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We study the complexity of the problem of allocating m modules to n processors in a distributed system to minimize total communication and execution costs. When the communication graph is a tree, Bokhari has shown that the optimum allocation can be determined in O(mr?) time. Recently, this result has been generalized by FernBndez-Baca, who has proposed an allocation algorithm in O(mnk+') when the communication graph is a partial k-tree. We show that in the case where communication costs aredoi:10.1109/71.273050 fatcat:ksdmk4d3s5h3ndlfydnnhfcg5a