Whole Genome Shotgun Sequencing

This is the Hamiltonian path problem, which is closed.

V(G)={a,b,c,d,e,f,g,h}

This is the graph of each dot.

E(G)={ab,bc,cd,de,ef,fg,gh,ha}

This is the graph of the Hamiltonian path.

Then you see the Whole Genome Shotgun Sequencing.

This isn't closed, but there is the Hamiltonian path.

S4→S2→S1→S3→S5

You cut the chain of your DNA, and you reorganize it.

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S1→ACCTG

S2→CGACC

S3→CTGAG

S4→CGTCG

S5→AGTAC

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∴

S4→CGTCG

S2→XXXCGACC

S1→XXXXXACCTG

S3→XXXXXXXCTGAG

S5→XXXXXXXXXXAGTAC

You connect the pattern.

CGTCGACCTGAGTAC