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We consider the optimization problem of a multi-resource, multi-unit VCG auction that produces an optimal, i.e., non-approximated, social welfare. We present an algorithm that solves this optimization problem with pseudo-polynomial complexity and demonstrate its efficiency via our implementation. Our implementation is efficient enough to be deployed in real systems to allocate computing resources in fine time-granularity. Our algorithm has a pseudo-near-linear time complexity on average (over all possible realistic inputs) with respect to the number of clients and the number of possible unit allocations. In the worst case, it is quadratic with respect to the number of possible allocations. Our experiments validate our analysis and show near-linear complexity. This is in contrast to the unbounded, nonpolynomial complexity of known solutions, which do not scale well for a large number of agents. For a single resource and concave valuations, our algorithm reproduces the results of a well-known algorithm. It does so, however, without subjecting the valuations to any restrictions and supports a multiple resource auction, which improves the social welfare over a combination of single-resource auctions by a factor of 2.5-50. This makes our algorithm applicable to real clients in a real system.

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