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

References

1. Y. Chen, X. Wang, C. Shi, and; et al. (December 2011). (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)
2. 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.
3. 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.
4. Y. Liao, P. Geurts & G. Leduc (2010). "Network Distance Prediction Based on Decentralized Matrix Factorization" (PDF). Proc. of IFIP Networking.
5. Shining Wu; Yang Chen; Xiaoming Fu; Jun Li (2012). (PDF). Proc. of the 20th IEEE/ACM International Workshop on Quality of Service (IWQoS'12). Archived from the original (PDF) on 2013-12-03.