Homework Help is Here – Start Your Trial Now!
Math
Advanced Math
Set Problem is in NP.

Set Problem is in NP.

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
See similar textbooks
icon
Related questions
Question

Please show steps clearly

3. The Independent Set Problem is: Given a graph G and an integer K, is there a set S of K vertices in G such that no two vertices in S are adjacent? The Exactly Half Independent Set Problem is: Given a graph G on n vertices where n is even, is there a set S of n/2 vertices in G such that no two vertices in S are adjacent? (a) Prove that the Exactly Half Independent Set Problem is in NP. (b) Prove that the Independent Set Problem reduces to the Exactly Half Independent Set Problem in polynomial time. (Hint: Given a graph G in the Independent Set Problem, add vertices and edges to turn the problem into the Exactly Half Independent Set Problem. For your reduction, you will need to consider separately the cases of independent problems where n > 2K from the cases where n<2K.) (Note that proving a) and b) proves that the Exactly Half Independent Set Problem is NP-complete.)
Transcribed Image Text:3. The Independent Set Problem is: Given a graph G and an integer K, is there a set S of K vertices in G such that no two vertices in S are adjacent? The Exactly Half Independent Set Problem is: Given a graph G on n vertices where n is even, is there a set S of n/2 vertices in G such that no two vertices in S are adjacent? (a) Prove that the Exactly Half Independent Set Problem is in NP. (b) Prove that the Independent Set Problem reduces to the Exactly Half Independent Set Problem in polynomial time. (Hint: Given a graph G in the Independent Set Problem, add vertices and edges to turn the problem into the Exactly Half Independent Set Problem. For your reduction, you will need to consider separately the cases of independent problems where n > 2K from the cases where n<2K.) (Note that proving a) and b) proves that the Exactly Half Independent Set Problem is NP-complete.)
Expert Solution
trending now

Trending now

This is a popular solution!

steps

Step by step

Solved in 3 steps

SEE SOLUTIONCheck out a sample Q&A here
Blurred answer
Recommended textbooks for you
Advanced Engineering Mathematics
Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated
Numerical Methods for Engineers
Numerical Methods for Engineers
Advanced Math
ISBN:
9780073397924
Author:
Steven C. Chapra Dr., Raymond P. Canale
Publisher:
McGraw-Hill Education
Introductory Mathematics for Engineering Applicat…
Introductory Mathematics for Engineering Applicat…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY
Mathematics For Machine Technology
Mathematics For Machine Technology
Advanced Math
ISBN:
9781337798310
Author:
Peterson, John.
Publisher:
Cengage Learning,
Basic Technical Mathematics
Basic Technical Mathematics
Advanced Math
ISBN:
9780134437705
Author:
Washington
Publisher:
PEARSON
Topology
Topology
Advanced Math
ISBN:
9780134689517
Author:
Munkres, James R.
Publisher:
Pearson,
SEE MORE TEXTBOOKS