DAA presentation

1. NP-Hard and NP-Complete
Presentation by Tejas

2. Introduction
• • NP-Hard and NP-Complete classify complex
computational problems.
• • Widely used in algorithm analysis and
computational theory.

3. What is NP?
• • NP: Nondeterministic Polynomial Time.
• • Solutions can be verified quickly (in
polynomial time).
• • Contains decision problems.

4. NP-Hard
• • Harder or equal to the hardest problems in
NP.
• • Not required to be in NP.
• • Verification may not be possible in
polynomial time.

5. NP-Hard Examples
• • Travelling Salesman Problem (Optimization)
• • Halting Problem
• • Knapsack Optimization Version

6. NP-Complete
• • Problems that are both NP and NP-Hard.
• • Solutions can be verified in polynomial time.
• • Hardest problems within NP.

7. NP-Complete Examples
• • SAT (Boolean Satisfiability Problem)
• • 3-SAT
• • Subset Sum
• • Clique Problem

8. Difference
• • NP-Hard: Not necessarily in NP.
• • NP-Complete: Must be in NP and NP-Hard.

9. Advantages
• • Helps classify computational problems by
difficulty.
• • Useful in optimization, AI, and algorithm
research.
• • Supports development of heuristics and
approximations.

10. Disadvantages
• • No known polynomial-time solution.
• • Very high computational cost.
• • Not suitable for real-time applications.

11. Conclusion
• • NP-Hard and NP-Complete are key concepts
in computational complexity.
• • They indicate the limits of fast algorithmic
solutions.