Online malleable job scheduling for m ≤ 3

A malleable parallel job is one that may be assigned to any number of processors in a parallel computing environment. In our particular problem, we assume that the execution time of a job j with processing requirement p(j) is p(j)/k(j) + (k(j) - 1)c if the job is assigned to k(j) epsilon {1,2, ... , m} processors, where c is a constant representing overhead and m is the number of processors. Given a sequence of jobs, an online algorithm must assign to each job, as it arrives, both a number of processors and a start time to minimize the makespan of the schedule. We provide online algorithms for m = 2 and m = 3 with asymptotically optimal competitive ratios of 3/2 and 5/3, respectively. We also provide a similar online algorithm for the more general problem with job dependent overhead term c(j) that has optimal competitive ratio empty set = (1 +root 5)/2 when m = 2. (c) 2010 Elsevier B.V. All rights reserved.