Complexity theory is a fundamental branch of theoretical computer science that categorises computational problems according to their inherent difficulty and the resources required to solve them. At ...

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, any ...

In this article we present applications of smooth numbers to the unconditional derandomization of some well-known integer factoring algorithms. We begin with Pollard's p – 1 algorithm, which finds in ...

Mark Jerrum, Alistair Sinclair (UC Berkeley) and Eric Vigoda (Georgia Tech) received the Association for Computing Machinery (ACM) Test of Time Award at a virtual ceremony on Wednesday 23 June at the ...

A new polynomial-time algorithm for linear programming was announced by Narendra Karmarkar of Bell Laboratories in 1984. This algorithm is claimed by Bell Labs significantly to outperform the simplex ...

What differentiates humans from computers? Is it only a matter of time before efficient algorithms enable a computer to perform the most creative tasks, even to the extent of proving mathematical ...