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This paper presents a cost-effective scheme for partitioning large data flow graphs. Standard data flow machine architectures are assumed in this work. The objective is to reduce the overhead due to token transfers through the communication network of the machine. When this scheme is employed on large graphs, the load distribution on the rings of the data flow machine is also improved. A canonical form of a data flow graph is introduced to establish the relationship between the communication overhead and the size reduction of the partition cut-set. General lower estimates on the overhead are derived in terms of processing and transmission delay parameters of the machine. The method uses heuristics and an evaluation function to guide the partition algorithm. Some implications of the proposed method on the organization of the data flow machines are discussed.