Scheduling independent jobs on hypercubes
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We consider the problem of scheduling k independent jobs on an n-dimensional hypercube system to minimize finishing time, where each job J i is associated with a dimension d i and a processing time t i , meaning that J i requires a d i -dimensional subcube for t i units of time. This problem is NP-complete if no preemption is allowed. We propose a simple heuristic called LDLPT (largest dimension largest processing time) for this problem and analyze its worst-case performance: the ratio of the heuristic finishing time to the optimal does not exceed 2 — 1/2n-1.
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