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Summary form only given. In the world of sequential computers, the abstract RAM model enables one to design provably efficient algorithms for a broad range of actual architectures and a broad range of workloads. In the world of multiprocessors, the abstract BSP model serves a similar function. No analogue of the RAM and BSP models is known for modern computing platforms such as clusters of workstations - especially heterogeneous ones, whose constituent workstations may differ in computational power - and the various modalities of Internet-based computing. In this talk, we present circumstantial evidence that no such single algorithmic model can exist for heterogeneous clusters. We describe three quite similar computational problems related to computing a large collection of mutually independent tasks on a cluster. (Two of the problems can be shown formally to be equivalent.) Despite their similarities, the three problems require drastically different algorithmic approaches if one wants provably optimal solutions.