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Abstract

In the 1960s, the world-renowned social psychologist Stanley Milgram conducted experiments that showed that not only do there exist ``short chains'' of acquaintances between any two arbitrary people, but that these arbitrary strangers are able to find these short chains. This phenomenon, known as the \emph{small-world phenomenon}, is explained in part by any model that has a low diameter, such as the Barabási and Albert's \emph{preferential attachment} model, but these models do not display the same efficient routing that Milgram's experiments showed. In the year 2000, Kleinberg proposed a model with an efficient \(\mathcal{O}(\log^2{n})\) greedy routing algorithm. In 2004, Martel and Nguyen showed that Kleinberg's analysis was tight, while also showing that Kleinberg's model had an expected diameter of only \(\Theta(\log{n})\) -- a much smaller value than the greedy routing algorithm's path lengths. In 2022, Goodrich and Ozel proposed the \emph{neighborhood preferential attachment} model (NPA), combining elements from Barabási and Albert's model with Kleinberg's model, and experimentally showed that the resulting model outperformed Kleinberg's greedy routing performance on U.S. road networks. While they displayed impressive empirical results, they did not provide any theoretical analysis of their model. In this paper, we first provide a theoretical analysis of a generalization of Kleinberg's original model and show that it can achieve expected \(\mathcal{O}(\log{n})\) routing, a much better result than Kleinberg's model. We then propose a new model, \emph{windowed NPA}, that is similar to the neighborhood preferential attachment model but has provable theoretical guarantees w.h.p. We show that this model is able to achieve \(\mathcal{O}(\log^{1 + \epsilon}{n})\) greedy routing for any \(\epsilon > 0\).

Details

1009240
Identifier / keyword
Title
Highway Preferential Attachment Models for Geographic Routing
Publication title
arXiv.org; Ithaca
Publication year
2024
Publication date
Dec 9, 2024
Section
Computer Science
Publisher
Cornell University Library, arXiv.org
Source
arXiv.org
Place of publication
Ithaca
Country of publication
United States
University/institution
Cornell University Library arXiv.org
e-ISSN
2331-8422
Source type
Working Paper
Language of publication
English
Document type
Working Paper
Publication history
 
 
Online publication date
2024-12-11
Milestone dates
2024-03-12 (Submission v1); 2024-12-09 (Submission v2)
Publication history
 
 
   First posting date
11 Dec 2024
ProQuest document ID
2956943588
Document URL
https://www.proquest.com/working-papers/highway-preferential-attachment-models-geographic/docview/2956943588/se-2?accountid=208611
Full text outside of ProQuest
Copyright
© 2024. This work is published under http://creativecommons.org/licenses/by/4.0/ (the “License”). Notwithstanding the ProQuest Terms and Conditions, you may use this content in accordance with the terms of the License.
Last updated
2025-05-21
Database
2 databases
  • ProQuest One Academic
  • ProQuest One Academic