We consider preemptive offline and online scheduling on identical machines and uniformly related machines in the hierarchical model, with the goal of minimizing the makespan. In this model, each job can be assigned to a subset of the machines which is a prefix of the machine set. We design optimal offline and online algorithms for two uniformly related machines, both when the machine of higher ...

In this paper, we address non-preemptive online scheduling of parallel jobs on a Grid. Our Grid consists of a large number of identical processors that are divided into several machines. We consider a Grid scheduling model with two stages. At the first stage, jobs are allocated to a suitable machine, while at the second stage, local scheduling is independently applied to each machine. We discus...

In this paper, we address non preemptive online scheduling of parallel jobs on a Grid. The Grid consists of a large number of identical processors that are divided into several machines. We consider a Grid scheduling model with two stages. At the first stage, jobs are allocated to a suitable machine while at the second stage, local scheduling is applied to each machine independently. We discuss...

Online algorithms are of importance for many practical applications. Typical examples involve scheduling and routing algorithms employed in operating systems and computer networks. Beside their practical significance, online algorithms are extensively studied from a theoretical point of view. Due to the nature of online problems, these algorithms fail to be optimal in general. The quality of th...

In this paper, we provide a new class of randomized approximation algorithms for parallel machine scheduling problems. The most general model we consider is scheduling unrelated machines with release dates (or even network scheduling) so as to minimize the average weighted completion time. We introduce an LP relaxation in time-indexed variables for this problem. The crucial idea to derive appro...