1. Infinite Unlimited Churn
Dianne Foreback
Mikhail Nesterenko
Sébastien Tixeuil
Lyon, France
November 9, 2016

2. Why Infinite Unlimited Churn
Overlay networks continuously undergo topology changes
An infinite number of churn requests (joining or leaving requests) and no bound on concurrently joining or leaving processes in a peer-to-peer overlay network
While overlay network maintains services (e.g. content retrieval)
. . .
join(h)
join(x2)
join(y1)
join(m)
join(k)
join(x2)
join(l)
join(j2)
. . . a b c d e f u v w x y z
leave(b)
leave(c)
leave(e)
leave(f)
leave(x)
leave(y)

3. Infinite Unlimited Churn Problem Statement
Message Safety: message in a transitional link is not lost
Terminating Transition: every transitional link eventually becomes stable
Message Progress: a message in a stable link is either delivered or forwarded closer to the destination
Linear Topology State Transition x y z
leave(y, z) received at x
join(y) received at x OR
Unfair Version
Fair Version
Request Progress: if there is a process that is requesting to join or to exit the network, then eventually some process respectively joins or exits the network
Fair Request: if there is a process that is requesting to join or to exit the network, then eventually this process joins or exits the network. c p g k
g requests to join
k joins
g eventually joins

4. Global vs. Local Solution
Global (centralized) solution: a single processes manages the processing of all churn requests
Local solution: only processes in the immediate vicinity of the joining/leaving process are involved in processing the request
Local Solution Impossible
Local Solution Possible
Unfair Version
Fair Version
Request Progress: if there is a process that is requesting to join or to exit the network, then eventually some process respectively joins or exits the network
Fair Request: if there is a process that is requesting to join or to exit the network, then eventually this process joins or exits the network. c p g k
g requests to join c p g k
g eventually joins c p g k
g requests to join c p g k
k joins

5. Local Fair Unlimited Infinite Churn Impossible
Fair Request (a particular churn request) cannot be satisfied
join(y3)
join(y1)
Request for y3 to join
but y’ joins first x y z
join(y3)
join(y2)
Request for y3 to join
but now y2 joins. Can be repeated infimum. x y y’ z

6. Unfair Infinite Unlimited Churn (UIUC) Algorithm
Linear Topology State Transition x y z
leave(y, z) received at x
join(y) received at x OR
UIUC join and leave request handling
5. ftd
a. join(y) x y z
3. tda
1.1 sua(z)
4. tdb
1.2 sua
2.2 sub
2.1 sub
b. leave(y, z)
1. sua
3.1 tda
2. sub
3.2 tda
4.2 tdb
4.1 tdb

7. Extending to Skip Lists
level join order
level leave order 3 2
levels 1 x y
processes

8. Infinite Unlimited Churn
Thank you!
Questions?