A dynamic algorithm for online scheduling of parallel processes

Abstract

We study the following general online scheduling problem. Parallel jobs arrive dynamically according to the dependencies between them. Each job requests a certain number of processors with a specific communication configuration, but its running time is not known until it is completed. We present optimal online algorithms for PRAMs, hypercubes and one — dimensional meshes, and obtain optimal tradeoffs between the competitive ratio and the largest number of processors requested by any job. Our work shows that for efficient online scheduling it is necessary to use virtualization, i.e., to schedule parallel jobs on fewer processors than requested while preserving the work. We prove that tree constraints are complete for the scheduling problem, i.e., any algorithm that solves the scheduling problem if the dependency graph is a tree can be converted to solve the general problem equally efficiently. This shows that the structure of a dependency graph is not as important for online scheduling as it is for offline scheduling, although even simple dependencies make the problem much harder than scheduling independent jobs.