Directed gossiping for distributed data aggregation

In this paper, we are studying a class of distributed data aggregation problems where a set of nodes in a network is interested in a function of data that is stored in another set of nodes. Assuming the function of interest is separable, we propose an algorithm based on gossiping schemes. Gossiping protocols are iterative methods based on near neighbor communications, and they are known to be efficient and robust to link/node failures. In this work, after formulating the problem mathematically, and introducing previously proposed necessary and sufficient conditions on the gossiping updates, we introduce several necessary conditions on the feasible codes which will provide significant intuition in determining the (in)feasibility of a given problem. By focusing on stochastic codes, we provide a necessary condition based on topology and discuss scenarios where the codes we seek cannot be found.