The Continuous-Discrete Approach for Designing P2P Networks and Algorithms

One of the most intriguing trends in the development of internet applications in past few years is the immense rise in popularity of peer-to-peer (P2P) applications and networks. Peer-to-peer networks are characterized by the lack of central control or a-priori hierarchical organization in which all or most communication is symmetric. Moreover a P2P system is expected to scale gracefully as the size of the network grows. The sheer scale and dynamism in which P2P networks are suppose to operate make the design of P2P systems challenging even for relatively simple applications. The thesis is divided into two main parts. In the first we propose a new general approach for designing P2P networks called the continuous discrete approach. We demonstrate our technique by suggesting several specific distributed data structures. The first is a design for the distributed hash table (DHT) abstract data structure which we call Distance Halving (DH). Our design has an optimal tradeoff between node degree and path hop length. A variant of our design is also robust against random faults and even against a form of adversarial behavior of a random subset of the nodes (which we call the spam generating model). An important feature of the DH hash table is a dynamic caching algorithm which completely prevents hot spots. The second data structure we suggest is a dynamic quorum system called Dynamic Paths. We prove some new lower bounds on the probe complexity of quorum systems. We then show that Dynamic Paths is optimal with respect to load, availability and probe complexity. Finally we show how the continuous-discrete approach could be used to emulate in a P2P setting any topology, thus basically showing that all the classical inter connection topologies (studied in the context parallel computing) may serve as a basis for a P2P network. In the second part of the Thesis we analyze some new algorithms for known P2P networks. Our main result shows that routing algorithms which take into account neighbors of neighbors for performing better routing decisions, are often provably better than Greedy algorithms and in some cases optimal. We analyze the Neighbor of Neighbor algorithms in the context of small world networks and Skip-Graphs. Finally we show that Skip-Graphs are in fact expanders with high probably and show how to utilize this fact for a variety of algorithms.