In this blog you will find the correct answer of the Coursera quiz Advanced Algorithms and Complexity Coursera Week 3 Quiz mixsaver always try to bring the best blogs and best coupon codes
 

 

Week 3

 

1.
Question 1
How many satisfying assignments does the following formula have?

1

1 point
Enter answer here

3

2.
Question 2
How many integer solutions does the following linear program have?

1
?

1 point
Enter answer here

10

3.
Question 3
Consider the following graph:

How many different independent sets does the following graph have?

1 point
Enter answer here

7

4.
Question 4
In the 3-coloring problem, you are given an undirected graph and the goal is to assign one of three available colors to its vertices such that the ends of each edge of the graph receive different colors. This is clearly a search problem: given a graph and a coloring of its vertices, one can check in polynomial time whether there are only three different colors and that no edge is monochromatic. This problem is known to be NP-complete. Do we have a polynomial time algorithm for this problem?

1 point

  • This is an open problem.
  • Yes, this problem can be solved in polynomial time.
  • No, this problem cannot be solved in polynomial time for sure.

5.
Question 5
In the lectures, we constructed a reduction from 3-SAT to Independent Set. Now, we show the reverse reduction. For this, we are going to reduce Independent set to SAT. We can then use the fact that SAT reduces to 3-SAT.

In the Independent Set problem we are given a graph GG with nn vertices and a positive integer bb. Our goal is to check whether the graph has bb vertices 

?.
The resulting formula is satisfiable if and only if the initial graph has an independent set of size bb.

Is this reduction correct?

1 point

  • No, it is not correct, because for a graph that does not have an independent set of size bb it might produce an a satisfiable formula.
  • No, it is not correct, because it might produce an unsatisfiable formula for a graph that has an independent set of size bb.
  • No, it is not correct, because it is not a polynomial time reduction.
  • Yes, the reduction is correct.

6.
Question 6
How many satisfying assignments does the following circuit have?

3

 

Programming Assignment: Programming Assignment 3

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