Question: The SPARSE SUBGRAPH problem is defined as follows: Input: where G is a graph and p, q ? Z. Question: Does G have p vertices

The SPARSE SUBGRAPH problem is defined as follows:

Input: where G is a graph and p, q ? Z.

Question: Does G have p vertices such that there are at most q edges between them? Prove that this problem is NP-hard by giving a polynomial-time reduction of INDEP-SET (known to be NP-hard) to SPARSE SUBGRAPH.

Hint. Any independent set of size k can be viewed as a sparse subgraph consisting of k vertices with no edges between them

Step by Step Solution

There are 3 Steps involved in it

1 Expert Approved Answer

Step: 1 Unlock blur-text-image

Question Has Been Solved by an Expert!

Get step-by-step solutions from verified subject matter experts

Step: 2 Unlock

Step: 3 Unlock

Students Have Also Explored These Related Databases Questions!

Exercise 2 (2 pts). You know a polynomial-time reduction of 3-SAT to INDEP-SET (see the slides or a dual reduction of 3-SAT to CLIQUE in Theorem 7.32 in the textbook) Apply the reduction described in...

Exercise 3 (2 pts). The SPARSE SUBGRAPH problem is defined as follows: Input: ?G, p, q? where G is a graph and p, q e z. Question: Does G have p vertices such that there are at most q edges between...

Exercise 3 (2 pts). The SPARSE SUBGRAPH problem is defined as follows: Input: (G, G is a graph and p,qE Z . Question: Does G have p vertices such that there are at most q edges between them? P,9)...

The SPARSE SUBGRAPH problem is defined as follows: Input: hG, p, qi where G is a graph and p, q Z. Question: Does G have p vertices such that there are at most q edges between them? Prove that this...

Exercise 5 (2 pts). The DENSE SUBGRAPH problem is defined as follows: . Input: (G, p, q) where G is a graph and p,q e Z . Question: Does G have p vertices such that there are at least q edges between...

Exercise 5 (2 pts). The DENSE SUBGRAPH problem is defined as follows: Input: hG, p, qi where G is a graph and p, q ? Z. Question: Does G have p vertices such that there are at least q edges between...

Exercise 5 (2 pts). The DENSE SUBGRAPH problem is defined as follows: . Input: (G.p. where G is a graph and p.qEZ Question: Does G have p vertices such that there are at least q edges between them?...

The "Best Independent Set" problem is defined as follows: Input: An undirected graph G, in which each vertex is marked by a positive value ; and a target value T. Goal: A set of vertices S such that...

The "Best Independent Set" problem is defined as follows: Input: An undirected graph G, in which each vertex is marked by a positive value; and a target value T. Goal: A set of vertices S such that...

Suppose there is a decrease in supply in a market where the supply curve slopes upwards and the demand curve slopes downwards. Which of the following would not occur An excess supply A fall in the...

When naphthalene is hydrogenated, the heat released is about 80 kcal/mol. Using an isolated cyclohexene unit for comparison, estimate the resonance energy of naphthalene. Why is the resonance energy...

E18.23 (LO 3, 4) (NOL Carryforward, Recognition vs. Non-Recognition) Sondgeroth Ltd. reports the following pretax income (loss) for both financial reporting purposes and tax purposes. Year Pretax...

Use the appropriate technique to identify and analyse the most possible risks for and contribute and risks to each which could have contributed to the delay of the above project delivery

Who responds to your customers complaint letters?

What are all the ways your customers can get back to you in written format?

What is your average response time to complaint letters? Do you use form letters when responding? If your response takes more time than usual, do you let your customers know why you havent gotten...