Finding the Optimal Communication Structure for Networked Computing

This paper studies the problem of distributed computation over a wireless network of resource constrained nodes. This problem applies to many emerging wireless sensor networks, including those used for body sensing, structural health monitoring, and various cyber-physical systems. Computational tasks in these networks typically require far more sophisticated data processing beyond commonly-studied data aggregation or simple functions like average and max/min, in order to enable real-time diagnosis and control. To determine how to accomplish this in the most energy efficient manner, possibly subject to a delay constraint, we need to first be able to decompose a computational task into components, and then be able to distribute these components over the network taking into account the fact that data input to the computation may originate from different parts of the network. In this paper, we propose a general optimization framework to determine the best communication structure given a fixed decomposition of a computational task represented in a data-flow graph. We do this for two classes of computations, those involving single-stream inputs and those requiring multi-stream inputs. For each category, we prove that finding the optimal communication structure is NP-hard. We then propose centralized integer linear programs to determine the optimal communication structure, and develop polynomial, distributed approximation algorithms to find a nearoptimal communication structure. We analytically derive the approximation factor for each approximation algorithm we propose, and evaluate their performance in realistic engineering applications through simulation.