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This paper formulates abstract problems of assigning subtasks to agents (processors) in a distributed system with a goal that they can perform its global task efficiently. The paper models the distributed system with a graph that describes the communication capabilities of the constituting agents. This graph is referred to as the "organizational graph.” In addition, the desired task-performing activity is modeled with another graph describing the required communications. Then, a few variants of the task assignment problem are formulated with potentially conflicting objectives (or constraints) of load balancing and communication costs. For some of these variants this paper provides efficient algorithms that solve the assignment problem. Some problems are proven NP-complete, and some others are left open.