Phoenix network coordinates explained

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

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

N internet nodes, the N x N internet distance matrix D can be factorized into two smaller matrices. D ≈ XY ^{T} where X and Y are N x 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

Notes and References

1. Y. Chen, X. Wang, C. Shi, and . Phoenix: a weight-based network coordinate system using matrix factorization . December 2011 . 8 . 4 . 334–347 . . 10.1109/tnsm.2011.110911.100079 . etal . dead . https://web.archive.org/web/20131202223236/http://www.cs.duke.edu/~ychen/papers/Phoenix_TNSM.pdf . 2013-12-02. 10.1.1.300.2851 . 8079061 .
2. B. Donnet . B. Gueye . M.A. Kaafar . A Survey on Network Coordinates Systems, Design, and Security . IEEE Communications Surveys & Tutorials . 12 . 4 . 488–503 . 2010 . 10.1109/SURV.2010.032810.00007. 10.1.1.217.5675 . 16908400 .
3. Yun Mao, Lawrence Saul . Jonathan M. Smith . amp . IDES: An Internet Distance Estimation Service for Large Networks . . December 2006 . 24 . 12 . 2273 - 2284 . 10.1109/JSAC.2006.884026. 10.1.1.136.3837 . 12931155 .
4. Y. Liao, P. Geurts . G. Leduc . amp . 2010 . Network Distance Prediction Based on Decentralized Matrix Factorization . Proc. of IFIP Networking.
5. Shining Wu . Yang Chen . Xiaoming Fu . Jun Li . 2012 . NCShield: Securing Decentralized, Matrix Factorization-Based Network Coordinate Systems . https://web.archive.org/web/20131203002137/http://www.cs.duke.edu/~ychen/papers/NCShield_IWQoS12.pdf . dead . 2013-12-03 . Proc. of the 20th IEEE/ACM International Workshop on Quality of Service (IWQoS'12) .