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On Job Scheduling on a Hypercube
January 1993 (vol. 4 no. 1)
pp. 62-69

The problem of scheduling n independent jobs on an m-dimensional hypercube system to minimize the finish time is studied. Each job J/sub i/, where 1>or=i>or=n, is associated with a dimension d/sub i/ and a processing time t/sub i/, meaning that J/sub i/ needs a d/sub i/-dimensional subcube for t/sub i/ units of time. When job preemption is allowed, an O(n/sup 2/ log/sup 2/ n) time algorithm which can generate a minimum finish time schedule with at most min(n-2,2/sup m/-1) preemptions is obtained. When job preemption is not allowed, the problem is NP-complete. It is shown that a simple list scheduling algorithm called LDF can perform asymptotically optimally and has an absolute bound no worse than 2-1/2/sup m/. For the absolute bound, it is also shown that there is a lower bound (1+ square root 6)/2 approximately=1.7247 for a class of scheduling algorithms including LDF.

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Index Terms:
Index TermsLDF algorithm; job scheduling; hypercube; job preemption; minimum finish time schedule; NP-complete; list scheduling algorithm; absolute bound; lower bound; scheduling algorithms; computational complexity; distributed algorithms; hypercube networks; scheduling
Y. Zhu, M. Ahuja, "On Job Scheduling on a Hypercube," IEEE Transactions on Parallel and Distributed Systems, vol. 4, no. 1, pp. 62-69, Jan. 1993, doi:10.1109/71.205653
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