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 ...

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 ...

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 ...

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.

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 ...

Which is to say, could the problems that seem so difficult in fact be solved with an algorithm in a reasonable amount of time, if only the right, devilishly fast algorithm could be found?

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 ...

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].