1. Gradient Topology: A Generalized Super-Peer Topology

2. Gossiping in Distributed Systems “Gossiping is the endless process of randomly choosing two members and subsequently letting these two exchange Information” [Kermarrec/Van Steen, Gossiping in distributed systems] Gossiping algorithms have been mostly developed for random overlay networks. Peer Sampling, topology construction, computation, monitoring

3. Random Networks and Gossiping Efficient and robust information propagation Low diameter networks, redundant paths. Symmetry of random networks makes it easier to analyse systems using mathematical tools. “By symmetry we mean the existence of different viewpoints from which the system appears the same.“ P. W. Anderson [More is Different] Symmetry of random networks means we can only use message-passing to share information between nodes.

4. Scale-Free Networks New nodes preferentially create links to those nodes with a higher number of links (positive feedback). Symmetry breaking from a random network. Nodes now can use information encoded in the topology to send search requests to hubs. Random Graph Barabasi’s Scale-Free Graph Preferential Attachment Algorithm

5. Ant Foraging – from Random to Ordered* *Foraging patterns break both spatial and temporal symmetry

6. Symmetry Breaking Symmetry breaking is about going from a more disordered state to a more ordered state. Self-organization: from a higher to a lower entropy state. More formally, symmetry breaking describes a phenomenon where small fluctuations acting on a system crossing a critical point determine which branch of a bifurcation is taken.

7. Mechanisms of Self-Organization* External events supplied to system Positive feedback to cascade external events Negative feedback to limit cascading effects Decay/exploration to regenerate the self- organized structure Temporal symmetry *Patterns of S.O. In Biology [Denouberg et al]

8. Gradient Overview A gossip-generated P2P overlay network that sorts peers into a overlapping redundant trees, where all trees have the same root. Peers are sorted by a local utility value Layered over a PSS to prevent partitioning Efficient search to find high utility peers Gradient ascent Gradient descent

9. Gradient Topology App-specific utility function at every peer. Highest utility peers are clustered in the centre, while peers with decreasing utility are found at increasing distance from the centre. Can be implemented as a ranking function using T- Man

10. Gradient Overlay Network

11. Greedy Preference Function Preference function for keeping neighbours. Peer p prefers neighbour a over neighbour b if and only if or where U p (a) and U p (b) are the p's cached utility values for neighbours a and b.

12. Soft-Max Preference Function Select neighbour a over neighbour b with higher probability: where P p (a) and P p (b) are the probabilities of selecting neighbours a and b, respectively. Probabilities are normalized over all neighbours.

13. Who should a peer gossip with? Again, you can use Greedy Policy Softmax Policy A neighbour to gossip with can be selected from Gradient neighbours or random neighbours (from Cyclon)

14. Discovering High Utility Peers Gradient structure allows an efficient search heuristic called gradient search. Next hop can be either greedily chosen as highest utility neighbour or probabilistically chosen. Boltzman exploration reduces traffic on popular paths. Improved performance over Random Walk.

15. Gvod: Layered Gossip Architecture P2P Video on Demand Gradient Overlay Network Peer Sampling Service (Cyclon)

16. Gvod Protocol Utility function returns download point in the video. VoD layer samples nodes in the Gradient Layer to build: 1. BitTorrent set: neighbours at similar download positions 2. Upper set: neighbours at slightly higher download positions In contrast to BitTorrent, nodes don’t need to exchange messages to know whether a neighbour has a piece of interest or not.

17. P2P Live Streaming: GradienTv Approximate auction algorithm uses node upload bandwidths to allocate places in streaming overlay trees.

18. GradienTv: Bandwidth Levels Utility is upload bandwidth capacity. Utility levels are ranges of upload bandwidth capacity. Long range links added to the similar set to utilise resources of higher bandwidth peers in centre. Modified preferential neighbour selection algorithm in Gradient to explore within a utility level.

19. The Project: Decentralized Resource Allocation Random Overlay Network Approach Requires lots of message passing to find ’good’ peers Gradient Overlay Network Approach? Bounded time to find free resources Short-range links to reduce time Bounded (but high?) gossiping overhead

20. Gossiping/Gradient References Kermerrac and Van Steen, “Gossiping in Distributed Systems”, ACM SIGOPS OS Review 2007. Jan Sacha, Bartosz Biskupski, Dominik Dahlem, Raymond Cunningham, René Meier,Jim Dowling, and Mads Haahr,"Decentralising a Service-Oriented Architecture", In the Peer-to-Peer Networking and Applications Journal (PPNA), ISSN 1936- 6442, Springer, Oct, 2009 Sacha et al, "Using Aggregation for Adaptive Superpeer Discovery on the Gradient Topology", In Proceedings of the 2nd International Workshop on Self-Managing Systems, LNCS 3996, pps 73-86, 2006. Sacha et al, "Discovery of Stable Peers in a Self-Organising Peer-to-Peer Gradient Topology", In the International Conference on Distributed Applications and Interoperable Systems (DAIS), LNCS 4025, pages 70-83, 2006.

21. Live Streaming/VoD References Amir Payberah, Jim Dowling, Fatemeh Rahimian and Seif Haridi. gradienTv: Market- based P2P Live Media Streaming on the Gradient Overlay, Dais 2010. Gautier Berthou, P2P VoD using the Self-Organizing Gradient Overlay Network, SOAR 2010.