12.5 Introduction to NP-completeness
There is no known "efficient" algorithm for the travelling
salesperson problem, optimal graph coloring problem, knapsack
problem, Hamiltonian cycle problem, integer programming
problem, or satisfiability of a Boolean expression problem.
On the other hand there is no known proof that even one of
these problems can't be solved efficiently.
It has been shown that all the problems above are
equivalent in the following sense:
If we were to discover an efficient algorithm for one of them,
we would be able to use what we know about the relationships
among the problems to find efficient solutions for all the
others.