# Phoenix network coordinates

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**Phoenix** is a decentralized [network coordinate system](/source/Network_Coordinate_System) based on the [matrix factorization](/source/Matrix_factorization) model.[1]

## Background

- Network coordinate (NC) systems[2] are an efficient mechanism for internet distance ([round-trip latency](/source/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](/source/Vuze) BitTorrent, application layer multicast, PeerWise overlay, multi-player online gaming.
- [Triangle inequality](/source/Triangle_inequality) violations (TIVs) widely exist on the Internet due to sub-optimal [internet routing](/source/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](/source/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](/source/Matrix_factorization) (MF) model, which does not have the constraint of TIV.
- The [linear dependence](/source/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.

## 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](/source/Peer_exchange) (PEX), which is used in [BitTorrent (protocol)](/source/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)](/source/Regularization_(mathematics)) is introduced in NC calculation.
- NCShield[5] is a decentralized, goosip-based trust and [reputation system](/source/Reputation_system) to secure Phoenix and other matrix factorization-based NC systems.

## See also

- [Vivaldi coordinates](/source/Vivaldi_coordinates)
- [Pharos network coordinates](/source/Pharos_network_coordinates)
- [Global network positioning](/source/Global_network_positioning)
- [An open source simulator of Phoenix](http://www.cs.duke.edu/~ychen/Project_Phoenix.html)

## References

1. Y. Chen, X. Wang, C. Shi, and et al. (December 2011). ["Phoenix: a weight-based network coordinate system using matrix factorization"](https://web.archive.org/web/20131202223236/http://www.cs.duke.edu/~ychen/papers/Phoenix_TNSM.pdf). *[IEEE Transactions on Network and Service Management](/source/IEEE_Transactions_on_Network_and_Service_Management)*. **8** (4): 334–347. [CiteSeerX 10.1.1.300.2851](https://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.300.2851). [doi:10.1109/tnsm.2011.110911.100079](https://doi.org/10.1109/tnsm.2011.110911.100079). [S2CID 8079061](https://api.semanticscholar.org/CorpusID:8079061). Archived from [the original](http://www.cs.duke.edu/~ychen/papers/Phoenix_TNSM.pdf) on 2013-12-02.

1. B. Donnet; B. Gueye; M.A. Kaafar (2010). ["A Survey on Network Coordinates Systems, Design, and Security"](http://planete.inrialpes.fr/people/kaafar/survey-normal.pdf). *IEEE Communications Surveys & Tutorials*. **12** (4): 488–503. [CiteSeerX 10.1.1.217.5675](https://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.217.5675). [doi:10.1109/SURV.2010.032810.00007](https://doi.org/10.1109/SURV.2010.032810.00007). [S2CID 16908400](https://api.semanticscholar.org/CorpusID:16908400)

1. Yun Mao, Lawrence Saul & Jonathan M. Smith (December 2006). ["IDES: An Internet Distance Estimation Service for Large Networks"](http://www2.research.att.com/~maoy/pub/ides_jsac06.pdf). *[IEEE Journal on Selected Areas in Communications](/source/IEEE_Journal_on_Selected_Areas_in_Communications)*. **24** (12): 2273–2284. [CiteSeerX 10.1.1.136.3837](https://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.136.3837). [doi:10.1109/JSAC.2006.884026](https://doi.org/10.1109/JSAC.2006.884026). [S2CID 12931155](https://api.semanticscholar.org/CorpusID:12931155)

1. Y. Liao, P. Geurts & G. Leduc (2010). [*Network Distance Prediction Based on Decentralized Matrix Factorization*](http://www.run.montefiore.ulg.ac.be/~liao/papers/networking2010_liao.pdf). Proc. of IFIP Networking.

1. 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). Proc. of the 20th IEEE/ACM International Workshop on Quality of Service (IWQoS'12). Archived from [the original](http://www.cs.duke.edu/~ychen/papers/NCShield_IWQoS12.pdf) on 2013-12-03.

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Adapted from the Wikipedia article [Phoenix network coordinates](https://en.wikipedia.org/wiki/Phoenix_network_coordinates) by Wikipedia contributors ([contributor history](https://en.wikipedia.org/wiki/Phoenix_network_coordinates?action=history)). Available under [Creative Commons Attribution-ShareAlike 4.0 International](https://creativecommons.org/licenses/by-sa/4.0/). Changes may have been made.