On suitability of euclidean embedding for host-based network coordinate systems

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

Research output: Contribution to journalArticlepeer-review

25 Scopus citations


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. Based on these insights, we propose a new hybrid model for embedding the network nodes using only a two-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 seven-dimensional Euclidean embedding.

Original languageEnglish (US)
Article number5235089
Pages (from-to)27-40
Number of pages14
JournalIEEE/ACM Transactions on Networking
Issue number1
StatePublished - Feb 1 2010


  • Euclidean embedding
  • Suitability
  • Triangle inequality

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