Prove using the steps from the class that n/2-Clique problem is NP-Hard. You can use without proof that n/3-Clique is NP-Complete problem.

Solution PreviewSolution Preview

These solutions may offer step-by-step problem-solving explanations or good writing examples that include modern styles of formatting and construction of bibliographies out of text citations and references. Students may use these solutions for personal skill-building and practice. Unethical use is strictly forbidden.

We prove that n/2-clique is NP-Complete in two steps, as the lecture shows.
1). n/2-clique is in NP class
2). n/2-clique is in NP-Hard
For the step 1), we make a “guess” of a sequence of vertices for a graph provided as input and we verify whether the size of the sequence is n/2 and whether there is a clique determined by these n/2 vertices. Since each of these can be done in polynomial time (assuming that n is finite, then n/2 is also finite and gives the input size since the number of edges in this case is (n/2)*(n/2 -1)), it follows that our problem is in NP.
For step 2), we need to build a reduction in polynomial time from another known NP-Complete problem. We use n/3-clique problem in this case....

By purchasing this solution you'll be able to access the following files:

for this solution

or FREE if you
register a new account!

PayPal, G Pay, ApplePay, Amazon Pay, and all major credit cards accepted.

Find A Tutor

View available Data Structures and Algorithms Tutors

Get College Homework Help.

Are you sure you don't want to upload any files?

Fast tutor response requires as much info as possible.

Upload a file
Continue without uploading

We couldn't find that subject.
Please select the best match from the list below.

We'll send you an email right away. If it's not in your inbox, check your spam folder.

  • 1
  • 2
  • 3
Live Chats