Constant density spanners for wireless ad-hoc networks

An important problem for wireless ad hoc networks has been to design overlay networks that allow time- and energy-efficient routing. Many local-control strategies for maintaining such overlay networks have already been suggested, but most of them are based on an oversimplified wireless communication model. In this paper, we suggest a model that is much more general than previous models. It allows the path loss of transmissions to significantly deviate from the idealistic unit disk model and does not even require the path loss to form a metric. Also, our model is apparently the first proposed for algorithm design that does not only model transmission and interference issues but also aims at providing a realistic model for physical carrier sensing. Physical carrier sensing is needed so that our protocols do not require any prior information (not even an estimate on the number of nodes) about the wireless network to run efficiently. Based on this model, we propose a local-control protocol for establishing a constant density spanner among a set of mobile stations (or nodes) that are distributed in an arbitrary way in a 2-dimensional Euclidean space. More precisely, we establish a backbone structure by efficiently electing cluster leaders and gateway nodes so that there is only a constant number of cluster leaders and gateway nodes within the transmission range of any node and the backbone structure satisfies the properties of a topological spanner. Our protocol has the advantage that it is locally self-stabilizing, i.e., it can recover from any initial configuration, even if adversarial nodes participate in it, as long as the honest nodes sufficiently far away from adversarial nodes can in principle form a single connected component. Furthermore, we only need constant size messages and a constant amount of storage at the nodes, irrespective of the distribution of the nodes. Hence, our protocols would even work in extreme situations such as very simple wireless devices (like sensors) in a hostile environment.