On an on-line scheduling problem for parallel jobs

Job Scheduling Techniques for Distributed Systems with Heterogeneous Processor Cardinality

“…Albers improves the competitive ratio to 1.923 in [1]. Naroska and Schwiegelshohn [10] show that the same bound in [1] holds when the jobs need more than one processor. Dell'Amico et al [4] summarize lower and upper bounds on scheduling jobs on multiprocessors.…”

“…Some researchers focus on total completion time [3,7]. However, most of the research [1,4,6,10] focus on the makespan -the completion time of the last job. As a result we will focus on the makespan in this paper.…”

Online scheduling in grids

“…Due to Theorem 3.1, the multiprocessor list scheduling bound 2 − 1 m , see Garey and Graham [4] (concurrentsubmission) as well as Naroska and Schwiegelshohn [7] (submission-over-time), does not apply to Grids. Even more, the next example shows that already in the concurrent-submission case, list scheduling cannot guarantee a constant bound for Cmax C * max for all problem instances.…”

“…Regarding the job model, we stick to the submissionover-time version of Garey and Graham, see Naroska and Schwiegelshohn [7]: Jobs are independent and submitted over time. A job is characterized by its submission time, its fixed degree of parallelism (rigid jobs), and its processing time that is unknown until the job has completed its execution (nonclairvoyant jobs).…”

Multiprocessor Jobs, Preemptive Schedules, and One-Competitive Online Algorithms

“…The survey paper [4] by Drozdowski summarizes the complexity landscape around scheduling multiprocessor jobs. On the approximation side, Johannes [8] and independently Naroska & Schwiegelshohn [11] show that the List Scheduling algorithm yields an approximation ratio of 2.…”