Sequoia: Supporting Latency-Aware Applications through Prediction Trees

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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

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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

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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

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Goals
Internet Topology is not directly known to
end-hosts
Inter-node Ping latencies are available
End-Host Pings
Model
Clustering, Closest Node Discovery
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Big Insight
It's not a big truck. It's a series of tubes.
Ted Stevens, Senator from Alaska
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Prediction Trees
Tree of Virtual Routing Nodes
Interior Virtual Routing Nodes Leaves Physical
End-hosts
Distance between nodes is path length on the tree
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Metric Embedding into Trees

• Generally hard
• Ultra-metric MST yields HST representing
  distances precisely
• Tree MST yields the right tree
• Tree-metric Bunemans Steiner tree yields the
  right tree

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Is the Internet a Tree?

• The Four-Point Condition
• Given 4 points A,B,C,D
• If ACBD ADBC ABCD,
• ACBC ADBC ABCD

ACBD ADBC
ABCD
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Is the Internet a Tree? We can model it as one!
Relaxed Four Point Condition ACBDADBC2?
minAB,CD
Internet Latencies are very close to a tree metric
Random power-law graph latencies are also very
close to a tree metric
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New Challenge Embed Relaxed Tree Metrics in
Trees

• Teriffic experimental evidence
• Distance prediction, clustering, finding closest
  nodes, spanning-trees
• (1O(e log(n)) ) / (1 O(e log(n)) ) Steiner
  approximation
• (1O(e log(n)) ) stretch lower bound
• (1 O(e)) Steiner approximation for metrics
  generated from relaxed tree metric graphs
• (1 O(e)) approximation by log(n) Steiner trees

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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

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Thanks!
Sponsored link LOCALITY 2007, Satellite
workshop at PODC 2007, August, Portland Oregon
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(Re)constructing the Tree
A B C
A 0.0 3.0 5.0
B 3.0 0.0 4.0
C 5.0 4.0 0.0
Cx (ACBC-AB)/2 Ax (ABAC-BC)/2 Bx
(ABBC-AC)/2
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Growing the Tree
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Growing the Tree
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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

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Latency Prediction Mechanism

• Distance Labels
• Path to Root

planet0.jaist.ac.jp label (13063473,15203380,6
0223214) 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
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Latency Prediction Performance I
PlanetLab, 117 nodes, 1 month
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Latency Prediction Performance II
King Dataset (Harvard), 1835 nodes
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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

T1
T2
T3
dist(B,C) median(distT1(B,C), distT2(B,C))
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Latency Prediction Multiple Trees
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Closest Node Discovery Mechanism
y
Traverse the tree, always picking the neighbor
thats closer to the target
B
D
C
B
x
z
Problem Cant ping inner virtual nodes, only
physical leaf nodes Solution Each virtual node
maintains ping-able representatives for each
virtual neighbor
A
B
C
D
T

• More Overhead ? More Accuracy
• Number of representatives per neighbor

• Number of parallel queries

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Closest Node Discovery Performance I
PlanetLab, 117 nodes, 1 month ping data
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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
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Clustering PlanetLab
Europe
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Clustering PlanetLab
Poland, Germany, Scandinavia
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Clustering PlanetLab
Poland
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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

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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

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THANK YOU!
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King Dataset (harvard)

• 1835 Nodes

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Four Point Condition

• Relaxed 4PC
• d(AC)d(BC) d(AD)d(BC) ? d(AB)d(CD)

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Prediction Trees

• Interior nodes are virtual steiner nodes
• Leaf nodes are physical end-hosts
• Estimated Distance is Path Length on the Tree

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Clustering PlanetLab
All European Nodes
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Clustering PlanetLab
German and Scandinavian nodes Hostname ends with
de OR fi OR no OR se