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

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 (doublycentered, 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 closeby hosts cannot be estimated accurately using a...

• Type: Journal
• Year: 2010
• Where: TON
• Authors: Sanghwan Lee, Zhi-Li Zhang, Sambit Sahu, Debanjan Saha
• Keywords: Embedding, Euclidean Space, Negative Eigenvalues, TON 2010