research-article

Greedy Routing and the Algorithmic Small-World Phenomenon

Authors:

Karl Bringmann,

Johannes Lengler,

Anisur Rahaman MollaAuthors Info & Claims

PODC '17: Proceedings of the ACM Symposium on Principles of Distributed Computing

Pages 371 - 380

https://doi.org/10.1145/3087801.3087829

Published: 25 July 2017 Publication History

Abstract

The algorithmic small-world phenomenon, empirically established by Milgram's letter forwarding experiments from the 60s, was theoretically explained by Kleinberg in 2000. 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 of the algorithmic small-world phenomenon, we study decentralized greedy routing in a more flexible random graph model (geometric inhomogeneous random graphs) which overcomes all previous shortcomings. Apart from exhibiting good properties in theory, it has also been extensively experimentally validated that this model reasonably captures real-world networks. In this model, the greedy routing protocol is purely distributed as each vertex only needs to know information about its direct neighbors. We prove that it succeeds with constant probability, and in case of success almost surely finds an almost shortest path of length Θ(log log n), where our bound is tight including the leading constant. Moreover, we study natural local patching methods which augment greedy routing by backtracking and which do not require any global knowledge. We show that such methods can ensure success probability 1 in an asymptotically tight number of steps.

These results also address the question of Krioukov et al. whether there are efficient local routing protocols for the internet graph. There were promising experimental studies, but the question remained unsolved theoretically. Our results give for the first time a rigorous and analytical affirmative answer.

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cover image ACM Conferences

PODC '17: Proceedings of the ACM Symposium on Principles of Distributed Computing

July 2017

480 pages

ISBN:9781450349925

DOI:10.1145/3087801

General Chair:
Elad Michael Schiller
Chalmers University of Technology, Sweden
,
Program Chair:
Alexander A. Schwarzmann
University of Connecticut, USA

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Published: 25 July 2017

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https://doi.org/10.1017/jpr.2022.44
Bringmann KKeusch RLengler JMaus YMolla A(2022)Greedy routing and the algorithmic small-world phenomenonJournal of Computer and System Sciences10.1016/j.jcss.2021.11.003125(59-105)Online publication date: May-2022
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