Network coordinate (NC) systems provide a lightweight and scalable way for predicting the distances, i.e., round-trip latencies among Internet hosts. Most existing NC systems embed hosts into a low dimensional Euclidean space. Unfortunately, the persistent occurrence of Triangle Inequality Violation (TIV) on the Internet largely limits the distance prediction accuracy of those NC systems. Some alternative systems aim at handling the persistent TIV, however, they only achieve comparable prediction accuracy with Euclidean distance based NC systems. In this paper, we propose an NC system, so-called Phoenix, which is based on the matrix factorization model. Phoenix introduces a weight to each reference NC and trusts the NCs with higher weight values more than the others. The weight-based mechanism can substantially reduce the impact of the error propagation. Using the representative aggregate data sets and the newly measured dynamic data set collected from the Internet, our simulations show that Phoenix achieves significantly higher prediction accuracy than other NC systems. We also show that Phoenix quickly converges to steady state, performs well under host churn, handles the drift of the NCs successfully by using regularization, and is robust against measurement anomalies. Phoenix achieves a scalable yet accurate end-to-end distances monitoring. In addition, we study how well an NC system can characterize the TIV property on the Internet by introducing two new quantitative metrics, so-called RERPL and AERPL. We show that Phoenix is able to characterize TIV better than other existing NC systems.

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