CS6515 CERTIFICATION EVALUATION
EXAM 3 VERSION C 2026 LATEST 46 PLUS
QUESTIONS AND VERIFIED DETAILED
ANSWERS GRADED A+
⩥What is a NP problem? Answer: NP = Non-Deterministically
Polynomial
-A problem where the Solution can be VERIFIED in Polynomial-Time
⩥What are differences in P and NP? 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? 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? 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? 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? Answer: An edge between vertices in the same
clause
⩥What is a variable edge? Answer: An edge between complimentary
vertices
- x and x' have a variable edge between them.
⩥How to reduce 3SAT to Independent Set? Answer: 1. Create a graph
representation of 3SAT input
- 1 vertex for each literal and each clause.
2. Add Clause Edges
-An edge between each literal in a clause
3. Add variable edges
-An edge between x and x'
⩥What vertices do we choose to be in the IS? Answer: 1. No Clause
Edges between vertices.
EXAM 3 VERSION C 2026 LATEST 46 PLUS
QUESTIONS AND VERIFIED DETAILED
ANSWERS GRADED A+
⩥What is a NP problem? Answer: NP = Non-Deterministically
Polynomial
-A problem where the Solution can be VERIFIED in Polynomial-Time
⩥What are differences in P and NP? 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? 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? 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? 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? Answer: An edge between vertices in the same
clause
⩥What is a variable edge? Answer: An edge between complimentary
vertices
- x and x' have a variable edge between them.
⩥How to reduce 3SAT to Independent Set? Answer: 1. Create a graph
representation of 3SAT input
- 1 vertex for each literal and each clause.
2. Add Clause Edges
-An edge between each literal in a clause
3. Add variable edges
-An edge between x and x'
⩥What vertices do we choose to be in the IS? Answer: 1. No Clause
Edges between vertices.
