Using networks as a means of computing can reduce the communication flow over networks. We propose to distribute the computation load in stationary networks and formulate a flow-based delay minimization problem that jointly captures the costs of communications and computation. We exploit the distributed compression scheme of Slepian-Wolf that is applicable under any protocol information. We introduce the notion of entropic surjectivity as a measure of function’s sparsity and to understand the limits of functional compression for computation. We leverage Little’s law for stationary systems to provide a connection between surjectivity and the computation processing factor that reflects the proportion of flow that requires communications. This connection gives us an understanding of how much a node (in isolation) should compute to communicate the desired function within the network. Our results suggest that to effectively compute different function classes with different surjectivities, the networks can be restructured with the transition probabilities being tailored for functions, i.e., task-based link reservations, which can enable mixing versus separately processing of a diverse function class. We numerically evaluate our technique for search, MapReduce, and classification functions, and infer how sensitive the processing factor to the surjectivity of each computation task is.
