In this paper we introduce two general techniques for the design and analysis of approximation algorithms for NP-hard scheduling problems in which the objective is to minimize the weighted sum of the ...

In the flow shop weighted completion time problem, a set of jobs has to be processed on m machines. Every machine has to process each one of the jobs, and every job has the same routing through the ...

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 ...