We present an approximately-efficient and approximately-strategyproof auction mechanism for a single-good multi-unit allocation problem. The bidding language allows marginaldecreasing piecewise constant curves and quantity-based side constraints. We develop a fully polynomial-time approximation scheme for the multi-unit allocation problem, which computes a

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Abstract. Grid computing systems pool together the resources of many workstations to create a virtual computing reservoir. Users can "draw" resources using a pay-as-you-go model, commonly used for utilities (electricity and water). We model such a system as a capacitated graph, and study a basic allocation problem: given a set of jobs, each demanding computing and bandwidth resources and yielding a profit, determine which feasible subset of jobs yields the maximum total profit.