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We study the problem of scheduling 11 independent if a job may be preempted before its completion; otherwise, jobs on an tit-dimensional hypercube system to minimize the finish time. Each job J , , where 1 5 i 5 I t , is associated with a dimension d, and a processing time f , , meaning that J , needs a d,-dimensional subcube for f , units of time. When job preemption is allowed, we give an O ( rt log' 11 ) time algorithm which can generate a minimum finish time schedule with at most inin{ i t -2.2"' -l} preemptions. When job preemption is not allowed, the problem is NP-complete. We show that a simple list scheduling algorithm called LDF can perform asymptotic optimal and has an absolute bound no worse than 2 -112"'. For the absolute bound, we also show that there is a lower bound (1 + &)I2 1.7247 for a class of scheduling algorithms including LDF.