Non-Metric Coordinates for Predicting Network Proximity

Abstract

Abstract-We consider the problem of determining the "closest", or best Internet host to connect to, from a list of candidate servers. Most existing approaches rely on the use of metric, or more specifically Euclidean coordinates to infer network proximity. This is problematic, given that network distances such as latency are known to violate the triangle inequality. This leads us to consider non-metric coordinate systems. We perform an empirical comparison between the "min-plus" non-metric coordinates and two metric coordinates, namely L-infinity and Euclidean. We observe that, when sufficiently many dimensions are used, min-plus outperforms metric coordinates for predicting Internet latencies.We also consider the prediction of "widest path capacity" between nodes. In this framework, we propose a generalization of min-plus coordinates. These results apply when node coordinates consist in measured network proximity to a random subset of landmark nodes. We perform empirical validation of these results on widest path bandwidth between PlanetLab nodes.We conclude that appropriate non-metric coordinates such as generalized min-plus systems are better suited than metric systems for representing the underlying structure of Internet distances, measured either via latencies or bandwidth.

On Greedy Routing in Degree-Bounded Graphs over d-Dimensional Internet Coordinate Embeddings

“…Key et al [5] further supports this, by showing that coordinate embeddings under L ∞ are comparably accurate to those under L 2 . Like both works show, Internet Coordinate Embeddings achieve higher accuracy for higher dimensions.…”

On the treeness of internet latency and bandwidth

“…Shavitt and Tankel [36] observe that hyperbolic spaces are more suitable than Euclidean space to model Internet latency and propose a system to embed latency into a hyperbolic poincaré disk. In other related work, Key et al [17] explore the idea of embedding latency into a non-metric space that retains symmetry but accommodates triangle inequality violations, and Mao et al [26] embed latency in a non-metric space that supports both asymmetry and triangle inequality violations.…”