### Abstract

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 language | English (US) |
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Title of host publication | IMC'08 |

Subtitle of host publication | Proceedings of the 2008 ACM SIGCOMM Internet Measurement Conference |

Pages | 157-168 |

Number of pages | 12 |

DOIs | |

State | Published - Dec 1 2008 |

Event | Internet Measurement Conference 2008, IMC'08 - Vouliagmeni, Greece Duration: Oct 20 2008 → Oct 22 2008 |

### Publication series

Name | Proceedings of the ACM SIGCOMM Internet Measurement Conference, IMC |
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### Conference

Conference | Internet Measurement Conference 2008, IMC'08 |
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Country | Greece |

City | Vouliagmeni |

Period | 10/20/08 → 10/22/08 |

### Fingerprint

### Keywords

- Delay space
- Dimensionality
- Internet structure
- Network embedding

### ASJC Scopus subject areas

- Software
- Computer Networks and Communications

### Cite this

*IMC'08: Proceedings of the 2008 ACM SIGCOMM Internet Measurement Conference*(pp. 157-168). (Proceedings of the ACM SIGCOMM Internet Measurement Conference, IMC). https://doi.org/10.1145/1452520.1452541

**On the Internet delay space dimensionality.** / Abrahao, Bruno; Kleinberg, Robert.

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

*IMC'08: Proceedings of the 2008 ACM SIGCOMM Internet Measurement Conference.*Proceedings of the ACM SIGCOMM Internet Measurement Conference, IMC, pp. 157-168, Internet Measurement Conference 2008, IMC'08, Vouliagmeni, Greece, 10/20/08. https://doi.org/10.1145/1452520.1452541

}

TY - GEN

T1 - On the Internet delay space dimensionality

AU - Abrahao, Bruno

AU - Kleinberg, Robert

PY - 2008/12/1

Y1 - 2008/12/1

N2 - 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.

AB - 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.

KW - Delay space

KW - Dimensionality

KW - Internet structure

KW - Network embedding

UR - http://www.scopus.com/inward/record.url?scp=63049112027&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=63049112027&partnerID=8YFLogxK

U2 - 10.1145/1452520.1452541

DO - 10.1145/1452520.1452541

M3 - Conference contribution

AN - SCOPUS:63049112027

SN - 9781605583341

T3 - Proceedings of the ACM SIGCOMM Internet Measurement Conference, IMC

SP - 157

EP - 168

BT - IMC'08

ER -