CS 6515 UPDATED ACTUAL EXAM QUESTIONS CORRECT ANSWERS GRADED A PLUS
Question:
What is a NP problem?
Answer:
NP = Non-Deterministically Polynomial A problem where the Solution can be VERIFIED in
Polynomial-Time
Question:
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
Question:
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.
Question:
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.
, Question:
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.
Question:
What is a clause edge?
Answer:
An edge between vertices in the same clause
Question:
What is a variable edge?
Answer:
An edge between complimentary vertices x and x' have a variable edge between them.
Question:
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'
Question:
What vertices do we choose to be in the IS?
Answer:
1. No Clause Edges between vertices. Vertices cannot be neighbors of each other. 2. No Variable
Edges Vertices cannot be compliment of each other x and x' cannot both be in IS.
Question:
What is a NP problem?
Answer:
NP = Non-Deterministically Polynomial A problem where the Solution can be VERIFIED in
Polynomial-Time
Question:
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
Question:
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.
Question:
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.
, Question:
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.
Question:
What is a clause edge?
Answer:
An edge between vertices in the same clause
Question:
What is a variable edge?
Answer:
An edge between complimentary vertices x and x' have a variable edge between them.
Question:
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'
Question:
What vertices do we choose to be in the IS?
Answer:
1. No Clause Edges between vertices. Vertices cannot be neighbors of each other. 2. No Variable
Edges Vertices cannot be compliment of each other x and x' cannot both be in IS.
