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Summary form only given. We consider the task allocation problem for computing a large set of equal-sized independent tasks on heterogeneous computing systems. This problem represents the computation paradigm for a wide range of applications such as SETl@home and Monte Carlo simulations. We consider a general problem in which the interconnection between the nodes is modeled using a graph. We maximize the throughput of the system by using an extended network flow representation. We then develop a decentralized adaptive algorithm. This algorithm leads to a simple decentralized protocol that coordinates the resources in the system. The effectiveness of the proposed task allocation approach is verified through simulations.