Complexity Theory: The study of the intrinsic difficulty of computational problems and the classification of algorithms according to the resources required for their solution.

This paper considers the design and analysis of algorithms for vehicle routing and scheduling problems with time window constraints. Given the intrinsic difficulty of this problem class, approximation ...

The researchers also considered an extension of the STSP that includes time windows for simultaneous pickups and deliveries, creating a more realistic and challenging problem. The core method involves ...

In fact, we don’t know any problem that is in the class NP of easily-verified problems but for which there is definitely no polynomial-time algorithm.

Computer Scientists Discover Limits of Major Research Algorithm The most widely used technique for finding the largest or smallest values of a math function turns out to be a fundamentally difficult ...

While the worst-case complexity of most scheduling problems is known, the average-case complexity has not been studied. This paper examines the average-case complexity of the following NP-hard open ...

It might turn out that a P algorithm capable of solving the NP-complete problem is on a time scale of, say, n ^100. “Technically that falls under P: it’s a polynomial,” says James.

These algorithms are significant because they can solve the noncommutative weighted Edmonds' problem in polynomial time, demonstrating that certain complex problems can be tackled efficiently [2].