A solution to P vs NP could unlock countless computational problems—or keep them forever out of reach. 1. On Monday, July 19, 2021, in the middle of another strange pandemic summer, a leading computer ...

Has the biggest question in computer science been solved? On 6 August, Vinay Deolalikar, a mathematician at Hewlett-Packard Labs in Palo Alto, California, sent out draft copies of a paper titled ...

A diagram showing the relevant complexity classes in the P vs NP problem. “P” problems are solvable in polynomial time; “NP” problems might be solvable in polynomial time, and are checkable in ...

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 ...

"The P-NP problem is the most important open problem in computer science, if not all of mathematics. Simply stated, it asks whether every problem whose solution can be quickly checked by computer can ...

Sometimes people read these definitions and infer that all problems in P are easy, or conversely all in NP are difficult. This is an incorrect view, since these analysis look at worst case scenarios, ...

In this paper, we establish hardness and approximation results for various Lp-ball constrained homogeneous polynomial optimization problems, where p ∈ [2, ∞]. Specifically, we prove that for any given ...

The potential of Internet-based collaboration was vividly demonstrated this month when complexity theorists used blogs and wikis to pounce on a claimed proof for one of the most profound and difficult ...