Interval Job Scheduling with Machine Launch Cost

Runtian Ren*, Yuqing Zhu, Chuanyou Li, Xueyan Tang

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review


We study an interval job scheduling problem in distributed systems. We are given a set of interval jobs, with each job specified by a size, an arrival time and a processing length. Once a job arrives, it must be placed on a machine immediately and run for a period of its processing length without interruption. The homogeneous machines to run jobs have the same capacity limits such that at any time, the total size of the jobs running on any machine cannot exceed its capacity. Launching each machine incurs a fixed cost. After launch, a machine is charged a constant cost per time unit until it is terminated. The problem targets to minimize the total cost incurred by the machines for processing the given set of interval jobs. We focus on the algorithmic aspects of the problem in this article. For the special case where all the jobs have a unit size equal to the machine capacity, we propose an optimal offline algorithm and an optimal 2-competitive online algorithm. For the general case where jobs can have arbitrary sizes, we establish a non-trivial lower bound on the optimal solution. Based on this lower bound, we propose a 5-approximation algorithm in the offline setting. In the non-clairvoyant online setting, we design a O(μ)-competitive Modified First-Fit algorithm which is near optimal (μ is the max/min job processing length ratio). In the clairvoyant online setting, we propose an asymptotically optimal O(logμ)-competitive algorithm based on our Modified First-Fit strategy.

Original languageEnglish
Article number9119143
Pages (from-to)2776-2788
Number of pages13
JournalIEEE Transactions on Parallel and Distributed Systems
Issue number12
StatePublished - 1 Dec 2020
Externally publishedYes


  • Job scheduling
  • approximation algorithm
  • online algorithm


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