On-Line Scheduling of Parallel Jobs

We study an on-line parallel job scheduling problem, where jobs arrive over list. A parallel job may require a number of machines for its processing at the same time. Upon arrival of a job, its processing time and the number of requested machines become known, and it must be scheduled immediately without any knowledge of future jobs. We present a 8-competitive on-line algorithm, which improves the previous upper bound of 12 by Johannes [8]. Furthermore, we investigate two special cases in which jobs arrive in non-increasing order of processing times or jobs arrive in non-increasing order of sizes. Better bounds are shown.