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Parallel machine scheduling with job assignment restrictions
Author(s) -
Glass Celia A.,
Kellerer Hans
Publication year - 2007
Publication title -
naval research logistics (nrl)
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.665
H-Index - 68
eISSN - 1520-6750
pISSN - 0894-069X
DOI - 10.1002/nav.20202
Subject(s) - computer science , multiprocessing , multiprocessor scheduling , job shop scheduling , scheduling (production processes) , preemption , time complexity , parallel computing , mathematical optimization , algorithm , mathematics , flow shop scheduling , schedule , operating system
Abstract In the classical multiprocessor scheduling problem independent jobs must be assigned to parallel, identical machines with the objective of minimizing the makespan. This article explores the effect of assignment restrictions on the jobs for multiprocessor scheduling problems. This means that each job can only be processed on a specific subset of the machines. Particular attention is given to the case of processing times restricted to one of two values, 1 and λ, differing by at most 2. A matching based polynomial time ε‐approximation algorithm is developed that has a performance ratio tending to $2-{1 \over 1+\lambda}$ . This algorithm is shown to have the best possible performance, tending to 3/2, for processing times 1 and 2. For the special case of nested processing sets, i.e., when the sets of machines upon which individual jobs may be assigned are non‐overlapping, the behavior of list scheduling algorithms is explored. Finally, for assignment restrictions determined by just one characteristic of the machines, such as disc storage or memory constraint in the case of high performance computing, we contribute an algorithm that provides a 3/2 worst case bound and runs in time linear in the number of jobs. © 2006 Wiley Periodicals, Inc. Naval Research Logistics, 2007