Citation
New Tight Np-hardness Of Preemptive Multiprocessor And Open Shop Scheduling. In proceedings of the 2nd Multidisciplinary International Conference on Scheduling : Theory and Applications (MISTA 2005), 18 -21 July 2005, New York, USA, pages 606-629, 2005.
Paper
Abstract
We show that preemptive versions of some NP-hard scheduling problems remain NP-hard, but only for a restricted number of preemptions. If we allow a “sufficient” number of preemptions, then these problems become polynomially solvable. We find, as we call, the critical number of preemptions for our problems, i.e., the minimal number of preemptions for which they become polynomially solvable. First we establish that the critical number of preemptions for scheduling m identical processors is m - 1 (we show that scheduling identical processors with at most m - 2 preemptions is NP-hard). Then we consider so-called acyclic open-shop scheduling problem with m machines, a strongly restricted version of the classical open-shop scheduling, and show that m - 2 is the critical number of preemptions for this problem (the earlier known related well-known result was that non-preemptive open shop scheduling is NP-hard). Finally, we consider a slightly restricted version of scheduling on m unrelated processors. The restriction is that the processing time of any job on any processor is no more than the optimal schedule makespan. We call such processors non-lazy unrelated processors. We show that 2m - 3 is the critical number of preemptions for scheduling non-lazy unrelated processors.
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Bibtex
@INPROCEEDINGS{2005-606-629-P, author = {E. Shchepin and N. Vakhania},
title = {New Tight Np-hardness Of Preemptive Multiprocessor And Open Shop Scheduling},
booktitle = {In proceedings of the 2nd Multidisciplinary International Conference on Scheduling : Theory and Applications (MISTA 2005), 18 -21 July 2005, New York, USA},
year = {2005},
editor = {G. Kendall and L. Lei and M. Pinedo},
pages = {606--629},
note = {Paper},
abstract = {We show that preemptive versions of some NP-hard scheduling problems remain NP-hard, but only for a restricted number of preemptions. If we allow a “sufficient” number of preemptions, then these problems become polynomially solvable. We find, as we call, the critical number of preemptions for our problems, i.e., the minimal number of preemptions for which they become polynomially solvable. First we establish that the critical number of preemptions for scheduling m identical processors is m - 1 (we show that scheduling identical processors with at most m - 2 preemptions is NP-hard). Then we consider so-called acyclic open-shop scheduling problem with m machines, a strongly restricted version of the classical open-shop scheduling, and show that m - 2 is the critical number of preemptions for this problem (the earlier known related well-known result was that non-preemptive open shop scheduling is NP-hard). Finally, we consider a slightly restricted version of scheduling on m unrelated processors. The restriction is that the processing time of any job on any processor is no more than the optimal schedule makespan. We call such processors non-lazy unrelated processors. We show that 2m - 3 is the critical number of preemptions for scheduling non-lazy unrelated processors.},
owner = {Faizah Hamdan},
timestamp = {2012.05.21},
webpdf = {2005-606-629-P.pdf} }