In the greedy routing scheme, the routing decision is based on decreasing distances between vertex locations. For this idea to work, however, the routing decision does not have to be based on decreasing distances. As long as the routing decision is solely based on the location information of the source, the destination, and the neighbors of the source, the geometric routing scheme will work fine.
In this paper, we introduce a new model of geometric routing. Instead of relying on decreasing distance for routing decisions, our algorithm uses other criterion to determine the routing path, solely based on location information. Our routing algorithms are based on Schnyder coordinates which are derived from Schnyder realizers for plane triangulations and Schnyder woods for 3-connected plane graphs. The coordinates of vertex locations consist of three integers between 0 and , hence the representation only needs bits. In order to send a message from the origin to the destination , our routing algorithm determines the routing path from the Schnyder coordinates of , and all neighbors of . The algorithms are natural and simple to implement.