Solving

NP-complete problem using ACO algorithm, In: Emerging Technologies, 2009.

Nevertheless, the

NP-complete problems seem to be much harder in the following sense: every algorithm known so far for solving any

NP-complete problem requires running times that are exponential, not polynomial, functions of the problem size.

That is, it can be shown that any

NP-complete problem can be transformed into each other

NP-complete problem by a polynomial-time procedure.

This class is potentially harder to solve than

NP-complete problems, because if any

NP-complete problem is intractable, then all NP-bard problems are intractable.

SCP is the

NP-complete problem of partitioning a given set into mutually independent subsets while minimizing a cost function defined as the sum of the costs associated to each of the eligible subsets.

The Security of RSA Cryptosystein, from the last names of inventors, Rivest, Shamir, and Adleman (1978) depends solely on the lack of existence of a known polynomial time algorithm for factorization of integers, while the security of Diffie & Hellman (1976), ElGamal (1985), and Massey (1988) revolved around the fact that computing the discrete logarithm in finite fields is an

NP-complete problem.

On the one hand, we plan to use complexity lower bound techniques as inspiration to design new and improved algorithms for Satisfiability and other

NP-complete problems, as well as to analyze existing algorithms better.

DNA computing was introduced by Adleman in 1994 who has explained how to use biological tools to solve

NP-Complete problems [1, 8].

The class of

NP-Complete problems is a subset of NP problems.

It is one of the most famous

NP-Complete problems, and even approximating the chromatic number within an acceptable ratio is NP-hard [7].

Also

NP-complete problems, their role in our daily life, and the crucial role in technology in their study, will be discussed.

BAKER, Approximation algorithms for

np-complete problems on planar graphs, in Proc.