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Partitioned memory with bus interconnect architecture in its most general form consists of several functional units with associated memory accessible to the functional unit via local interconnect and global buses to communicate data values across from one functional unit to another. As can be expected, the time at which certain values are c ommunicated aect the size of the local memories and the number of buses that are n e e ded. We address the problem of scheduling communications in a bus architecture under memory constraints. We present here a network ow formulation for the problem and obtain an exact algorithm to schedule the communications, such that the constraint on the number of registers in each functional unit is satised. As an increasing number of architectures use multiple memories in addition to (or instead of) one central RAM, this work is especially interesting. Several authors have already studied this problem in related a r chitectures, yet all use heuristic approaches to schedule the communications. Our technique is the rst exact solution to the problem. Also, our graph theoretic formulation provides a clearer insight into the problem.