A fast preemptive scheduling algorithm with release times and inclusive processing set restrictions

Authors:
Yumei Huo;Joseph Y. -T. Leung;Xin Wang
Affiliations:
Department of Computer Science, CUNY at Staten Island, Staten Island, NY 10314, United States;Department of Computer Science, New Jersey Institute of Technology, Newark, NJ 07102, United States;Department of Computer Science, New Jersey Institute of Technology, Newark, NJ 07102, United States
Venue:
Discrete Optimization
Year:
2009

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Abstract

We consider the problem of preemptively scheduling n independent jobs on m parallel machines so as to minimize the makespan. Each job J"j has a release time r"j and it can only be processed on a subset of machines M"j. The machines are linearly ordered. Each job J"j has a machine index a"j such that M"j={M"a"""j,M"a"""j"+"1,...,M"m}. We first show that there is no 1-competitive online algorithm for this problem. We then give an offline algorithm with a running time of O(nklogP+mnk^2+m^3k), where k is the number of distinct release times and P is the total processing time of all jobs.