QuestionQuestion

1.Describe a Non deterministic polynomial time algorithm for deciding if a simple graph G=(V,E) has a Hamiltonian cycle, i.e Hamilton path for which the begin and end vertices are adjacent.

2. Let C be a 3-CNF formula. A≠-assignment to C is a truth assignment that satisfies C, but in such a way that every clause of C has at least one literal set to true, but also has one literal set to false. Prove that, if a is a≠-assignment for a set of clauses, then so it is its inversion a ̅, where the inversion of an assignment is the assignment that is obtained by inverting each assignment value of a (i.e. 1 to 0, and 0 to 1).

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 assume that as input we have the graph G encoded as an adjacency list in a binary notation.
1) We also assume its vertices are counted from 1 to n.
The non-deterministic algorithm will must first call a method to determine a sequence of n+1 numbers from 1 to n.
Then we put the algorithm to verify that each number from the range [1..n] appears only once in the sequence. This can be done simpler by sorting the sequence. The only constraint involves the first and last numbers, which must be the same....

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

$18.00
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.

Decision:
Upload a file
Continue without uploading

SUBMIT YOUR HOMEWORK
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