Prof. Dr. Tobias Friedrich

Hyperbolic Embeddings for Near-Optimal Greedy Routing

Greedy routing computes paths between nodes in a network by successively moving to the neighbor closest to the target with respect to coordinates given by an embedding into some metric space. Its advantage is that only local information is used for routing decisions. We present different algorithms for generating graph embeddings into the hyperbolic plane that are well suited for greedy routing. In particular our embeddings guarantee that greedy routing always succeeds in reaching the target and we try to minimize the lengths of the resulting greedy paths. We evaluate our algorithm on multiple generated and real wold networks. For networks that are generally assumed to have a hidden underlying hyperbolic geometry, such as the Internet graph [1], we achieve near-optimal results, i.e., the resulting greedy paths are only slightly longer than the corresponding shortest paths. In the case of the Internet graph, they are only 6% longer when using our best algorithm, which greatly improves upon the previous best known embedding, whose creation required substantial manual intervention.

[1] https://www.nature.com/articles/ncomms1063

This page contains the code for the following paper that was accepted for presentation at ALENEX 2018. More of our reasearch about the hyperbolic geometry of networks can be found here.

  • Hyperbolic Embeddings for... - Download
    Bläsius, Thomas; Friedrich, Tobias; Katzmann, Maximilian; Krohmer, Anton Hyperbolic Embeddings for Near-Optimal Greedy RoutingAlgorithm Engineering and Experiments (ALENEX) 2018: 199–208


You can download the experiment setup, including code and instructions here: groheg.zip