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Resource management systems (RMS) are an important component in heterogeneous computing (HC) systems. One of the jobs of an RMS is the mapping of arriving tasks onto the machines of the HC system. Many different mapping heuristics have been proposed in recent years. However, most of these heuristics suffer from several limitations. One of these limitations is the performance degradation that results from using outdated global information about the status of all machines in the HC system. This paper proposes several heuristics which address this limitation by only requiring partial information in making the mapping decisions. These heuristics utilize the solution to a linear programming (LP) problem which maximizes the system capacity. Simulation results show that our heuristics perform very competitively while requiring dramatically less information.