Error-correcting codes are efficient methods for handling communication channels in the context of technological networks. However, such elaborate methods differ a lot from the unsophisticated way biological entities are supposed to communicate. Yet, it has been recently shown by Feinerman, Haeupler, and Korman [ PODC 2014 ] that complex coordination tasks such as and can plausibly be achieved in biological systems subject to noisy communication channels, where every message transferred through a channel remains intact with small probability @math , without using coding techniques. This result is a considerable step towards a better understanding of the way biological entities may cooperate. It has been nevertheless be established only in the case of 2-valued : rumor spreading aims at broadcasting a single-bit opinion to all nodes, and majority consensus aims at leading all nodes to adopt the single-bit opinion that was initially present in the system with (relative) majority. In this paper, we extend this previous work to @math -valued opinions, for any @math . Our extension requires to address a series of important issues, some conceptual, others technical. We had to entirely revisit the notion of noise, for handling channels carrying @math - messages. In fact, we precisely characterize the type of noise patterns for which plurality consensus is solvable. Also, a key result employed in the bivalued case by is an estimate of the probability of observing the most frequent opinion from observing the mode of a small sample. We generalize this result to the multivalued case by providing a new analytical proof for the bivalued case that is amenable to be extended, by induction, and that is of independent interest.
Over the last decade, we have seen a revolution in connectivity between computers, and a resulting paradigm shift from centralized to highly distributed systems. With massive scale also comes massive instability, as node and link failures become the norm rather than the exception. For such highly volatile systems, decentralized gossip-based protocols are emerging as an approach to maintaining simplicity and scalability while achieving fault-tolerant information dissemination. In this paper, we study the problem of computing aggregates with gossip-style protocols. Our first contribution is an analysis of simple gossip-based protocols for the computation of sums, averages, random samples, quantiles, and other aggregate functions, and we show that our protocols converge exponentially fast to the true answer when using uniform gossip. Our second contribution is the definition of a precise notion of the speed with which a node's data diffuses through the network. We show that this diffusion speed is at the heart of the approximation guarantees for all of the above problems. We analyze the diffusion speed of uniform gossip in the presence of node and link failures, as well as for flooding-based mechanisms. The latter expose interesting connections to random walks on graphs.