Route Discovery with Constant Memory in Oriented Planar Geometric Networks

We address the problem of discovering routes in strongly connected planar geometric networks with directed links. We consider two types of directed planar geometric networks: Eulerian (in which every vertex has the same number of ingoing and outgoing edges) and outerplanar (in which a single face contains all the vertices of the network). Motivated by the necessity for establishing communication in wireless networking based only on geographic proximity, in both instances we give algorithms that use only information that is geographically local to the vertices participating in the route discovery.