Question

What is the significance of the ‘NP-complete’ class in computational complexity?

• A. Problems that can be solved in polynomial time
• B. Problems that are both NP-hard and in NP
• C. Problems that require exponential time to solve
• D. Problems that are unsolvable by any algorithm

Hint:

NP-complete problems are the hardest in NP, and any NP problem can be reduced to an NP-complete problem in polynomial time.

Answer 1

The Correct Option is B

The NP-complete class refers to a set of problems that are both NP (nondeterministic polynomial time) and NP-hard. A problem is in NP if a solution can be verified in polynomial time, and it is NP-hard if every problem in NP can be reduced to it in polynomial time. Thus, NP-complete problems are the hardest problems in NP.
- Problems that can be solved in polynomial time (A) refers to P problems, not NP-complete problems.
- Problems that require exponential time to solve (C) is not true for NP-complete problems. While solving them might take exponential time in the worst case, the focus is on polynomial-time verifiability.
- Problems that are unsolvable by any algorithm (D) is incorrect; NP-complete problems are solvable, but they may not have efficient solutions.
Thus, the correct answer is (B), problems that are both NP-hard and in NP.