An Experimental Study of Low Stretch Factor on Greedy Geometric routing based Algorithm

Greedy routing has drawn a lot of attention in research community. To our best knowledge, stretch factor has not been studied for greedy routing algorithms. In this paper, we propose a new greedy routing algorithm and take the initiative to evaluate its stretch factor. Our algorithm generalizes the algorithm presented in [1]. It embeds an n-vertex connected graph G(V,E) in a semi-metric space. With an appropriate distance notion, greedy routing works fine, just like for the case of embedding graphs in metric spaces. Theoretically, our algorithm runs in linear time. The virtual coordinates of each vertex u can be represented in deg(u)O(logn) bits. The distance between any two vertices can be computed in constant time. We observe that stretch factors are always small constant numbers. We present their values and patterns in the paper. To our best knowledge, this is the first study towards a practical low-stretch-factor greedy routing algorithm.