Abstract
This paper investigates the problem of maximizing utility for job scheduling where each job consists of multiple tasks, each task has utility and each job also has extra utility if all tasks of that job are completed. We provide a 2-approximation algorithm for the single-machine case and a 2-approximation algorithm for the multi-machine problem. Both algorithms include two steps. The first step employs the Earliest Deadline First method to compute utility with only extra job utility, and it is proved that it obtains the optimal result for this sub-problem. The second step employs a Dynamic Programming method to compute utility without extra job utility, and it also derives the optimal result. An approximation result can then be obtained by combining the results of the two steps.
Highlights
Job scheduling is a widely studied topic in computer science
A job should be preemptive and it can be divided into many small tasks in order to provide interactive services and improve the utilization ratio of the computing resources
We study the multi-task job scheduling problem in this paper
Summary
Job scheduling is a widely studied topic in computer science. Many systems such as parallel and distributed computing, cloud computing, workforce management, energy management, and network communications require scheduling of jobs [1,2,3,4,5]. Bar-Yehuda and Rawitz [22] studied the uniform case of the basic SplitJob problem and derived a (6r)-approximation algorithm by utilizing the fractional local ratio technique. A closely related problem is considered by Zheng et al in [10] which study the problem of scheduling interactive jobs at a data center with the goal of maximizing the total utility of all the jobs. In their problem, the utility of a job is a function of the completed workload of that job. If the scheduling can be preemptive, the authors can provide an optimal solution to solve the problem
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