Phoenix: A Weight-Based Network Coordinate System Using Matrix Factorization Yang Chen Department of Computer Science Duke University

Outline Background System Design Evaluation Perspective Future Work 2

BACKGROUND 3

Internet Distance Round-trip propagation / transmission delay between two Internet nodes What? Strong indicator of network proximity Relatively stable Why? Measurement tool “Ping” is with major operating systems How? 4 50ms AliceBob

Use Cases Knowledge of Internet distance is useful for… –P2P content delivery (file sharing/streaming) –Online/mobile games –Overlay routing –Server selection in P2P/Cloud –Network monitoring 5

Scalability Huge number of end-to-end paths in large scale systems SLOW and COSTLY when the system becomes large! 6 N nodes measurements

Network Coordinate (NC) Systems 7 (5, 10, 2) (-3, 4, -2) Distance Function 22ms Scalable measurement: N 2  NK (K << N) Every node is assigned with coordinates Distance function: compute the distance between two nodes without explicit measurement Alice Bob [Ng et al, INFOCOM’02]

Deployments 8 They are all using Network Coordinate Systems! They are all using Network Coordinate Systems!

Basic models Euclidean Distance-based NC (ENC) –Modeling the Internet as a Euclidean space –Systems: Vivaldi [Dabek et al., SIGCOMM’04], GNP [Ng et al, INFOCOM’02], NPS [Ng et al., USENIX ATC’04], PIC [Costa et al., ICDCS’04] … Matrix Factorization-based NC (MFNC) –Factorizing an Internet distance matrix as the product of two smaller matrices –Systems: IDES [Mao et al., JSAC’06], Phoenix, … 9

Modeling the Internet as a Euclidean space In a d-dimensional Euclidean space, each node will be mapped to a position Compute distances based on coordinates using Euclidean distance 10 d=3

Triangle Inequality Violation Czech Republic Slovakia Hungary 5.6 ms 3.6 ms 29.9 ms A Triangle Inequality Violation (TIV) example in GEANT network 29.9 > Lots of TIVs in the Internet due sub-optimal routing!! Lots of TIVs in the Internet due sub-optimal routing!! Predicted distances in Euclidean space must satisfy triangle inequality [Zheng et al, PAM’05]

Correlation in Internet Distance Matrices DukeUNCYaleAachenOxfordTorontoTHUNUS Duke UNC Internet paths with nearby end nodes are often overlap!! Internet paths with nearby end nodes are often overlap!! Rows in different Internet distance matrices are large correlated (low effective rank) [Tang et al, IMC’03], [Lim et al, ToN’05], [Liao et al, CoNEXT’11] Distance measurement using PlanetLab nodes

Factorization of an Internet Distance Matrix 13 N rows N columns d columns [Mao et al., JSAC’06]

Matrix Factorization-Based NC Each node i has an outgoing vector X i and an incoming vector Y i Distance function is the dot product. 14 N rows N columns d columns No triangle inequality constrain in this model!

SYSTEM DESIGN 15

Goals Substantial improvement in prediction accuracy Decentralized and scalable Robust to dynamic Internet 16

Workflow of Phoenix System Initialization Peer Discovery Scalable Measurement Coordinates Calculation 17 System Initialization Peer Discovery Scalable Measurement Coordinates Calculation

System Initialization Early nodes (N<K): Full-mesh measurement Compute coordinates of early nodes by minimizing the overall discrepancy between predicted distances and measured distances 18 Measured Distance Predicted Distance (X 1,Y 1 ) (X 2,Y 2 ) (X 3,Y 3 ) (X 4,Y 4 ) Nonnegative matrix factorization: [D. D. Lee and H. S. Seung, Nature, 401(6755):788–791, 1999.]

Dynamic Peer Discovery 19 Tracker H2H2 H3H3 H5H5 H3H3 H4H4 H6H6 H2H2 H3H3 H4H4 H5H5 H6H6 H1H1 H3H3 H4H4 H5H5 H6H6 Gossip among nodes N>K, all nodes become ordinary nodes

Reference Node Selection 20 Every new node randomly selects K existing nodes as reference nodes

Measurement and Bootstrap Coordinates Calculation 21 Measured Distance Predicted Distance Node H new computes its own coordinates by minimizing the overall discrepancy between predicted distances and measured distances (Non-negative least squares) (X 1,Y 1 ) (X K,Y K ) (X 2,Y 2 ) (X new,Y new )

Accuracy of Reference Coordinates 22 (X A,Y A ) Distance between Node A and every other node Node A

Accuracy of Reference Coordinates (cont.) 23 Distance between Node B and every other node (X B,Y B ) Misleading the nodes referring to Node B!! Node B

Referring to Inaccurate Coordinates 24 (X 1,Y 1 ) (X K,Y K ) (X 2,Y 2 ) (X new,Y new ) Error Propagation: H new may mislead nodes refer to it Minimize the impact of R K Give preference to accurate reference coordinates Give preference to accurate reference coordinates

Heuristic Weight Assignment 25 Bootstrap Coordinates Distance between H new and every reference node Enhanced Coordinates Updating coordinates regularly

EVALUATION 26

Evaluation Setup Data sets –PL: 169 PlanetLab nodes –King: 1740 Internet DNS servers Metric –Relative Error (RE) 27

Evaluation: Relative Error th Percentile Relative Error PhoenixPhoenix (Simple) VivaldiIDES

Evaluation (cont.) Other findings through evaluation –Robust to node churn –Fast convergence –Robust to measurement anomalies –Robust to distance variation 29

FUTURE WORK 30

Perspective Topics NC systems in mobile-centric environment –Access latency, host mobility, host churn Scalable Prediction of other important network parameters –Available bandwidth, shortest-path distance in social graph 31

Software NCSim –Simulator of Decentralized Network Coordinate Algorithms – Phoenix –Original Phoenix simulator in IEEE TNSM paper – M_2011.ziphttp:// M_2011.zip 32