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CS6515 EXAM 3 STUDY GUIDE 2025 QUESTIONS AND VERIFIED SOLUTIONS| ABSOLUTE SUCCESS, Exams of Algorithms and Programming

CS6515 EXAM 3 STUDY GUIDE 2025 QUESTIONS AND VERIFIED SOLUTIONS| ABSOLUTE SUCCESS GUARANTEED.

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P a g e | 1
CS6515 EXAM 3 STUDY GUIDE 2025
QUESTIONS AND VERIFIED SOLUTIONS|
ABSOLUTE SUCCESS GUARANTEED.
What is a P problem? - Correct Answer-P = Polynomial
-A problem that can be solved in Polynomial time.
-There is a Polynomial time algorithm to solve it.
What is a NP problem? - Correct Answer-NP = Non-
Deterministically Polynomial
-A problem where the Solution can be VERIFIED in Polynomial-
Time
What are differences in P and NP? - Correct Answer-All P
problems are in NP but all NP problems are not in P. P is a subset
of NP.
-Problems may be verifiable in Polynomial-Time but not solvable
in Polynomial-Time
What are NP-Complete Problems? - Correct Answer-The hardest
problems in the NP class.
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Download CS6515 EXAM 3 STUDY GUIDE 2025 QUESTIONS AND VERIFIED SOLUTIONS| ABSOLUTE SUCCESS and more Exams Algorithms and Programming in PDF only on Docsity!

CS6515 EXAM 3 STUDY GUIDE 2025

QUESTIONS AND VERIFIED SOLUTIONS|

ABSOLUTE SUCCESS GUARANTEED.

What is a P problem? - Correct Answer-P = Polynomial

  • A problem that can be solved in Polynomial time.
  • There is a Polynomial time algorithm to solve it. What is a NP problem? - Correct Answer-NP = Non- Deterministically Polynomial
  • A problem where the Solution can be VERIFIED in Polynomial- Time What are differences in P and NP? - Correct Answer-All P problems are in NP but all NP problems are not in P. P is a subset of NP.
  • Problems may be verifiable in Polynomial-Time but not solvable in Polynomial-Time What are NP-Complete Problems? - Correct Answer-The hardest problems in the NP class.

A problem is NP-Complete if it is in NP and in NP-Hard. What are NP-Hard problems? - Correct Answer-A problem at least as hard as every problem in the class NP. A problem is NP-Hard if all other problems in NP can be polynomially reduced to it. NP-Hard problems don't have to be NP problems. What is the difference between NP-Complete and NP-Hard? - Correct Answer-NP-Complete problems are the hardest in the set NP. NP-Hard is not necessarily in NP. NP-Hard problems are at least as hard as everything in the set NP. What is a clause edge? - Correct Answer-An edge between vertices in the same clause What is a variable edge? - Correct Answer-An edge between complimentary vertices

  • x and x' have a variable edge between them.

What are the claims of 3SAT reduction to Independent Set? - Correct Answer-- 3SAT input, f, has a satisfying assignment <==> G has an independent set of size ≥ g

  • g = m = # of clauses For the above implication, what is the forward proof? - Correct Answer-Given the 3SAT input and a satisfying assignment, show that G has an independent set of size ≥ g.
  • For each clause C, take 1 of the satisfied literals and add to the set S
  • S has 1 vertex per clause. For the above implication, what is the reverse proof? - Correct Answer-Given an independent set of size ≥ g, show that f has a satisfying assignment.
  • IS has 1 vertex per clause. Each vertex is satisfying assignment.
  • Set that vertex to true.
  • Every clause is now satisfied What problems are known NP-Hard? - Correct Answer-1. Max- Independent-Set problem.

What problems are known NP-Complete? - Correct Answer-1. Max-Independent-Set

  1. Clique
  2. Vertex Cover
  3. SAT
  4. 3SAT
  5. Independent Set What problems are known NP? - Correct Answer- What problems are known P? - Correct Answer- What is Vertex Cover? - Correct Answer-A set of vertices where every edge is "covered".
  • For every edge, at least one vertex is in the VC How to prove a problem is NP-Complete? - Correct Answer-1. Prove the problem is in NP