Phoenix network coordinates

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.

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 $N\times N$ internet distance matrix D can be factorized into two smaller matrices. $D\approx XY^{T}$ where $X$ and $Y$ are $N\times d$ matrices (d << N). This matrix factorization is essentially a problem of linear dimensionality reduction and Phoenix tries to solve it in a distributed way.

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.

^ Y. Chen, X. Wang, C. Shi, and; et al. (December 2011). "Phoenix: a weight-based network coordinate system using matrix factorization" (PDF). IEEE Transactions on Network and Service Management. 8 (4): 334–347. CiteSeerX 10.1.1.300.2851. doi:10.1109/tnsm.2011.110911.100079. S2CID 8079061. Archived from the original (PDF) on 2013-12-02.{{cite journal}}: CS1 maint: multiple names: authors list (link)
^ B. Donnet; B. Gueye; M.A. Kaafar (2010). "A Survey on Network Coordinates Systems, Design, and Security" (PDF). IEEE Communications Surveys & Tutorials. 12 (4): 488–503. CiteSeerX 10.1.1.217.5675. doi:10.1109/SURV.2010.032810.00007. S2CID 16908400.
^ Yun Mao, Lawrence Saul & Jonathan M. Smith (December 2006). "IDES: An Internet Distance Estimation Service for Large Networks" (PDF). IEEE Journal on Selected Areas in Communications. 24 (12): 2273–2284. CiteSeerX 10.1.1.136.3837. doi:10.1109/JSAC.2006.884026. S2CID 12931155.
^ Y. Liao, P. Geurts & G. Leduc (2010). "Network Distance Prediction Based on Decentralized Matrix Factorization" (PDF). Proc. of IFIP Networking.
^ Shining Wu; Yang Chen; Xiaoming Fu; Jun Li (2012). "NCShield: Securing Decentralized, Matrix Factorization-Based Network Coordinate Systems" (PDF). Proc. of the 20th IEEE/ACM International Workshop on Quality of Service (IWQoS'12). Archived from the original (PDF) on 2013-12-03.