝑚1)
. . .
. . .
. . .
. . .
. . .
32
≤𝑛(𝑑𝑚1+𝑑𝑚2
𝑑𝑚1)
![Page 33: Mid-labeled Partial Digest Student: 蕭禕廷 Advisor: 傅恆霖 教授 1](https://reader036.vdocuments.mx/reader036/viewer/2022062304/56649f0e5503460f94c222a1/html5/thumbnails/33.jpg)
Mid-Labeled Partial Digest Algorithm
Each node needs . The total time is .
33
1 2 𝑘
𝑛
. . .
𝑑𝑚1+𝑑𝑚2
≤2𝑛𝑘+1
Stirling`s approximation : The total time is
![Page 34: Mid-labeled Partial Digest Student: 蕭禕廷 Advisor: 傅恆霖 教授 1](https://reader036.vdocuments.mx/reader036/viewer/2022062304/56649f0e5503460f94c222a1/html5/thumbnails/34.jpg)
Conclusion
For partial digest problem, Skiena et al. gave an algorithm.
For mid-labeled partial digest problem, there is an algorithm for adding labels inside DNA .
for .
34
![Page 35: Mid-labeled Partial Digest Student: 蕭禕廷 Advisor: 傅恆霖 教授 1](https://reader036.vdocuments.mx/reader036/viewer/2022062304/56649f0e5503460f94c222a1/html5/thumbnails/35.jpg)
References
T. H. Cormen, C. E. Leiserson, R. L. Rivest and C. Stein, Introduction to Algorithms, Second Edition, 2001.
B. Lewin, Genes VII, 2000.
S. S. Skiena, W. D. Smith and P. Lemke, Reconstructing Sets From Interpoint Distances, SOCG, 1990.
D. B. West, Introduction to graph theory, 1996.
35
![Page 36: Mid-labeled Partial Digest Student: 蕭禕廷 Advisor: 傅恆霖 教授 1](https://reader036.vdocuments.mx/reader036/viewer/2022062304/56649f0e5503460f94c222a1/html5/thumbnails/36.jpg)
36