Succinct Greedy Geometric Routing in R

In greedy geometric routing, messages are passed in a network embedded in a metric space according to the greedy strategy of always forwarding messages to nodes that are closer to the destination. In this paper, we study greedy geometric routing in R, using the standard Euclidean metric. Greedy geometric routing is not always possible in fixed-dimensional Euclidean spaces, of course, as is the case, for example, with star graphs. Nevertheless, we show that such greedy geometric routing schemes exist in R, for 3-connected planar graphs, using the standard Euclidean metric, with coordinates that can be represented succinctly, that is, with O(log n) bits. Moreover, our embedding strategy introduces a coordinate system for R that supports distance comparisons using our succinct coordinates. Thus, our scheme can be used to significantly reduce bandwidth, space, and header size over other recently discovered greedy geometric routing implementations for R. ar X iv :0 81 2. 38 93 v1 [ cs .C G ] 1 9 D ec 2 00 8