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Mid-labeled Partial Digest. Student : 蕭禕廷 Advisor : 傅恆霖 教授. Contents. 1. Introduction 2. Partial Digest 3. Mid-labeled Partial Digest. 1. Introduction. DNA. T C A G G T C A C A. A G T C C A G T G T. Restriction Enzyme ( 限制內切酶 ). EcoRI. G A A T T C. C T T A A G. - PowerPoint PPT Presentation
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Mid-labeled Partial Digest
Student: 蕭禕廷Advisor: 傅恆霖 教授
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Contents
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1. Introduction 2. Partial Digest 3. Mid-labeled Partial Digest
1. Introduction
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DNA
T C A G G T C A C AA G T C C A G T G T
. . .
. . .. . .. . .
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Restriction Enzyme (限制內切酶 )
G A A T T CC T T A A G
EcoRI
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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
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2. Partial Digest
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Partial Digest Problem
Partial digest problem is to find , by knowing .
𝑥1 𝑥2 𝑥𝑛. . .. . .8
Partial Digest Problem Example
0 2 104 72 345
67
810
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Partial Digest Problem Algorithm
Skiena et al. gave an algorithm
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max ∆ 𝑋
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22334567810
8
0 10
12
0 10
223345678
8?
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0 10
223345678
88
82
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0 10
2334567
87
7 3
1 ?
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0 10
2334567
83
3 7
5
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⨉ o
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. . . . .
... .... . . 𝑛
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2𝑛− 1
2𝑛 (+
2𝑛+1−1
...
Partial Digest ProblemAlgorithm
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∆ 𝑋
?
𝑛
Each node needs time.
The total cost is .
3. Mid-labeled Partial Digest
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Mid-Labeled Partial Digest
𝑥1 𝑥2 𝑥𝑛. . .. . .
partial digest
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Mid-Labeled Partial Digest
,
contains exactly labels
𝑥1 𝑥2 𝑥𝑛. . .. . .
𝑙1 𝑙2 𝑙𝑘. . .
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Mid-Labeled Partial Digest
𝑥1 𝑥2 𝑥6
𝑙1 𝑙2 𝑙3
𝑥3 𝑥4𝑥5𝑙1
∆ 𝑋 𝑙 1, 𝑙1 ∆ 𝑋 𝜙𝑙1 𝑙2 𝑙3
∆ 𝑋 𝑙 1, 𝑙322
Mid-Labeled Partial Digest Example
𝑙1
0 2 104 7
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22343567810
𝑙1
𝑑1 𝑑2
¿ {𝑑1,𝑑2 }={2 ,3 }
*
$
$
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22343567 10
𝑙1
*
0 104 7
$
4 33
67 $
$ $
$
8
8
$
Mid-Labeled Partial Digest Algorithm
𝑙1
𝑑1 𝑑2
2𝑛(𝑑1+𝑑2𝑑1 )$
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Mid-Labeled Partial Digest Algorithm
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𝑑2 𝑑𝑖
𝑙1 𝑙2 𝑙𝑖 −1 𝑙𝑖
𝑑1. . .
. . .
. . .
. . .𝑙𝑘
𝑑𝑘+1
Mid-Labeled Partial Digest Algorithm
. . .𝑙𝑖 −1 𝑙𝑖 𝑙 𝑗 𝑙 𝑗+1. . . . . .
𝑑𝑖 𝑑 𝑗+1
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. . .
Mid-Labeled Partial Digest Algorithm
. . .𝑙𝑖 −1 𝑙 𝑗+1𝑙𝑖 𝑙 𝑗 . . .
𝑑𝑖 𝑑 𝑗+1
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𝑙𝑖 , 𝑙𝑖+1 , …, 𝑙 𝑗
𝑙1
𝑑1 𝑑2
∆ 𝑋 𝑙 1, 𝑙1
∆ 𝑋 𝑙 𝑖 ,𝑙 𝑗
Mid-Labeled Partial Digest Algorithm
𝑙1 𝑙𝑖𝑙𝑖 −1. . .. . .. . .
𝑚𝑎𝑥 ∆𝑋 𝑙 1, 𝑙𝑖 −1
$𝑚𝑎𝑥 ∆𝑋 𝑙 1, 𝑙𝑖 −1
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done?
Mid-Labeled Partial Digest Algorithm. .
. . . .. . .
. . .
𝑛
(𝑑𝑚 1+𝑑𝑚2
𝑑𝑚1)
. . .
. . .
. . .
. . .
. . .
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𝑙𝑚 1,…, 𝑙𝑚 2−1
𝑑𝑚1𝑑𝑚2
𝑚𝑎𝑥 ∆𝑋 𝑙 1, 𝑙𝑖 −1
𝑙1 𝑙𝑖𝑙𝑖 −1
Mid-Labeled Partial Digest Algorithm. .
. . . .. . .
. . .
𝑛
(𝑑𝑚 1+𝑑𝑚2
𝑑𝑚1)
. . .
. . .
. . .
. . .
. . .
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≤𝑛(𝑑𝑚1+𝑑𝑚2
𝑑𝑚1)
Mid-Labeled Partial Digest Algorithm
Each node needs . The total time is .
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1 2 𝑘
𝑛
. . .𝑑𝑚1
+𝑑𝑚2≤ 2𝑛𝑘+1
Stirling`s approximation : The total time is
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 .
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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.
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