On suitability of Euclidean embedding of internet hosts

Sanghwan Lee, Zhi Li Zhang, Sambit Sahu, Debanjan Saha

Research output: Chapter in Book/Report/Conference proceedingConference contribution

38 Scopus citations

Abstract

In this paper, we investigate the suitability of embedding Internet hosts into a Euclidean space given their pairwise distances (as measured by round-trip time). Using the classical scaling and matrix perturbation theories, we first, establish the (sum of the) magnitude of negative eigenvalues of the (doubly-centered, squared) distance matrix as a measure of suitability of Euclidean embedding. We then show that the distance matrix among Internet hosts contains negative eigenvalues of large magnitude, implying that embedding the Internet hosts in a Euclidean space would incur relatively large errors. Motivated by earlier studies, we demonstrate that the inaccuracy of Euclidean embedding is caused by a large degree of triangle inequality violation (TIV) in the Internet distances, which leads to negative eigenvalues of large magnitude. Moreover, we show that the TIVs are likely to occur locally, hence, the distances among these close-by hosts cannot be estimated accurately using a global Euclidean embedding, in addition, increasing the dimension of embedding does not reduce the embedding errors. Bused on these insights, we propose a new hybrid model for embedding the network nodes using only a 2-dimensional Euclidean coordinate system and small error adjustment terms. We show that the accuracy of the proposed embedding technique is as good as, if not better, than that of a 7-dimensional Euclidean embedding.

Original languageEnglish (US)
Title of host publicationSIGMETRICS 2006/Performance 2006 - Joint International Conference on Measurement and Modeling of Computer Systems, Proceedings
Pages157-168
Number of pages12
Edition1
DOIs
StatePublished - Jun 2006
EventSIGMETRICS 2006/Performance 2006 - Joint International Conference on Measurement and Modeling of Computer Systems - Saint Malo, France
Duration: Jun 26 2006Jun 30 2006

Publication series

NamePerformance Evaluation Review
Number1
Volume34
ISSN (Print)0163-5999
ISSN (Electronic)0163-5999

Other

OtherSIGMETRICS 2006/Performance 2006 - Joint International Conference on Measurement and Modeling of Computer Systems
Country/TerritoryFrance
CitySaint Malo
Period6/26/066/30/06

Keywords

  • Euclidean embedding
  • Suitability
  • Triangle inequality

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