On geographic routing without location information

One of the most interesting problems in wireless adhoc networks is finding scalable routing algorithms for message passing from source nodes to destination nodes in. Several routing algorithms exist in the literature. In particular, the ones that use geographic location information as the address seem to be more scalable to large networks. These methods however, require that all nodes in the network know the geographic location of all the others. While this is the case in certain sensor net applications, there are plenty of scenarios where geographic location information is not obtainable for all nodes. Recently, a new routing algorithm was proposed by Rao et al. which does not require geographic information for all of the nodes in the network, but assumes that peripheral nodes located at the boundary of the region of interest have location information. The algorithm is based on the use of a set of virtual coordinates which are calculated by averaging the x - y coordinates of each node in the network with its nearest neighbors, while keeping the coordinates of the peripheral nodes on the boundary fixed. Simulations indicate that the virtual coordinates converge to fixed values when the graph is connected. It has been shown that such a routing scheme has a surprisingly high success rate, close to that of location aware routing algorithms, and performs even better when there are obstacles in the network. In this paper, we will explicitly calculate a closed form solution for the virtual coordinates, explore the connections to distributed coordination algorithms and provide a possible explanation for the high success rate of the algorithm. We further explore connections to several other areas such as distributed coordination algorithms as well as distance geometry, as well as the notion of resistance distance in graphs.