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This paper presents a hybrid compile and run-time memory management technique for a 3D-stacked reconfigurable accelerator including a memory layer composed of multiple memory units whose parallel access allows a very high bandwidth. The technique inserts allocation, free and data transfers into the code for using the memory layer and avoids memory overflows by adding a limited number of additional copies to and from the host memory. When compile-time information is lacking, the technique relies on run-time decisions for controlling these memory operations. Experiments show that, compared to a pessimistic approach, the overhead for avoiding overflows can be cut on average by 27%, 45% and 63% when the size of each memory unit is respectively 1kB, 128kB and 1MB.