Department of Computer Science | Institute of Theoretical Computer Science | CADMO

Prof. Emo Welzl and Prof. Bernd Gärtner

Mittagsseminar Talk Information |

**Date and Time**: Tuesday, May 31, 2016, 12:15 pm

**Duration**: 30 minutes

**Location**: CAB G51

**Speaker**: Ralph Keusch

Greedy routing is a principle for sending a packet from a starting node s to a target t using only local information: In every hop, the packet is forwarded to the neighbour which is closest to t or which is most likely to be connected to t. On many real-world networks, due to their structural properties Greedy routing is surprisingly succesful. Since Milgram's experiment from 1967, this is known for human society. In 2010, Boguñá et al. demonstrated that mapping the Internet to hyperbolic space makes it amenable for Greedy routing. However, in general only empirical results are known.

In the last year, with Geometric Inhomogeneous Random Graphs we introduced a new, natural model for real-world networks. We rigorously prove that on this model, Greedy routing has constant success probability. More precisely, the failure probability is almost exponentially decreasing in the average degree (which is required to be a constant). Suprisingly, in the case of success, the routing finds an asymptotically shortest s-t-path. As a corollary, our results apply as well for Greedy routing on Hyperbolic Random Graphs and therefore formally prove the experimental results of Krioukov et al.

This is joint work with Karl Bringmann, Johannes Lengler, Yannic Maus and Anisur Molla.

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