Parallel machine scheduling with nested processing set restrictions |
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Authors: | Yumei Huo Joseph Y.-T. Leung |
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Affiliation: | 1. Department of Computer Science, CUNY at Staten Island, Staten Island, NY 10314, USA;2. Department of Computer Science, New Jersey Institute of Technology, Newark, NJ 07102, USA |
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Abstract: | We consider the problem of scheduling a set of n independent jobs on m parallel machines, where each job can only be scheduled on a subset of machines called its processing set. The machines are linearly ordered, and the processing set of job j is given by two machine indexes aj and bj; i.e., job j can only be scheduled on machines aj,aj+1,…,bj. Two distinct processing sets are either nested or disjoint. Preemption is not allowed. Our goal is to minimize the makespan. It is known that the problem is strongly NP-hard and that there is a list-type algorithm with a worst-case bound of 2-1/m. In this paper we give an improved algorithm with a worst-case bound of 7/4. For two and three machines, the algorithm gives a better worst-case bound of 5/4 and 3/2, respectively. |
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Keywords: | Nested processing set restrictions Nonpreemptive scheduling Makespan NP-hard Approximation algorithm Worst-case bound |
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