With innovations in computational power, there has been an increase in algorithms that are much smarter than before. Under such circumstances, the pressure to tackle P versus NP problem, is considerably increasing. Moreover, this P versus NP problem is invading all fields of science as just not a theoretical question but as a basic principle. Author of the article surmises herein, the simple description of the issue and the change in working direction related to computer science attained because of efforts to solve this question.
P versus NP problem actually computes combinational issues. Jack Edmonds, first in the history, provided a program that can help in developing a program to solve combination problem, and formally defined it as ‘efficient computation’. P in this problem stands for ‘Polynomial Time’ and defines problem class which has efficient solution. Likewise, NP in this problem stands for ‘Nondeterministic Polynomial-Time’ and refers to the problems that have solutions that can be verified in an efficient manner. Furthermore, author describes that extremely complicated NP problems are termed as ‘NP-complete’ problems.
Examples of such problems are Clique, Partition and triangles, 3D-coloring and Hamiltonian cycle. Basically, the idea promoted by NP-complete asserts that if an efficient algorithm can be developed for one problem, it can also be developed for other complicated problems too. Thus to simplify, P defines the type or the category of the problem that comes with efficient solution whereas, NP defines a group of problems, each of which has an efficient recognizable solution. By saying P = NP, we mean to say that for any problem that has an efficient verifiable solution, we can efficiently identify that solution. However, there are many scientists who believed that P ≠ NP and defined it as inability to find the solution efficiently.