Distributed systems are often dynamic in the sense that there are frequent membership changes (nodes joining and leaving the network), either due to regular churn or due to an attack. Maintaining availability and full functionality of such a system under continuous topological changes hence constitutes an important algorithmic challenge. This paper reports on some of our recent results on robust distributed systems. We review two randomized architectures that build upon the continuous-discrete approach by Naor and Wieder, namely the SHELL network which allows for fast joins and leaves and organizes more reliable (or stronger) nodes in a core network where their communication is not affected by malicious (or weak) nodes, and the Chameleon network whose replica placement strategy and whose intentional topological updates ensure resiliency against denial-of-service attacks, even from past insiders. To complement our investigations on randomized architectures, we discuss algorithms to maintain hypercubic networks under worstcase churn. Finally, we advocate the design of self-stabilizing topologies—a very appealing and still not well-understood notion of robustness—that converge quickly to a desirable structure from arbitrarily degenerated states. As a use case, graph linearization is examined in more detail. This invited paper complements the WRAS’10 talk and is joint work with Matthias Baumgart, Dominik Gall, Riko Jacob, Fabian Kuhn, Andrea Richa, Stephan Ritscher, Christian Scheideler, Joest Smit, Hanjo Täubig, and Roger Wattenhofer.

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