Until now, the analysis of fault tolerance of peerto-peer 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 are hardly considered. In this paper, we devise techniques to build dynamic peer-to-peer systems which remain fully functional in spite of an adversary which continuously adds and removes peers. We exemplify our algorithms on a pancake topology and present a system which maintains peer degree and network diameter O( log n log log n ), where n is the total number of peers in the system.

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