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In the process of mapping compute-intensive algorithms onto arrays of processing elements (PEs) an efficient usage of channels between PEs and registers within PEs is crucial for achieving a significant algorithm acceleration. In this paper this problem is solved for algorithms represented as systems of uniform recurrence equations. We address an optimization problem in order to realize the algorithmic data dependencies within the processor array (PA) with minimum cost for channels and registers. There, we use a new mapping approach which allows a direct mapping of the algorithm onto the PA by a partitioning method. In contrast to existing approaches, we consider the issue of avoiding redundant usage of channels and registers, which can appear if one instance of a variable has to be transferred from a source PE to several sink PEs. Further, a solution of the optimization problem determines the schedule for the transfer of the variable instances in the channels and their storage in registers as well as the inner schedule for the operations in the PEs. We illustrate our method on the edge detection algorithm.