Mittagsseminar (in cooperation with J. Lengler, A. Steger, and D. Steurer)

Date and Time: Tuesday, October 14, 2025, 12:15 pm

Duration: 30 minutes

Location: OAT S15

Speaker: Daniel Chiu

Geometric Routing in GIRGs

Geometric Inhomogeneous Random Graphs (GIRGs) capture both geometric locality and power-law degree distributions, making them a natural model for studying navigability in complex networks. Bringmann et al. (Greedy Routing and the Algorithmic Small-World Phenomenon, 2022) showed that greedy routing in GIRGs succeeds with constant probability and finds ultra-short paths of length Θ(log log n). In this talk, I will discuss a weight-agnostic variant called geometric routing, where messages are forwarded greedily using only local geometric information. We show that geometric routing also achieves asymptotically optimal success probability and stretch to the shortest path under suitable parameter conditions. Furthermore, both routing schemes follow comparable two-phase trajectories toward the target through the network’s heavy core, while geometric routing exhibits an additional intermediate step during the phase transition that is not observed in greedy routing.
This talk is based on joint work with Marc Kaufmann, Kostas Lakis, and Ulysse Schaller.

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