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

20/12/ 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

20/12/ 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

20/12/ Epidemic protocols Performance Fanout Proportion of infection in non atomic multicast Proportion of atomic multicast

20/12/ Epidemic protocols Reliability %10%20%30%40%50% Percentage of faulty nodes Proportion of infection in non atomic multicast Proportion of atomic multicast

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

20/12/ 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

20/12/ Epidemic protocols Join algorithm new contact Join request to a random member Join request forwarded P=1/sizeof view (1-P)

20/12/ Epidemic protocols Subscription algorithm Local view

20/12/ 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)

20/12/ 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.

20/12/ 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

20/12/ 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

20/12/ Epidemic protocols Out-degrees

20/12/ Epidemic protocols Impact of lease Partial View Size Number of nodes Without Lease With Lease Max = 29Max = 37 log(50000)= Mean=10.12 Mean=11.36

20/12/ Epidemic protocols Reliability %10%20%30%40%50%60%70% Percentage of node failures Proportion of nodes reached by the multicast Full membership SCAMP

20/12/ Unstructured overlays

20/12/ Loosely structured overlays

20/12/ Degree balancing in Scamp Mean = 18

20/12/ Rewiring Balanced number of neighbours Topology-aware Minimize the cost function d i : degree of node I (neighbours) c(i,j): cost of transmission i→j (e.g. distance) Keeping the number of edges fixed Local knowledge

20/12/ Distributed rewiring rule Select “open triangle” i—j—k at random; Evaluate locally cost of rewiring to i—k—j : Change to i—k—j with probability i j k i j k

20/12/ 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/ 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

20/12/ Degree distribution

20/12/ 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

20/12/ Graph Connectivity Number of Disconnected nodes Number of faulty nodes (10,1,1000) (10,1,100) (0,0,0)

20/12/ 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

20/12/ Delay penalty Nb iterations (w=10, T=1) RDP Max RDP Mean RMDRAD SW SW

20/12/ Relative delay penalty

20/12/ Tree shape Nb iterations (w=10,T=1) Mean nb of hops Tree depth Max nb of chidren SW SW

20/12/ Node load

20/12/ Impact on the network Nb iterationsMean Link stress Max Link Stress SW SW

20/12/ 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

20/12/ 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

20/12/ Unsubscriptions Unsub (0), [1,4,5] Local view z x y x y z