A Competitive Online Algorithm for a Parallel Job Scheduling Problem

We study a parallel job scheduling problem in which parallel jobs may be assigned to any number of processors in a parallel computing system. If a job of size p j is assigned to k j processors, its running time is assumed to be p j=k j + k jc, where c is a constant representing communication overhead for each processor. This model explicitly takes into account the increase in overhead arising from the use of more processors and the fact that a small job may be easily overwhelmed by overhead, and actually see its running time increase, if it is assigned to too many processors. Mao, Chen, and Watson (1999) introduced this parallel job scheduling problem and showed that the competitive ratio of a particular deterministic online scheduling algorithm is 2 when the machine has two processors. We show that, for an arbitrary number of processors, the competitive ratio of their algorithm (slightly modified) is asymptotically 4.