Forr the purposes of this problem, you should not assume anything other than wha

Question

Forr the purposes of this problem, you should not assume anything other than what is stated in the problem. For example, you should not assume that the Vertex Cover problem or the Independent Set problem is in NP or is NP-hard.

(a) Suppose we knew that

• there is a polynomial-time reduction from Vertex Cover to Independent Set and

• the Vertex Cover Problem can be solved in polynomial time. With these assumptions, indicate which of the following choices is the right one (you don’t have to give any explanations.)

1. We know for sure that Independent Set can be solved in polynomial time.

2. We know for sure that Independent Set can’t be solved in polynomial time.

3. We can’t say for sure whether or not Independent Set can be solved in polynomial time

Explanation / Answer

Solution:

2)

1)

1. We know for sure that Independent Set can be solved in polynomial time.

is the correct option in this case.

Explanation:

Independent Set <= P  Vertex Cover?

Since vertex cover is polynomially reducible to independent set, this means that independent is also can be solved in polynomial time since vertex cover can be solved in polynomial time based on assumption given.

I hope this helps if you find any problem. Please comment below. Don't forget to give a thumbs up if you liked it. :)

Related Questions

Navigate

• Browse (All)
• Browse F
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.