Slab Routing: Adapting Two-Dimensional Geographic Routing to Three-Dimensions

Geographic routing, an attractive routing solution for wireless ad hoc networks, has been studied extensively in two-dimensional environments. However, three-dimensional space has proven to be much more challenging, with only a few existing proposals. In this paper, we present Slab Routing - a novel projection based method that adapts two-dimensional geographic face routing techniques to three-dimensional space, avoiding flooding and preserving route optimality properties. Slab Routing accomplishes this by dynamically creating a space partition, which we call a slab, and executing face routing over the planar projected graph of nodes contained within. While the adaptation does not guarantee delivery, we provide an analysis of the conditions required to achieve a desired delivery probability and verify the results through simulation.