NP Problems

NP Problems

Introduction

There are mainly two types of problem P and NP which are common for discussion. P deals with the Polynomial problems and NP deals with the non deterministic Polynomial problems. When we consider P problems they are solved by Polynomial-time algorithm. These problems are run by runs in, where is a polynomial. This may include many things like sorting and triangulation. In NP, problems are always checkable, but it is not necessary that they are also solvable.

Discussion

When we say NP that is mean NP minus P and it is always checkable. It gives us facility of verification of the solution, and we can easily verify it whether it is the exact solution or not. Let us consider an example of subset sum in which there is a set of given numbers. The question arises that there exists a subset whose sum is zero. It sounds that it will not be solved by Polynomial time, but, answer will be checked easily that it is correct. What is reducibility? Reducibility is when notion of any complex problem is given, and we construct another problem whose solution will help to solve this problem. There should be a strong logic and fast algorithm to solve subset sum.

If the sums are easily reduced to each other, than these problems said to equivalent. In NP, all identical problems are said to be NP- complete.

If NP-Complete problem is reduced to H problem, then it will be NP Hard. This also means that, that H is hard to some extent, as all the NP-Complete problems, but there will be no need to reduce any NP-Complete Problem to H. This is because, it is possible, that H will be harder than all the NP-Complete problems.

Problems, which are known for P, trivially is in NP. NP is said to ...