TY - JOUR

T1 - Interval Job Scheduling with Machine Launch Cost

AU - Ren, Runtian

AU - Zhu, Yuqing

AU - Li, Chuanyou

AU - Tang, Xueyan

N1 - Publisher Copyright:
© 1990-2012 IEEE.

PY - 2020/12/1

Y1 - 2020/12/1

N2 - 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.

AB - 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.

KW - Job scheduling

KW - approximation algorithm

KW - online algorithm

UR - http://www.scopus.com/inward/record.url?scp=85087768815&partnerID=8YFLogxK

U2 - 10.1109/TPDS.2020.3002786

DO - 10.1109/TPDS.2020.3002786

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AN - SCOPUS:85087768815

SN - 1045-9219

VL - 31

SP - 2776

EP - 2788

JO - IEEE Transactions on Parallel and Distributed Systems

JF - IEEE Transactions on Parallel and Distributed Systems

IS - 12

M1 - 9119143

ER -