Distributed node placement algorithms for constructing well-connected sensor networks

We study the problem of node placement in a sensor network. We consider proximity-based communication models where each sensor can only communicate with the ones within a given distance from it and the quality of communication between two sensors decreases with their distance. Each sensor can move locally and our goal is to improve the network connectivity by locally relocating the sensors. We use tools from spectral graph theory to determine the criticality of each edge to the global network connectivity. Based on the criticality measure, we develop algorithms that iteratively move the sensors in directions that improve the communication along more critical edges. Our algorithms are fully decentralized and only use local information exchange which are essential features for the sensor network application due to lack of centralized control and access to information in such networks. We formulate our problem as a convex optimization and use techniques from proximal minorant methods to prove the convergence of our iterative algorithms. Further, to make the algorithms fully local we use ideas such as the alternating direction method of multipliers from the distributed optimization literature. We also quantitatively illustrate the effectiveness of our schemes using simulation on a few sample networks.