On Dimensionality of Coordinate-Based Network Distance Mapping

Abstract

In this paper, we investigate the veracity of a basic premise, “that network distance is Euclidean”, assumed in a class of recently proposed techniques that embed Internet hosts in a Euclidean space for the purpose of estimating the delay or “distance” between them. Using the classical scaling method on a number of network distance measurement datasets, we observe “non-Euclidean-ness” in the network distance. We find that this “non-Euclideanness” is caused by the clustering effect of Internet hosts. We also observe that the distance between the nodes in the same cluster is significantly more non-Euclidean than the distance between nodes in different clusters. Our correlation dimension based analysis of intrinsic dimensionality of the datasets reveals that the network distances seem to have a fractional dimension between 2 and 3. We observe that further increasing the dimensionality does not improve the accuracy of the embedding in Euclidean space. Motivated by these results, we propose a new hybrid model for embedding the network nodes using only a 2-dimensional Euclidean coordinate system and small 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.