Unstructured overlays: construction, optimization, applications
Anne-Marie Kermarrec Joint work with Laurent Massouli and Ayalvadi
Ganesh
Slide 2
20/12/2002 2 Epidemic protocols Epidemic multicast N nodes in a
group. Each node gossips new messages to K other nodes chosen at
random. How large should K be so that ever node receive the message
with high probability? Stronger than requiring that nearly 100% get
the message with high probability 0 1 2 5 7 6 3 9 4 8
Slide 3
20/12/2002 3 Epidemic protocols Performance Modelled as a
random graph Erdos and Renyi result applies to connectivity of
undirected graph. Sharp threshold at log N. Main results If K=
log(N) + c, the probability that every node is reached is
exp(exp(c)). Result applies if mean out-degree is log(N) + c,
irrespective of the degree distribution Use of these results to
parameterize protocols
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20/12/2002 4 Epidemic protocols Performance 0 0.1 0.2 0.3 0.4
0.5 0.6 0.7 0.8 0.9 1 1234567891011121314151617 Fanout Proportion
of infection in non atomic multicast Proportion of atomic
multicast
Slide 5
20/12/2002 5 Epidemic protocols Reliability 0 10 20 30 40 50 60
70 80 90 100 0%10%20%30%40%50% Percentage of faulty nodes
99.9899.94 Proportion of infection in non atomic multicast
Proportion of atomic multicast
Slide 6
20/12/2002 6 Epidemic protocols Research issues Gossip-based
algorithms Scalable: load on each node grows logarithmically with
group size Highly Reliable : Probabilistic guarantees Proactive
Graceful degradation in the presence of failures Major drawbacks
Non-scalable membership protocol Oblivious to network topology
Generates a large number of messages in non faulty
environments
20/12/2002 8 Epidemic protocols SCAlable Membership Protocol
Partial knowledge: Each node has only a partial knowledge of the
membership: local view Adequate for reliability: O(log(n))
Self-organizing and fully decentralized: size of local views
converges to (c+1) log(N) Membership management Graph growth Graph
maintenance
Slide 9
20/12/2002 9 Epidemic protocols Join algorithm new contact Join
request to a random member Join request forwarded P=1/sizeof view
(1-P)
20/12/2002 11 Epidemic protocols Average case analysis D(n) :
Average size of local view with n nodes present. Subscription adds
D(n)+1 directed arcs, so (n+1) D(n+1) = n D(n) + D(n)+1 Solution of
this recursion is D(N) = D(1) + 1/2 + 1/3 + + 1/N log(N)
Slide 12
20/12/2002 12 Epidemic protocols Graph maintenance: Redirection
Analysis assumes that new nodes subscribe to a random pre-existing
node. Redirection Use of weights reflecting the connectivity of the
graph A node receiving a new subscription request may redirect it
to a member of its local view. Subscription request performs random
walk on membership until it is eventually kept at some node.
Stopping rule: random walk is close to uniform on all nodes.
Slide 13
20/12/2002 13 Epidemic protocols Graph maintenance: Lease Lease
associated with each join request Nodes have to re-join when the
lease on their subscription expires. Effects Nodes having failed
permanently will time out Rebalances the partial views: limits the
risk of disconnection due to failures
Slide 14
20/12/2002 14 Epidemic protocols Performance Convergence of
view size Confirms theoretical analysis Impact of redirection
Impact of lease Reliability Comparison with traditional gossip
Attests to the good quality (uniformity) of views
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20/12/2002 15 Epidemic protocols Out-degrees
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20/12/2002 16 Epidemic protocols Impact of lease 0 1000 2000
3000 4000 5000 6000 7000 8000 9000 10000 0510152025303540 Partial
View Size Number of nodes Without Lease With Lease Max = 29Max = 37
log(50000)= 10.819 Mean=10.12 Mean=11.36
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20/12/2002 17 Epidemic protocols Reliability 0 0.1 0.2 0.3 0.4
0.5 0.6 0.7 0.8 0.9 1 0%10%20%30%40%50%60%70% Percentage of node
failures Proportion of nodes reached by the multicast Full
membership SCAMP
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20/12/2002 18 Unstructured overlays
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20/12/2002 19 Loosely structured overlays
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20/12/2002 20 Degree balancing in Scamp Mean = 18
Slide 21
20/12/2002 21 Rewiring Balanced number of neighbours
Topology-aware Minimize the cost function d i : degree of node I
(neighbours) c(i,j): cost of transmission ij (e.g. distance)
Keeping the number of edges fixed Local knowledge
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20/12/2002 22 Distributed rewiring rule Select open triangle
ijk at random; Evaluate locally cost of rewiring to ikj : Change to
ikj with probability i j k i j k
Slide 23
20/12/2002 23 Experiments Simulations GT Topologies Overlay
created by Scamp Metrics Mean distance to neighbors Maximum and
distribution of degree Graph connectivity Average on 100
simulations
20/12/2002 26 Impact on the distance to neighbours
(W,iterations) T=1 Mean distance to neighbors (GT-5050) (0,0)484
(10,100)363 (10,1000)238 (10,5000)155 (50,1000)266 50,000
Nodes
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20/12/2002 27 Graph Connectivity Number of Disconnected nodes
Number of faulty nodes (10,1,1000) (10,1,100) (0,0,0)
Slide 28
20/12/2002 28 Application-level multicast Good quality
underlying overlay Tree-based multicast Source initiates the tree
building by flooding A node takes as a parent the first node it
hears from Small-world optimization Diameter (in hops) Failure
resilience
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20/12/2002 29 Delay penalty Nb iterations (w=10, T=1) RDP Max
RDP Mean RMDRAD 0726.123.13.62.58 100513.112.491.922.09
10002291.661.161.48 SW-100488.132.371.881.99
SW-1000238.261.621.11.43
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20/12/2002 30 Relative delay penalty
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20/12/2002 31 Tree shape Nb iterations (w=10,T=1) Mean nb of
hops Tree depth Max nb of chidren 04.911.1542.65 1005.2411.2220.12
10007.1318.5919.59 SW-1004.8710.735.92 SW-10006.4517.3435.21
Slide 32
20/12/2002 32 Node load
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20/12/2002 33 Impact on the network Nb iterationsMean Link
stress Max Link Stress 031448 10021232 100011319 SW-10021180
SW-10001927
Slide 34
20/12/2002 34 Conclusion Reshaping unstructured into loosely
structured overlays: degree balancing and locality Support for
efficient application-level multicast More work on network
load/overhead Others reshaping metrics
Slide 35
20/12/2002 35 Epidemic protocols Performance Convergence of
view size Confirms theoretical analysis Impact of redirection
Impact of lease Reliability Comparison with traditional gossip
Attests to the good quality (uniformity) of views
Slide 36
20/12/2002 36 Unsubscriptions 0 1 5 4 1 4 5 Unsub (0), [1,4,5]
Local view z x y 8 9 0 7 3 0 6 0 2 8 9 4 x y z 7 3 5 6 0 1