Advisor: Professor R. C. T. Lee Speaker: Jui Peng Lu ( 盧瑞鵬 )

1. DNA Sequence Assembly Advisor: Professor R. C. T. Lee Speaker: Jui Peng Lu (盧瑞鵬)

2. Original Sequence s1 s2 s3 First Cutting s4 s5 Second Cutting … DNA Sequence Assembly Problem • We are given a set of strings S = {s1, s2,…, sn} which are cut from an original sequence by using shotgun method, our job is to reconstruct the original string.

3. Original Sequence s1 s2 s3 First Cutting s4 s5 Second Cutting Basic Ideas of Our Algorithm • For each input string si, there is a string sj whose prefix is equal to the suffix of si.

4. Example Suppose we are given the following sequence: AGCCTGCCTAGCCCTAATCTG AGCCT, GCCTAGCCC, TAATCTG AGC, CTGCC, TAGCCCTA, ATCTG Assume the first shot gun method cuts the sequence into the following segments: The second cutting produces the following segments:

5. AGC AGCCT CTGCC GCCTAGCCC TAGCCCTA TAATCTG ATCTG Example • Input strings S = {AGCCT, GCCTAGCCC, TAATCTG, AGC, CTGCC, TAGCCCTA, ATCTG} AGCCTGCCTAGCCCTAATCTG

6. Experimental Results

7. A 2 5 9 B 3 6 7 C 2 1 4 2 7 2-Matching Double Digest Problem • Given three sets of distances : A = {2, 9, 5} B = {7, 3, 6} C = {1, 4, 2, 7, 2} Our job is to find the following solution: i1 = 1, 2, …, p i2 = 1, 2, …, q i3 = 1, 2, …, r

8. A 2 5 9 B 3 6 7 C 2 1 4 2 7 Basic Ideas of Our Algorithm • There are two blocks in A or B whose lengths are equal to the length of starting and ending block in C. • For each two adjacent blocks in C, there is a block in either A or B whose length is equal to the sum of length of those two adjacent blocks in C.

9. 4 3 7 A 5 6 3 B 4 1 2 4 3 C Example • Input: A = {3, 4, 7} B = {6, 3, 5} C = {1, 2, 3, 4, 4}

10. Experimental Results • We designed a visual displaying tool to display our experimental results.