To date, it is not known whether NP problems can be solved in polynomial time by a deterministic Turing machine. If that were the case, we could finally provide an answer to the most outstanding ...

A certain class of mathematical problems, called NP-complete, can seemingly only be solved by exploring every possible solution, which conventional computers have to do one at a time.

MILLENNIUM PRIZE SERIES: The Millennium Prize Problems are seven mathematics problems laid out by the Clay Mathematics Institute in 2000. They’re not easy – a correct solution to any one ...

In computational complexity theory, P and NP are two classes of problems. P is the class of decision problems that a deterministic Turing machine can solve in polynomial time. In useful terms… ...

We show that the problem of determining this minimum length, given A, is NP-complete. Thus the problem of finding optimum rectilinear Steiner trees is probably computationally hopeless, and the ...

Although NP-complete problems are hard to solve efficiently, once solutions are found, they can be verified trivially. The challenge that the team at CNRS (the French National Centre for Scientific ...