Respondent-driven Sampling for Characterizing Unstructured Overlays

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Respondent-driven Sampling for Characterizing
Unstructured Overlays
A. H. Rasti University of Oregon
M. Torkjazi University of Oregon
R. Rejaie University of Oregon

N. Duffield ATT Labs - Research
W. Willinger ATT Labs - Research

D. Stutzbach Stutzbach Enterprises
Graciously Presented By Shubho Sen ATT Labs
- Research
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Motivation

• P2P systems are very popular in practice.
• Millions of simultaneous users.
• A significant fraction of Internet traffic
• Measurement studies aid understanding existing
  systems and user behavior.
• Capturing an accurate global snapshot is often
  infeasible.
• P2P systems are distributed, large, and rapidly
  changing.
• P2P crawlers are likely to capture incomplete or
  distorted snapshots
• Sampling is a natural approach, and has been used
  implicitly in most earlier P2P measurement
  studies.
• How can we collect representative samples?

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The Graph Sampling Problem

• We focus on sampling peer properties, such as
  number of neighbors (degree), access link
  bandwidth, session time, files
• Sampling peer properties has two steps
• Discovering and selecting peers (or samples)
• Measuring the desired properties of selected
  peers
• Selecting peers uniformly at random is hard
  there are two sources of bias StutzbachIMC06
• Topological high-degree peers are more likely to
  be selected
• Temporal short-lived peers are more likely to
  be selected
• Random walks are a promising approach to sampling
• The resulting bias is precisely known
• Samples can be collected in parallel by multiple
  walkers

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Sampling Using Random Walk

• Random walks can be described with a transition
  matrix P(x,y)
• P(x,y) probability of moving from x to y
• Pr(x,y) probability of moving from x to y after
  r moves
• Random walks converge to a stationary
  distribution
• Problem we need a uniform distribution

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Metropolized Random Walk (MRW)

• The Metropolis-Hastings method modifies the
  transition matrix to yield the desired uniform
  distribution StutzbachIMC06
• MRW method
• Select a neighbor y of x uniformly at random
• Transition to y with probability min(
  deg(x)/deg(y) , 1)
• Otherwise, self-loop to x.
• Results in uniform stationary dist. ?(x) 1/V
• MRW compensates for bias as samples are collected

y
x
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This paper

• Presents a new graph sampling technique,
  Respondent-Driven Sampling (RDS)
• Compares the performance of RDS and MRW sampling
  techniques using simulations experiments

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Respondent-driven Sampling

• A development of Snowball Sampling Salganik04
• Commonly used in social sciences to sample
  hidden populations, e.g. HIV individuals
• Social relationships (references) are used by
  sampler to diffuse into hidden populations
• Each person introduces n other persons
• Similar to random walk (n 1)
• We adopt the RDS technique from social sciences
  for sampling P2P networks

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RDS Formulation

• Goal Estimate the distribution of node property
  X
• Perform regular random walk, collect values of
  property X and node degree (deg(v)) at each
  visited node
• Deal with the bias during the post-processing as
  follows
• Divide possible values for X into several ranges
  R1, . . . ,Rm
• Partition nodes with the X value within the same
  range V1, . . . ,Vm
• Using Hansen-Hurwitz estimator to compensate for
  the bias, the proportion of all nodes in group i
  is estimated as follows

• Ti visited samples in group i
• T all visited samples

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Evaluation Overview

• Performance metric
• Consider only peer properties that may interact
  with the walk
• 1) Peer Degree, 2) Peer Uptime, 3) Peer RTT
• Compare the dist. of the these peer properties
  from samples and ground truth using
  Kolmogorov-Smirnov (KS) statistics
• Evaluation Methodology
• Evaluation over static graphs
• Effect of graph structure
• Evaluation over dynamic graphs (session level
  simulation)
• Benefits of parallel Sampling (see the paper)
• Effect of 1) churn, 2) peer discovery, 3)
  target peer degree
• Experiments over Gnutella network

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Evaluation Static Graphs

• Using graphs with different degree distribution
  clustering characteristics
• Random graphs (ER) Erdos-Renyi
• Small-world graphs (SW) Watts and Strogatz
• Scale-free graphs (BA) Barabasi and Albert
• Hierarchical Scale-Free graphs (HSF) Barabasi
  02
• Power-law degree distribution
• Node clustering is inversely proportional to node
  degree
• Gnutella graphs (GA) Snapshots of Gnutella
  Ultrapeer topology

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Hierarchical Scale-Free (HSF)
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Static Graphs

• Accuracy of both techniques is improved with the
  number of samples in most cases
• The rate of improvement in accuracy is much lower
  over HSF especially for MRW
• Walkers are likely to get trapped within clusters
  in HSF graphs
• Leaving a cluster requires visiting high degree
  nodes but MRW is less likely to visit these nodes
• Rewiring a small fraction of randomly selected
  edges in HSF significantly improves accuracy for
  both techniques
• RDS is less sensitive to graph clustering than MRW

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Dynamic Graphs

• Churn is a primary limiting factor for accuracy
• Session len.gt 5m ? Very good sampling accuracy
• Churn model has little effect
• Similar impact on other peer properties (see the
  paper)
• Sampling error is small once nodes have
  sufficient connectivity (gt 5)
• Lower accuracy for smaller degree is due to graph
  partitioning
• Partitioned nodes in History mech. reduce the
  accuracy of sampling

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Experiment Gnutella

• Run crawler, 1000 RDS 1000 MRW walkers in
  parallel
• 500 steps per walker
• Use captured snapshots by crawler as a rough
  reference
• Show min, max, avg KS over 6 experiments
• Focus only on degree dist
• The degree dist from samples crawls are very
  similar (KS0.03)
• The accuracy is an order of magnitude lower than
  dynamic sim due to inaccurate reference.
• Both sampling technique achieve similar accuracy

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Conclusions Future Work

• RDS always performs as good or better than MRW
• High level of graph clustering can significantly
  degrade the accuracy of both RDS and MRW
• RDS is less sensitive than MRW to graph
  clustering
• There is sweet spot for the number of parallel
  samplers.
• Poor connectivity high dynamics adversely
  affect the accuracy of both techniques.
• Future Work
• RDS is a promising approach for sampling user
  properties in Online Social Networks
• Sampling over directed graphs raises new
  challenges.

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• Thank You !

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Different Grpah Structures
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Dynamic Simulation Setting

• Simulation environment
• Session-time distributions Weibull,
  Exponential, Pareto
• Poisson arrival process
• Peer discovery Oracle, FIFO, HeartBeat, History
• Target population 100000
• Min. Degree 3-30
• Sampling Parameters
• Node degree (DEG)
• Node query latency (RTT)
• Session length/uptime (UT)

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Evaluation Static Graphs Conclusion

• Combination of highly skewed degree distribution
  and highly skewed clustering traps samplers
• RDS samplers get out of the clusters quickly
• MRW samplers get stuck in low-degree clusters
• Shuffling provides short-cuts out of clusters
• HSF can be a model for some natural and social
  networks

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Dynamic Graphs Effect of Parallelism

• Too much parallelism does not improve performance
• Too long random walks have negative effect
• Sweet spot exists