Competitively Scheduling Tasks with Intermediate Parallelizability

We introduce a scheduling algorithm Intermediate-SRPT, and show that it is O(logP)-competitive with respect to average flow time when scheduling jobs whose parallelizability is intermediate between being fully parallelizable and sequential. Here, the parameter P denotes the ratio between the maximum job size to the minimum. We also show a general matching lower bound on the competitive ratio. Our analysis builds on an interesting combination of potential function and local competitiveness arguments.