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On job scheduling on a hypercube

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2 Author(s)
Y. Zhu ; Dept. of Comput. Sci., North Dakota State Univ., Fargo, ND, USA ; M. Ahuja

The problem of scheduling n independent jobs on an m -dimensional hypercube system to minimize the finish time is studied. Each job Ji, where 1⩽in, is associated with a dimension d i and a processing time ti, meaning that Ji needs a di-dimensional subcube for ti units of time. When job preemption is allowed, an O(n2 log2 n) time algorithm which can generate a minimum finish time schedule with at most min{n-2,2m-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 2-1/2m. For the absolute bound, it is also shown that there is a lower bound (1+√6)/2≈1.7247 for a class of scheduling algorithms including LDF

Published in:

IEEE Transactions on Parallel and Distributed Systems  (Volume:4 ,  Issue: 1 )