In this lecture we’ll study online preemptive scheduling on m machines of arbitrary speeds. We’ll first review the problem and it’s associated literature, then give an optimal deterministic algorithm known as ”RatioStretch”. RatioStretch uses the optimal competitive ratio R > 1 as an input, and achieves R whenever such an R is obtainable. The exact optimal R maybe computed via a linear program,...

In this work we study the problem of scheduling tasks with dependencies in multiprocessor architectures where processors have different speeds. We present the preemptive algorithm “Save-Energy” that given a schedule of tasks it post processes it to improve the energy efficiency without any deterioration of the makespan. In terms of time efficiency, we show that preemptive scheduling in an asymm...

We consider a scheduling problem, which we call the scheduling and wavelength assignment (SWA) problem, arising in optical networks that are based on the wavelength-divisionmultiplexing (WDM) technology. We prove that the SWA problem is -complete for both the preemptive and the nonpreemptive cases. Furthermore, we propose two efficient approximation algorithms. The first is for the preemptive c...

CPU scheduling is the basis of multi-programmed operating systems. The scheduler is accountable for multiplexing processes on the CPU. By switching the CPU among processes, the operating system results in the computer more prolific. Various CPU scheduling algorithms exist for a multi-programmed operating system like First Come First Served (FCFS), Shortest Job First (SJF), Shortest Remaining Ti...

Scheduling jobs with pairwise conflicts is modeled by the graph multicoloring problem. It occurs in two versions: in the preemptive case, each vertex may get any set of colors, while in the non-preemptive case, the set of colors assigned to each vertex has to be contiguous. We study these versions of the multicoloring problem on trees, under the sum-of-completiontimes objective. In particular, ...

Emerging video surveillance, environmental monitoring applications, and constantly evolving large scientific setups require large, high-performance, and reliable storage systems with guaranteed real-time data access. These systems are often implemented using redundant arrays of independent disks (RAID). In this paper we investigate the effectiveness of preemptive disk-scheduling algorithms to a...

We consider the NP-hard problem of scheduling parallel jobs with release dates on identical parallel machines to minimize the makespan. A parallel job requires simultaneously a prespecified, job-dependent number of machines when being processed. We prove that the makespan of any nonpreemptive list-schedule is within a factor of 2 of the optimal preemptive makespan. This gives the best-known app...