Dynamic & Fault-Tolerant P2P-Topologies

Until now, the analysis of fault tolerance of peer-to-peer (p2p) systems usually only covers random faults of some kind. Contrary to traditional algorithmic research, faults as well as joins and leaves occurring in a worst-case manner in p2p systems are hardly considered. Most fault tolerance analyzes are static in the sense that it is shown that a system tolerates a certain number of simultaneous faults. The much more realistic dynamic case where faults steadily occur has not found much attention. The goal of this thesis is to work towards a general understanding of fault tolerance especially for the case of dynamic and worst-case failures. The thesis introduces a simple dynamic model where a malicious adversary — controlling the arrivals and departures of the peers — and a repairing algorithm take turns. The insights gained from this model are then used to study the more realistic scenario where a repairing algorithm maintains certain properties of the topology against a concurrent adversary. Besides the comparison of different fault-tolerance models, the thesis presents a distributed hash table which maintains an efficient search structure as well as a low peer degree in spite of the worst-case failures. By a dynamic analysis we prove that no data item is lost by the system.