Question

Guidelines for reduction problems. A reduction needs to be an accurate description of a polynomial-time process for converting instances of the input problem to instances of the target problem. You can use the examples from the slide deck as a basis for your descriptive level, while keeping to the following guidelines. Reduction descriptions: should be both clear and concise. should be composed of clearly enumerated steps that a well-practiced programmer could follow to construct an implementation. should include an analysis showing that the reduction can be performed in polynomial time. need not include pseudo-code, but pseudo-code may be used if you feel it adds clarity or completeness. Provide a reduction from the Hamiltonian path problem to the traveling salesman problem. Provide a reduction from the clique problem to the independent set Problem.

Answer 1

ansewr(3):

The trick is to understand that if a graph features a coterie of size kk, the inverse graph has AN freelance set of size kk. A coterie of size kk implies that kk nodes al have edges in between them. within the inverse graph these kk nodes don't seem to be (directly) connected and might be accustomed produce AN freelance set of size kk Hence, the polynomial time formulayou're cravingfor issimply the one that invertsthe graph. You will realize a youtube rationalization here. inverses of same graphs you'll understand why this can be true. As for (2), you wish to point out that AN formula to the freelance set drawback may be accustomed solve the coterie drawback. moreover you wish to pointout that victimisation the answer to the freelance set drawback may be accustomed realize the answer to the coterie drawback in polynomial time. This proves the following: You can currently scale back the coterie drawback to freelance set. Asall issues in NP may bereduced to the coterie drawback (the def inition of coterie being in office) all issues in NP may be reduced to freelance set too so it's in NPC. And since you reduced oterieto freelance set in polynomial time it can not be more durable than the coterie drawback either. So (2) is reminiscent of thefollowing: f you got a polynomial timefomulafor the freelanceset drawback, however would you utilize it to search out out whether or not a graph had a coterie of size kk?