Brief Announcement: Practical Summation via Gossip

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Brief AnnouncementPractical Summation via Gossip

• Wesley W. Terpstra, Christof Leng, Alejandro P.
  Buchmann
• Databases and Distributed Systems Group
• Technische Universität Darmstadt
• Germany

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Sum calculation in peer-to-peer

• Input every peer has a value
• Output (at least) one peer knows
• Useful in computing many global statistics
• Network size
• Average utilization
• Load balance (standard deviation)
• Churn (rate of peer replacement)
• Size of stored data
• For our system, BubbleStorm, we compute ? degi(p)

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Build on an existing solution

• Approaches can be compared by
• Message rounds (latency)
• Total messages (bandwidth)
• Parameters system size (n), accuracy (?)
• We improve the Push-Sum algorithm for practical
  use

Rounds Messages
Push-Sum (2003, FOCS)
SampleCollide (2006)
Random Tour (2006)
CompSpread (2006)
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Analogy Measuring a lakes volume
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Push-Sum visualized
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Stationary Distribution (Steady State)
Equilibrium edges carry the same water and fish
in both directions peers have
water and fish proportional to degree and clock
Perturbations of equilibrium do not affect
water/fish ratio
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Improvement Big Fish eat smaller fish
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Fish eating in the Network
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Stationary Distribution (Steady State)
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Other improvements

• Round switching
• Once the result is accurate enough, restart
• Provides a running estimate on network statistics
• Compensate for message loss
• Prevent adding two of the most aggressive fish
• Save bandwidth for multiple measurements

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Synchrony

• Kempe et al. prove correctness with synchronous
  model, but conjecture that it works
  asynchronously
• We validate this claim by simulation
• 1 million peers, 5s gossip interval, find network
  size

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Open Problem

• Push-Sum is very vulnerable to attack
• Any peer can completely change the result
• This is largely due to the problem statement
  (sum!)
• Simplistic prevention (bounds) easily defeated
• Introduce too few of the largest fish type ? too
  large
• Switch rounds prematurely ? too small unstable
• What is a useful adversary model for summation?

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Thanks for listening!