On the choice of a spanning tree for greedy embedding of network graphs

Greedy embedding is a graph embedding that makes the simple greedy geometric packet forwarding successful for every source-destination pair. It is desirable that graph embeddings also yield low hop overhead (stretch) of the greedy paths over the corresponding shortest paths. In this paper we study how topological and geometric properties of embedded graphs influence the hop stretch. Based on the obtained insights, we design embedding heuristics that yield minimal hop stretch greedy embeddings and verify their effectiveness on models of synthetic graphs. Finally, we verify the effectiveness of our heuristics on instances of several classes of large, real-world network graphs.