Complexity theory is a branch of computer science that studies the resources required to solve computational problems, particularly focusing on the classification of problems based on their inherent ...

The original version of this story appeared in Quanta Magazine. One July afternoon in 2024, Ryan Williams set out to prove himself wrong. Two months had passed since he’d hit upon a startling ...

The density matrix renormalization group method has been extensively used to study the ground state of 1D many-body systems since its introduction two decades ago. In spite of its wide use, this ...

One July afternoon in 2024, Ryan Williams set out to prove himself wrong. Two months had passed since he’d hit upon a startling discovery about the relationship between time and memory in computing.

Primal methods constitute a common approach to solving (combinatorial) optimization problems. Starting from a given feasible solution, they successively produce new feasible solutions with ...

A class of production planning problems is considered in which known demands have to be satisfied over a finite horizon at minimum total costs. For each period, production and storage cost functions ...