Phoenix network coordinates

Phoenix is a decentralized network coordinate system based on the matrix factorization model.^[1]

Weighted-based NC calculation in Phoenix

Background

• Network coordinate (NC) systems^[2] are an efficient mechanism for internet distance (round-trip latency) prediction with scalable measurements. For a network with N hosts, by performing O(N) measurements, all N*N distances can be predicted.
• Use cases: Vuze BitTorrent, application layer multicast, PeerWise overlay, multi-player online gaming.
• Triangle inequality violation (TIV) is widely exist on the Internet due to the current sub-optimal internet routing.

Model

• Most of the prior NC systems use the Euclidean distance model, i.e. embed N hosts into a d-dimensional Euclidean space R^d. Due to the wide existence of TIVs on the internet, the prediction accuracy of such systems is limited. Phoenix uses a matrix factorization (MF) model, which does not have the constraint of TIV.
• The linear dependence among the rows motivates the factorization of internet distance matrix, i.e. for a system with ${\displaystyle N}$ internet nodes, the ${\displaystyle N\times N}$ internet distance matrix D can be factorized into two smaller matrices. ${\displaystyle D\approx XY^{T}}$ where ${\displaystyle X}$ and ${\displaystyle Y}$ are ${\displaystyle N\times d}$ matrices (d << N). This matrix factorization is essentially a problem of linear dimensionality reduction and Phoenix tries to solve it in a distributed way.

Design choices in Phoenix

• Different from the existing MF based NC systems such as IDES^[3] and DMF,^[4] 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.
• For node discovery, Phoenix uses a distributed scheme, so-called peer exchange (PEX), which is used in BitTorrent (protocol). The usage of PEX reduces the load of the tracker, while still ensuring the prediction accuracy under node churn.
• Similar to DMF, for avoiding the potential drift of the NCs, Regularization (mathematics) is introduced in NC calculation.
• NCShield^[5] is a decentralized, goosip-based trust and reputation system to secure Phoenix and other matrix factorization-based NC systems.

See also

• Vivaldi coordinates
• Pharos network coordinates
• Global network positioning
• An open source simulator of Phoenix