Viceroy: A scalable and dynamic emulation of the Butterfly

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Viceroy A scalable and dynamic emulation of the
Butterfly

• Presented in CS294-4
• by
• Sailesh Krishnamurthy
• Sep 22, 2003

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Viceroy

• Goals An overlay routing network with
• Logarithmic path lengths
• Constant join/leave cost
• Balanced congestion ( log(n)/n)
• Keys, servers mapped to unit ring 0,1)
• In Chord each node has all log(n) links
• In Viceroy
• Each node has one log(n) link
• A link to 1/2k distance points to a node with a
  link to 1/2(k1) distance

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Viceroy Topology

• Each node has a level between 1..log(n)
• A level-k node has
• right child A long-range link to distance 1/2k
  (approx.), to a level-(k1) node
• left child A local link to level-(k1) node
• Level ring links (pred,succ of the same level)
• up A local link to level-(k-1) node
• Ring links (pred,succ on the ring)

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Viceroy Topology
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Distributed level selection

• Select Level (s)
• Let n0 1/d(s,succ(s))
• Select a level among 1 log(n0) uniformly at
  random
• Sanity
• When n servers present, then w.h.p. every server
  estimates log(n/2logn)ltlog(n0)lt3logn
• Any level l ltlog(n/2logn) is sane

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Lookup target in Viceroy

• Three phases
• Proceed to root up-links to a level-1 node
• for level k 1..log(n)
• If distance lt 1/2k use down-left (short link)
• If distance gt 1/2k use down-right (long link)
• If reqd down link doesnt exist (or if you
  overshoot target) break to next phase
• Traverse the ring (pred/succ links, whichever is
  closer)

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Analysis

• Constant out-degree
• Expected constant in-degree
• log(n ) w.h.p.
• O(log(n )) lookup steps w.h.p
• log(n ) to level-1 node
• log(n ) for binary search
• log(n ) for final local search
• Congestion
• Expected log(n )/n lookup load
• O(log2(n )/n) w.h.p.

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Improving Lookup

• Simple lookup - third phase may be too long
• May be log2n links to traverse -(
• Fancy lookup
• Use a combination of global and level rings to
  get a dilation of log(n) w.h.p.
• Greedy approach - use the level links if you are
  still too far away from the target.

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What happens on node leave?

• Problem we have constant out-degree, but even
  with a sparse network we could have log(n)
  in-degree on average
• Solution buckets - extra background process
• Idea improve identity/level-selection so that we
  have constant number of nodes in each stretch of
  (log(n)/n) nodes
• Maintain n buckets of log(n) contiguous
  non-overlapping nodes.

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Bucket properties

• Size always ?(log(n))
• Merge with neighbouring bucket when size falls
  below log(n)
• Split bucket when size grows above clog(n)
• Diversity in bucket
• Each level in 1..log(n) is represented by (1,c)
  nodes. Claim this limits the indegree to 2c -
  how ?

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Some comparisons
SkipNets log(n) log(n) ??
SkipList
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Some questions

• How important are const degree networks ?
• Dilation and congestion same as chord
• Depends on bucket mechanism
• What about fault tolerance ?