1. Fast Parallel Solution for Set-Packing by DNA-Based Computing Michael(Shan-Hui)ho,Weng-long CHANG, Nonmember, Minyi GUO, Member,and Laurence T.YANG, Nonmember Reporter : yu-wen CHANG

2. outline  Introduction  Introduction of DNA Structure  Set-Packing Program  DNA model of Computation  Preliminaries  Algorithm  Conclusion

3. Introduction of DNA Structure(1/3)  In the biochemical world of large and small molecules, polymers, and monomers, DNA is a polymer, which is strung together from monomers called deoxyriboNucleotides.  Each deoxyribonucleotide contains three components: a sugar, a phosphate group, and a nitrogenous base.  This sugar has five carbon atoms and they are numbered from 1’ to 5’.

4. Introduction of DNA Structure(2/3)

5. Introduction of DNA Structure(3/3)  Using sticker to construct solution space of DNA for the library sequences in the set-packing program.

6. Set-Packing Program(1/3)  Suppose we have a finite set S and a list of subsets of S. Then, the set packing problem asks if some k subsets in the list are pairwise disjoint (in other words, no two of them intersect). The problem is clearly in NP, since given k subsets we can easily verify that they are disjoint. The NP-hard optimization version of the problem, maximum set packing, asks for the maximum number of pairwise disjoint sets in the list.

7. Set-Packing Program(2/3)  Suppose S={1,2,3,4}, subset of collection C={,{1},{2},{3},{4},{1,2}{1,3}{1,4}{2,3}{2,4} {3,4}{1,2,3}{1,2,4}{1,3,4}{2,3,4}{1,2,3,4}} if k=2 then set-packing is {1,2}{3,4}  先要有一個集合 S 然後列出 S 裡面所有的子 集合 接下來 在所有的子集合中 挑出 K 個 使 得 K 個被挑出來的子集合 彼此之間無重覆 那請問最多有幾種挑法

8. Set-Packing Program(3/3)

9. Preliminaries()  Given a tube, one can perform the following operations: 1. Extract 2. Merge 3. Detect 4. Append 5. Discard 6. Read

10. Preliminaries()  Extract: Given a tube P and a short single strand of DNA called S, we can produce two tubes +(P, S) and −(P, S ), where +(P, S ) is all of the molecules of DNA in P which consist of the short strand S, and −(P, S ) is all of the molecules of DNA in P which do not contain the short strand S. EX: set P = {1,2,3}, +(P, 1) ={1}, −(P, 1 ) = {2,3}.

11. Preliminaries()  Merge. Given tubes P1 and P2, yield ∪ (P1, P2), where ∪ (P1, P2) = P1 ∪ P2. This operation is to pour two tubes into one, with no change in the individual strands. EX: set P1={1,2},P2={3,4} then ∪ (P1, P2) ={1,2,3,4}.

12. Preliminaries()  Detect. Given a tube P, if it includes at least one DNA molecule we can say ‘yes’, and if it contains no DNA we can say ‘no’. EX: set P1={1},P2={};detect(P1)=yes, detect(P2)=no.

13. Preliminaries()  Append. Given a tube P and a short strand of DNA called Z, the operation will append the short strand Z onto the end of every strand in tube P. EX: set P={1,2};append(p,3)=>P={1,2,3}.

14. Preliminaries()  Discard. Given a tube P, the operation will discard the tube P.

15. Preliminaries()  Read. Given a tube P, the operation is used to describe a single molecule, which is contained in tube P. Even if P contains many different molecules, the operation can give an explicit description of only one of them. EX: set P ={1,2,3} ; read(P)={1,2,3}.

16. Algorithm()

17. Conclusions