We articulate the need for managing (data) locality automatically rather than leaving it to the programmer, especially in parallel programming systems. To this end, we propose techniques for coupling tightly the computation (including the thread scheduler) and the memory manager so that data and computation can be positioned closely in hardware. Such tight coupling of computation and memory management is in sharp contrast with the prevailing practice of considering each in isolation. For example, memory-management techniques usually abstract the computation as an unknown “mutator”, which is treated as a “black box”. As an example of the approach, in this paper we consider a specific class of parallel computations, nested-parallel computations. Such computations dynamically create a nesting of parallel tasks. We propose a method for organizing memory as a tree of heaps reflecting the structure of the nesting. More specifically, our approach creates a heap for a task if it is separately scheduled on a processor. This allows us to couple garbage collection with the structure of the computation and the way in which it is dynamically scheduled on the processors. This coupling enables taking advantage of locality in the program by mapping it to the locality of the hardware. For example for improved locality a heap can be garbage collected immediately after its task finishes when the heap contents is likely in cache.