It is considered as a subproblem of the most popular

NP-complete problem, the Travelling Salesman Problem (TSP), where the problem is to find the minimum weighted Hamiltonian cycle.

The selection of such disjoint or nondisjoint cover sets is proved to be

NP-complete problem [9,11].

As a well-known

NP-complete problem, SAT problem has been widely used in artificial intelligence and electronic design automation.

We will prove the theorem by reduction from the

NP-Complete problem X3C(3).

The 0/1 knapsack problem has been proved to be an

NP-complete problem [21].

In this paper we propose a new KAP based on

NP-complete problem and hence having a property of provable security.

Multi-Constraint 0-1 Knapsack problem is a

NP-complete problem [28], which implies that the computation time it requires to solve this problem is simply infeasible to be implemented in any real systems, and certainly not feasible in a IEEE 802.16m bandwidth request-grant interval where the computation must take place within a few milliseconds.

In 1994 [1] Adleman successfully solved the Direct Hamiltonian Path problem HPP (which is an

NP-complete problem) that opens a new area, called DNA computation.

Solving

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

There are two significant differences between that undecidable problem and our

NP-complete problem: we consider stationary policies and finite horizons.

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.