Designing peer-to-peer overlays : a small-world perspective

The Small-World phenomenon, well known under the phrase "six degrees of separation", has been for a long time under the spotlight of investigation. The fact that our social network is closely-knitted and that any two people are linked by a short chain of acquaintances was confirmed by the experimental psychologist Stanley Milgram in the sixties. However, it was only after the seminal work of Jon Kleinberg in 2000 that it was understood not only why such networks exist, but also why it is possible to efficiently navigate in these networks. This proved to be a highly relevant discovery for peer-to-peer systems, since they share many fundamental similarities with the social networks; in particular the fact that the peer-to-peer routing solely relies on local decisions, without the possibility to invoke global knowledge. In this thesis we show how peer-to-peer system designs that are inspired by Small-World principles can address and solve many important problems, such as balancing the peer load, reducing high maintenance cost, or efficiently disseminating data in large-scale systems. We present three peer-to-peer approaches, namely Oscar, Gravity, and Fuzzynet, whose concepts stem from the design of navigable Small-World networks. Firstly, we introduce a novel theoretical model for building peer-to-peer systems which supports skewed node distributions and still preserves all desired properties of Kleinberg's Small-World networks. With such a model we set a reference base for the design of data-oriented peer-to-peer systems which are characterized by non-uniform distribution of keys as well as skewed query or access patterns. Based on this theoretical model we introduce Oscar, an overlay which uses a novel scalable network sampling technique for network construction, for which we provide a rigorous theoretical analysis. The simulations of our system validate the developed theory and evaluate Oscar's performance under typical conditions encountered in real-life large-scale networked systems, including participant heterogeneity, faults, as well as skewed and dynamic load-distributions. Furthermore, we show how by utilizing Small-World properties it is possible to reduce the maintenance cost of most structured overlays by discarding a core network connectivity element – the ring invariant. We argue that reliance on the ring structure is a serious impediment for real life deployment and scalability of structured overlays. We propose an overlay called Fuzzynet, which does not rely on the ring invariant, yet has all the functionalities of structured overlays. Fuzzynet takes the idea of lazy overlay maintenance further by eliminating the need for any explicit connectivity and data maintenance operations, relying merely on the actions performed when new Fuzzynet peers join the network. We show that with a sufficient amount of neighbors, even under high churn, data can be retrieved in Fuzzynet with high probability. Finally, we show how peer-to-peer systems b