Fast arbitrary function computation over a wireless network: A linear programming

In-network function computation (INFC) is becoming an essential aspect of large database systems where the data is distributed over the network. Such situations arise often in resource constrained wireless sensor network making them a natural candidate for INFC. We study the problem of maximizing the rate of INFC in wireless networks. In this paper, we develop a functional flow model for INFC when the function computation sequence is represented by a directed acyclic graph. We propose a linear program formulation to maximize the rate of INFC over all possible embeddings. We also formulate a mixed integer linear program (MILP) for maximizing the rate of computation for a single embedding on a capacity constrained wireless network. The MILP for finding the single embedding that yields maximum rate turns out to be NP hard; we develop a heuristic to solve this problem by formulating a linear program. We provide numerical results to illustrate the performance of these formulations.