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ACDC Report Summary

Project ID: 336495
Funded under: FP7-IDEAS-ERC
Country: Germany

Mid-Term Report Summary - ACDC (Algorithms and Complexity of Highly Decentralized Computations)

The general objective of the ACDC project is to improve our understanding of the algorithmic and theoretical foundations of decentralized, possibly dynamic distributed systems. From an algorithmic point of view, decentralized networks and computations pose a number of unique challenges that are not present in sequential or more standard distributed systems. In particular, in such networks, every node has to base its decisions on limited, mostly local information about the state of the network and we aim to understand the resulting fundamental possibilities and limitations.

In the first half of the project, we made progress on different fundamental issues regarding large, decentralized (and possibly dynamic) systems. In almost any networking scenario, a core interest is to use the existing network infrastructure as efficiently as possible. In particular, in communication-intensive scenarios, we typically desire to maximize the throughput, i.e., the number of messages that can be transmitted per time unit through the network. In our work, we developed novel techniques to drastically improve the throughput when performing a large number of network-wide broadcasts. Our results tightly relate well-known graph connectivity measures to the broadcasting throughput. Moreover, we developed novel algorithmic and mathematical techniques that lead to a deeper general understanding of the vertex connectivity of graphs.

The main objective of the ACDC project is to better understand the what can and what cannot be computed in a distributed way a) if every node in a network can only (indirectly) talk to other nodes at a close distance and b) if the network topology changes dynamically during the distributed computation. An algorithm where the output of every node only depends on the behavior of nodes in a close proximity is known as a local distributed algorithm and one of the main problems that have been studied in this context is the problem of coloring the nodes of the given network with a small number of colors such that neighboring nodes obtain different colors. By weakening the standard communication model, we managed to derive the first substantial time lower bound for this graph coloring problem in general topologies. For dynamic networks, we intensively studied the complexity of broadcasting in dynamic wireless networks and for some settings, we found an almost tight characterization of the trade-offs between time complexity, certain dynamic connectivity properties of the network, and generally the type of dynamic (worst-case) topology changes in the network.

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