CS 6515 Exam 3 | Actual Questions
and Answers Latest Updated
2025/2026 (Graded A+)
Correct 116
Incorrect
CS 6515 Exam 3
Term
, Considered efficient or inctractable. Te runtime is bounded by a polynomial
function of the input size: O(n), O(n^2) even O(n^3000)
Definition Finds a path starting a S and finishing a T that visit each vertex exactly
once.
Input: Graph G and designated vertex S, T
Output: set of Vertex in order of the path.No otherwise.
NP (Non-deterministic polynomial time) This class contains all decisions
problems where if the answer is "yes " there is a proof at can be verified in
polynomial time
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2 of 116
Term
Np-Hard
Give this one a try later!
The set of all possible solution (x,y) that satisfy the constraints is the intersection of
these spaces. this region is always convex
These re the problems that are at least as hard as the hardest problem in NP. A
problem is NP-Hard if any problem in NP can be reduced to in in polynomial
time
, If the primal has an optimal solution x, then dual has an optimal solution y, and
their objective are equal c^t x = b^t y
Any feasible solution to the primal is less than or equal to any feasible solution of
the dual (c^t X <= B^t y)
Don't know?
3 of 116
Definition
C contains the coefficients of the objective function.
x contains the decision variables
Give this one a try later!
What is the feasible region What is the standard form of an LP:
What is the objective function What does it mean that a problem is
C^t x known to be in NP
Don't know?
4 of 116
Term
, What make a problem NPC
Give this one a try later!
C contains the coefficients of the objective function.
x contains the decision variables
The set of all possible solution (x,y) that satisfy the constraints is the intersection of
these spaces. this region is always convex
A Reduction is a formal way to say that Problem A is no harder than problem B. We
denote it as A <=p B. It's a polynomial-time algorithm that transform any instance of
problem A into an equivalent instances of problem B
1. It is in NP
2. It is in NP-Hard
Don't know?
5 of 116
Definition
Definition: decide if there is a perfect matching among three disjoint
set using a given set of triplets.
Input: Three disjoint sets and a set of triplets.
Output: yes if there is a perfect matching; No otherwise.
Give this one a try later!
and Answers Latest Updated
2025/2026 (Graded A+)
Correct 116
Incorrect
CS 6515 Exam 3
Term
, Considered efficient or inctractable. Te runtime is bounded by a polynomial
function of the input size: O(n), O(n^2) even O(n^3000)
Definition Finds a path starting a S and finishing a T that visit each vertex exactly
once.
Input: Graph G and designated vertex S, T
Output: set of Vertex in order of the path.No otherwise.
NP (Non-deterministic polynomial time) This class contains all decisions
problems where if the answer is "yes " there is a proof at can be verified in
polynomial time
Don't know?
2 of 116
Term
Np-Hard
Give this one a try later!
The set of all possible solution (x,y) that satisfy the constraints is the intersection of
these spaces. this region is always convex
These re the problems that are at least as hard as the hardest problem in NP. A
problem is NP-Hard if any problem in NP can be reduced to in in polynomial
time
, If the primal has an optimal solution x, then dual has an optimal solution y, and
their objective are equal c^t x = b^t y
Any feasible solution to the primal is less than or equal to any feasible solution of
the dual (c^t X <= B^t y)
Don't know?
3 of 116
Definition
C contains the coefficients of the objective function.
x contains the decision variables
Give this one a try later!
What is the feasible region What is the standard form of an LP:
What is the objective function What does it mean that a problem is
C^t x known to be in NP
Don't know?
4 of 116
Term
, What make a problem NPC
Give this one a try later!
C contains the coefficients of the objective function.
x contains the decision variables
The set of all possible solution (x,y) that satisfy the constraints is the intersection of
these spaces. this region is always convex
A Reduction is a formal way to say that Problem A is no harder than problem B. We
denote it as A <=p B. It's a polynomial-time algorithm that transform any instance of
problem A into an equivalent instances of problem B
1. It is in NP
2. It is in NP-Hard
Don't know?
5 of 116
Definition
Definition: decide if there is a perfect matching among three disjoint
set using a given set of triplets.
Input: Three disjoint sets and a set of triplets.
Output: yes if there is a perfect matching; No otherwise.
Give this one a try later!
