Resilience to failures and deliberate attacks is becoming an essential requirement in most communication networks today. This also applies to P2P Overlays which on the one hand are created on top of communication infrastructures, and therefore are equally affected by failures of the underlying infrastructure, but which on the other hand introduce new possibilities like the creation of arbitrary links within the overlay. In this article, we present a survey of strategies to improve resilience in communication networks as well as in P2P overlay networks. Furthermore, our intention is to point out differences and similarities in the resilience-enhancing measures for both types of networks. By revising some basic concepts from graph theory, we show that many concepts for communication networks are based on well-known graph-theoretical problems. Especially, some methods for the construction of protection paths in advance of a failure are based on very hard problems, indeed many of them are in NP and can only be solved heuristically or on certain topologies.
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