### NP-complete Problems

NP-complete problem,any of a class of computational problems for which no efficient solution algorithm has been found. Many significant computer-science problems belong to this class—e.g., thetraveling salesman problem, satisfiability problems, and graph-covering problems.So-called easy, or tractable, problems can be solved by computer algorithms that run in polynomial time; i.e., for a problem of size

n, the time or number of steps needed to find the solution is a polynomial function ofn. Algorithms for solving hard, or intractable, problems, on the other hand, require times that are exponential functions of the problem sizen. Polynomial-time algorithms are considered to be efficient, while exponential-time algorithms are considered inefficient, because the execution times of the latter grow much more rapidly as the problem size increases.A problem is called NP (nondeterministic polynomial) if its solution can be guessed and verified in polynomial time; nondeterministic means that no particular rule is followed to make the guess. If a problem is NP and all other NP problems are polynomial-time reducible to it, the problem is NP-complete. Thus, finding an efficient algorithm for any NP-complete problem implies that an efficient algorithm can be found for all such problems, since any problem belonging to this class can be recast into any other member of the class. It is not known whether any polynomial-time algorithms will ever be found for NP-complete problems, and determining whether these problems are tractable or intractable remains one of the most important questions in theoretical computer science. When an NP-complete problem must be solved, one approach is to use a polynomial algorithm to approximate the solution; the answer thus obtained will not necessarily be optimal but will be reasonably close.

List of NP-complete problems (not an exhaustive list), that you may face in a Job Interview.

**References:**

Britanica

April 6, 2013 at 10:47 pm

The problem of combinatorial explosion is characterized by the NP-complete problem. The potential set of solutions is growing exponentially as the complexity of the problems grows. One in the same aren’t they?

April 6, 2013 at 11:09 pm

A problem is called NP (nondeterministic polynomial) if its solution can be guessed and verified in polynomial time, combinatorial explosion time complexities grow exponentially.