On the Internet delay space dimensionality

Bruno Abrahao, Robert Kleinberg

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


We investigate the dimensionality properties of the Internet delay space, i.e., the matrix of measured round-trip latencies between Internet hosts. Previous work on network coordinates has indicated that this matrix can be embedded, with reasonably low distortion, into a 4- to 9-dimensional Euclidean space. The application of Principal Component Analysis (PCA) reveals the same dimensionality values. Our work addresses the question: to what extent is the dimensionality an intrinsic property of the delay space, defined without reference to a host metric such as Euclidean space? Is the intrinsic dimensionality of the Internet delay space approximately equal to the dimension determined using embedding techniques or PCA? If not, what explains the discrepancy? What properties of the network contribute to its overall dimensionality? Using datasets obtained via the King [14] method, we study different measures of dimensionality to establish the following conclusions. First, based on its power-law behavior, the structure of the delay space can be better characterized by fractal measures. Second, the intrinsic dimension is significantly smaller than the value predicted by the previous studies; in fact by our measures it is less than 2. Third, we demonstrate a particular way in which the AS topology is reflected in the delay space; subnetworks composed of hosts which share an upstream Tier-1 autonomous system in common possess lower dimensionality than the combined delay space. Finally, we observe that fractal measures, due to their sensitivity to non-linear structures, display higher precision for measuring the influence of subtle features of the delay space geometry.

Original languageEnglish (US)
Title of host publicationIMC'08
Subtitle of host publicationProceedings of the 2008 ACM SIGCOMM Internet Measurement Conference
Number of pages12
StatePublished - 2008
EventInternet Measurement Conference 2008, IMC'08 - Vouliagmeni, Greece
Duration: Oct 20 2008Oct 22 2008

Publication series

NameProceedings of the ACM SIGCOMM Internet Measurement Conference, IMC


ConferenceInternet Measurement Conference 2008, IMC'08


  • Delay space
  • Dimensionality
  • Internet structure
  • Network embedding

ASJC Scopus subject areas

  • Software
  • Computer Networks and Communications


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