Scheduling with Communication Delays

More and more parallel and distributed systems (cluster, grid and global computing) are both becoming available all over the world, and opening new perspectives for developers of a large range of applications including data mining, multimedia, and bio-computing. However, this very large potential of computing power remains largely unexploited this being, mainly due to the lack of adequate and efficient software tools for managing this resource. Scheduling theory is concerned with the optimal allocation of scarce resources to activities over time. Of obvious practical importance, it has been the subject of extensive research since the early 1950's and an impressive amount of literature now exists. The theory dealing with the design of algorithms dedicated to scheduling is much younger, but still has a significant history. An application which will be scheduled on a parallel architecture may be represented by an acyclic graph G = (V, E) (or precedence graph) where V designates the set of tasks, which will be executed on a set of m processors, and where E represents the set of precedence constraints. A processing time is allotted to each task i V. From the very beginning of the study about scheduling problems, models kept up with changing and improving technology. Indeed, • In the PRAM' s model, in which communication is considered instantaneous, the critical path (the longest path from a source to a sink) gives the length of the schedule. So the aim, in this model, is to find a partial order on the tasks, in order to minimize an objective function. • In the homogeneous scheduling delay model, each arc (i,j) E represents the potential data transfer between task i and task j provided that i and j are processed on two different processors. So the aim, in this model, is to find a compromise between a sequential execution and a parallel execution. These two models have been extensively studied over the last few years from both the complexity and the (non)-approximability points of view (see (Graham et al., 1979) and (Chen et al., 1998)). With the increasing importance of parallel computing, the question of how to schedule a set of tasks on a given architecture becomes critical, and has received much attention. More precisely, scheduling problems involving precedence constraints are among the most difficult problems in the area of machine scheduling and they are part of the most studied problems in the domain. In this chapter, we adopt the hierarchical communication model (Bampis et al., 2003) in which we assume that the communication delays are not homogeneous anymore; the processors are connected into clusters and the communications O pe n A cc es s D at ab as e w w w .ite ch on lin e. co m