Most prior theoretical research on partitioning algorithms for real-time multiprocessor platforms has focused on ensuring that the cumulative computing requirements of the tasks assigned to each processor does not exceed the processor?s processing power. However, many multiprocessor platforms have only limited amounts of local per-processor memory; if the memory limitation of a processor is not respected, thrashing between "main" memory and the processor?s local memory may occur during run-time and may result in performance degradation. We formalize the problem of task partitioning in a manner that is cognizant of both memory and processing capacity constraints as the memory constrained multiprocessor partitioning problem, prove that this problem is intractable, and present efficient algorithms for solving it under certain — well-defined — conditions.