Greedy routing and the algorithmic small-world phenomenon.

Karl Bringmann, Ralph Keusch, Johannes Lengler, Yannic Maus*, Anisur Rahaman Molla

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review


The algorithmic small-world phenomenon, empirically established by Milgram in the 60 s [1], was theoretically explained by Kleinberg in 2000 [2]. However, from today's perspective his model has several severe shortcomings that limit the applicability to real-world networks. In order to give a more convincing explanation, we study decentralized greedy routing in a random graph model (geometric inhomogeneous random graphs) which overcomes all previous shortcomings. We prove that greedy routing succeeds with constant probability, and in case of success almost surely finds an almost shortest path of length Θ(log⁡log⁡n), with stretch 1+o(1). Moreover, natural local patching methods ensure success probability 1, while maintaining the same stretch. These results also address the question whether there are efficient local routing protocols for the internet graph. Despite promising experimental studies the question remained unsolved theoretically. We give for the first time a rigorous, affirmative answer for a thoroughly validated model of the internet graph.

Original languageEnglish
Pages (from-to)59-105
Number of pages47
JournalJournal of Computer and System Sciences
Publication statusPublished - May 2022


  • Greedy routing
  • Internet routing
  • Random graph models
  • Real-world networks
  • Routing protocols
  • Small-world phenomenon

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Applied Mathematics
  • Computer Networks and Communications
  • Computational Theory and Mathematics


Dive into the research topics of 'Greedy routing and the algorithmic small-world phenomenon.'. Together they form a unique fingerprint.

Cite this