1. Sequoia: Supporting Latency-Aware Applications through Prediction Trees Dahlia Malkhi, MSR and Hebrew U Joint work with Ittai Abraham, Mahesh Balakrishnan, Fabian Kuhn, Rama Ramasubramanian, Nir Sonenschein, and Kunal Talwar

2. Introduction  Latency-awareness is critical for internet applications CDNs, P2P file sharing, network monitoring, etc.  Latency-enabled functionality: Closest node discovery Locality-based clustering Detour routing Spanning trees

3. Current State of the Art  Application-specific approaches Closest node [Meridian, Oasis, …] Detour routing [OneHop Source Routing, Detour, Akella et al…] Clustering [SDIMS, …]  General-purpose frameworks Measurement based inference [iPlane]  Requires intrusive, expensive measurements Coordinate-based latency prediction [Vivaldi, PIC, GNP, ICS, Virtual Landmarks, PCoord, NPS, Lighthouse, IDMaps]  Needs substantial work to support applications

4. Goals Internet Topology is not directly known to end-hosts Inter-node Ping latencies are available Model Clustering, Closest Node Discovery… End-Host Pings

5. Big Insight “It's not a big truck. It's a series of tubes.” Ted Stevens, Senator from Alaska

6. Prediction Trees Tree of Virtual Routing Nodes Distance between nodes is path length on the tree Interior: Virtual Routing Nodes Leaves: Physical End-hosts

7. Metric Embedding into Trees  Generally hard  Ultra-metric: MST yields HST representing distances precisely  Tree: MST yields the right tree  Tree-metric: Buneman’s Steiner tree yields the right tree

8. Is the Internet a Tree?  The Four-Point Condition: Given 4 points A,B,C,D: If AC+BD ≥ AD+BC ≥ AB+CD, AC+BC = AD+BC ≥ AB+CD AC+BD = AD+BC ≥ AB+CD

9. Is the Internet a Tree? We can model it as one! Relaxed Four Point Condition: AC+BD=[AD+BC]+2  * min{AB,CD} Internet Latencies are very close to a tree metric Random power-law graph latencies are also very close to a tree metric

10. New Challenge: Embed Relaxed Tree Metrics in Trees  Teriffic experimental evidence  Distance prediction, clustering, finding closest nodes, spanning-trees  (1+O(ε log(n)) ) / (1 – O(ε log(n)) ) Steiner approximation  (1+O(ε log(n)) ) stretch lower bound  (1 + O(ε)) Steiner approximation for metrics generated from relaxed tree metric graphs  (1 + O(ε)) approximation by log(n) Steiner trees

11. Some Open Directions  Close lower/upper gap  Embed random graphs with power-law degrees in trees Relaxed tree-metric condition of such graphs  Embed into distribution on trees  Embed into fixed-size collection of trees Lower bound  Instance-specific Steiner-tree approximation

12. Thanks! Sponsored link: LOCALITY 2007, Satellite workshop at PODC 2007, August, Portland Oregon

13. (Re)constructing the Tree ABC A0.03.05.0 B3.00.04.0 C5.04.00.0 Cx = (AC+BC-AB)/2 Ax = (AB+AC-BC)/2 Bx = (AB+BC-AC)/2

14. Growing the Tree…

16. Towards a Distributed System  Virtual nodes are emulated by ‘surrogate’ physical nodes  Distributed Tree-Building Protocol  Discrete Event Simulator: executed on ping data from PlanetLab, King Datasets

17. Latency Prediction: Mechanism  Distance Labels Path to Root planet0.jaist.ac.jp label = (13063473,15203380,60223214) planetlab1.cs.ubc.ca label= (25690090,15203380,60223214) Path between them = (13063473, 15203380, 25690090) Distance = 19.215 + 2.767 + 18.591 + 20.595 = 61.168 ms

18. Latency Prediction: Performance I PlanetLab, 117 nodes, 1 month

19. Latency Prediction: Performance II King Dataset (Harvard), 1835 nodes

20. Latency Prediction: Multiple Trees  Each node joins x randomly selected trees out of t total trees  Existing theoretical work on modeling a graph metric with a distribution of dominating trees…  To predict latencies between 2 nodes, select all trees both nodes belong to, and pick median T1T2T3 dist(B,C) = median(dist T1 (B,C), dist T2 (B,C))

21. Latency Prediction: Multiple Trees

22. Closest Node Discovery: Mechanism A xz y BCD Problem: Can’t ping inner virtual nodes, only physical leaf nodes Solution: Each virtual node maintains ping-able representatives for each virtual neighbor T Traverse the tree, always picking the neighbor that’s closer to the target More Overhead  More Accuracy Number of representatives per neighbor BD CB Number of parallel queries

23. Closest Node Discovery: Performance I PlanetLab, 117 nodes, 1 month ping data

24. Closest Node Discovery: Performance II King Dataset (Meridian), 2500 nodes Meridian performance on same data: ~1 ms Vivaldi, GNP: ranging from 8 ms to 18 ms (from Wong et al, Sigcomm 05) q = queries, r = reps

25. Clustering PlanetLab Europe

26. Clustering PlanetLab Poland, Germany, Scandinavia

27. Clustering PlanetLab Poland

28. Work in Progress  Explore better tree-building algorithms  Model other properties using these trees Loss rate, bandwidth  Build a robust distributed system: Failure Handling, Tree Balancing

29. Conclusions  Prediction Trees are a promising way of modeling internet latencies Simple yet powerful abstraction  Latency estimation comparable with coordinate schemes  Closest Node Discovery comparable to Meridian  Good locality-based Clustering

30. THANK YOU!

31. King Dataset (harvard)  1835 Nodes

32. Four Point Condition  Relaxed 4PC: d(AC)+d(BC) = [d(AD)+d(BC)] +  * [d(AB)+d(CD)]

33. Prediction Trees Tree of Virtual Routing Nodes End-hosts Interior nodes are virtual ‘steiner’ nodes Leaf nodes are physical end-hosts Estimated Distance is Path Length on the Tree

34. Clustering PlanetLab All European Nodes

35. Clustering PlanetLab German and Scandinavian nodes Hostname ends with “de” OR “fi” OR “no” OR “se”