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This work addresses the problem of automated memory partitioning for such architectures, taking into account potentially parallel data accesses to physically independent banks. Targeted at affine static control parts (SCoPs), the technique relies on the Z-polyhedral model for program analysis and adopts a partitioning scheme based on integer lattices. The approach enables the definition of a solution space including previous works as particular cases. The problem of minimizing the total amount of memory required across the partitioned banks, referred to as storage minimization throughout the article, is tackled by an optimal approach yielding asymptotically zero memory waste or, as an alternative, an efficient approach ensuring arbitrarily small waste. 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