ERC Starting Grant: Many of today’s and tomorrow’s computer systems are built on top of large-scale networks such as, e.g., the Internet, the world wide web, wireless ad hoc and sensor networks, or peer-to-peer networks. Driven by technological advances, new kinds of networks and applications have become possible and we can safely assume that this trend is going to continue. Often modern systems are envisioned to consist of a potentially large number of individual components that are organized in a completely decentralized way. There is no central authority that controls the topology of the network, how nodes join or leave the system, or in which way nodes communicate with each other. Also, many future distributed applications will be built using wireless devices that communicate via radio. The general objective of the ERC project "Algorithms and Complexity of Highly Decentralized Computations" is to improve our understanding of the algorithmic and theoretical foundations of decentralized distributed systems. From an algorithmic point of view, decentralized networks and computations pose a number of fascinating and unique challenges that are not present in sequential or more standard distributed systems. As communication is limited and mostly between nearby nodes, each node of a large network can only maintain a very restricted view of the global state of the system. This is particularly true if the network can change dynamically, either by nodes joining or leaving the system or if the topology changes over time, e.g., because of the mobility of the devices in case of a wireless network. Nevertheless, the nodes of a network need to coordinate in order to achieve some global goal. In particular, we plan to study algorithms and lower bounds for basic computation and information dissemination tasks in such systems. In addition, we are particularly interested in the complexity of distributed computations in dynamic and wireless networks.