NP Complete Problems
- 1. Topic- NP Complete Problems Submitted To:- Mr. Jitendra Gora Submitted By:- Nikhil Joshi
- 3. NP-complete problems What is NP-Complete? A problem X that is in NP is also in NP- Complete if and only if every other problem in NP can be quickly (i.e. in polynomial time) transformed into X. In other words: 1. X is in NP (X NP) 2. Every problem in NP is reducible to x
- 4. Reduction • A problem R can be reduced to another problem Q if any instance of R can be rephrased to an instance of Q, the solution to which provides a solution to the instance of R • This rephrasing is called a transformation • Intuitively: If R reduces in polynomial time to Q, R is “no harder to solve” than Q Q R
- 5. NP-Hard • What is NP-Hard? • NP-Hard are problems that are at least as hard as the hardest problems in NP. Note that NP- Complete problems are also NP-hard. However not all NP-hard problems are NP – If all problems R NP are polynomial-time reducible to Q, then Q is NP-Hard – We say Q is NP-Complete if Q is NP-Hard and Q NP
- 6. • We can say NP-Hard problem Pi when all the problems of NP Class is to be reduced under polynomial time. NP Pi NP Hard Polynomial Time
- 7. NP-Complete • NP Complete Problems are those Problems which are reducible to polynomial problem but the NP-Hard problem which comes Under NP or resides under NP class .
- 8. Thank You