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Unstructured overlays: construction, optimization, applications Anne-Marie Kermarrec Joint work with Laurent Massouli and Ayalvadi Ganesh

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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

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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

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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

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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

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20/12/2002 7 Reducing Traffic Topologically awareness Self-organizing membership protocols Partial membership Self-set fanout Decentralized Epidemic protocols Agenda SCAMP LOCALISER TREE-BASED APPLICATION-LEVEL MULTICAST

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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

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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)

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20/12/2002 10 Epidemic protocols Subscription algorithm 0 1 5 4 6 1 4 5 6 6 6 0 Local view 7 67 6 2 87 7 2 8 3 1 3 63 6 7 0 15 65 6 6 6 6

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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)

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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.

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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

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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

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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

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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

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20/12/2002 24 Impact on the degree (W, iterations) T=1Max degree (0,0)59.6 (10,100)22 (10,1000)19.8 (10,5000)20 (50,100)20.6 Scamp-GT Topology, 50,000 Nodes-mean degree = 18

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20/12/2002 25 Degree distribution

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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)

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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

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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

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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

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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

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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