In the classical problem of scheduling on unrelated parallel machines, a set of jobs has to be assigned to a set of machines. The jobs have a processing time depending on the machine and the goal is to minimize the makespan, that is the maximum machine load. It is well known that this problem is NP-hard and does not allow polynomial time approximation algorithms with approximation guarantees sm...

A new constructive heuristic for the scheduling problem of n independent jobs on m identical parallel machines with minimum makespan objective is described. The proposed algorithm, which is an n logn algorithm as the LPT algorithm of Graham, iteratively combines partial solutions that are obtained by partitioning the set of jobs in suitable families of subsets. The algorithm was tested using di...

The problem of scheduling G groups of jobs on m unrelated parallel machines is considered. Each group consists of several identical jobs. Implicit in a schedule is a partition of a group into batches; all jobs of a batch are processed jointly. It is possible for diierent batches of the same group to be processed concurrently on diierent machines. However, at any time, a batch can be processed o...

Three characteristics encountered frequently in real-world machine scheduling are jobs released over time, precedence constraints between jobs, and average performance optimization. The general constrained one-machine scheduling problem to minimize the average weighted completion time not only captures these features, but also is an important building block for more complex problems involving m...

The most popular framework for distributed training of machine learning models is the (synchronous) parameter server (PS). This paradigm consists n workers, which iteratively compute updates model parameters, and a stateful PS, waits aggregates all to generate new estimate parameters sends it back workers iteration. Transient computation slowdowns or transmission delays can intolerably lengthen...

We derive the first performance guarantees for a combinatorial online algorithm that schedules stochastic, nonpreemptive jobs on unrelated machines to minimize the expectation of the total weighted completion time. Prior work on unrelated machine scheduling with stochastic jobs was restricted to the offline case, and required sophisticated linear or convex programming relaxations for the assign...