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].

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 ...

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 ...

For each variant, we present exact branch-price-and-cut algorithms that rely on customized monodirectional and bidirectional labeling algorithms for generating feasible vehicle routes. In ...

Methods with cost growing as some power of the number of cities, or polynomial-time algorithms, are needed. The P in “P = NP” stands for problems that can be solved in polynomial time.

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 ...

"These quantum computer algorithms were originally developed in a completely different context. We used them here for the first time to calculate electron densities of molecules, in particular ...

They proved that one of two things must be true: Either all problems that can be efficiently solved using randomness also have fast deterministic algorithms, or many notoriously difficult problems are ...

New perspectives on algorithms and complexity from string theory Dr Ramgoolam has worked with “Research Features” to produce an expository article for general audiences on his recent research with an ...