The dynamic behavior of a network in which information is changing continuously over time requires robust and efficient mechanisms for keeping nodes updated about new information. Gossip protocols are mechanisms for this task in which nodes communicate with one another according to some underlying deterministic or randomized algorithm, exchanging information in each communication step. In a variety of contexts, the use of randomization to propagate information has been found to provide better reliability and scalability than more regimented deterministic approaches. In many settings, such as a cluster of distributed computing hosts, new information is generated at individual nodes, and is most “interesting ” to nodes that are nearby. Thus, we propose distance-based propagation bounds as a performance measure for gossip mechanisms: a node at distance d from the origin of a new piece of information should be able to learn about this information with a delay that grows slowly with d, and is independent of the size of the network. For nodes arranged with uniform density in Euclidean space, we present natural gossip mechanisms, called spatial gossip, that satisfy such a guarantee: new information is spread to

In recent years, gossip-based algorithms have gained prominence as a methodology for designing robust and scalable communication schemes in large distributed systems. The premise underlying distributed gossip is very simple: in each time step, each node v in the system selects some other node w as a communication partner — generally by a simple randomized rule — and exchanges information with w; over a period of time, information spreads through the system in an “epidemic fashion”. A fundamental issue which is not well understood is the following: how does the underlying low-level gossip mechanism — the means by which communication partners are chosen — affect one’s ability to design efficient high-level gossip-based protocols? We establish one of the first concrete results addressing this question, by showing a fundamental limitation on the power of the commonly used uniform gossip mechanism for solving nearest-resource location problems. In contrast, very efficient protocols for this problem can be designed using a non-uniform spatial gossip mechanism, as established in earlier work with Alan Demers. We go on to consider the design of protocols for more complex problems, providing an efficient distributed gossipbased protocol for a set of nodes in Euclidean space to construct an approximate minimum spanning tree. Here too, we establish a contrasting limitation on the power of uniform gossip for solving this problem. Finally, we investigate gossip-based packet routing as a primitive that underpins the communication patterns in many protocols, and as a way to understand the capabilities of different gossip mechanisms at a general level.

Many network problems are based on fundamental relationships involving time. Consider, for example, the problems of modeling the flow of information through a distributed network, studying the spread of a disease through a population, or analyzing the reachability properties of an airline timetable. In such settings, a natural model is that of a graph in which each edge is annotated with a time label specifying the time at which its endpoints “communicated. ” We will call such a graph a temporal network. To model the notion that information in such a network “flows ” only on paths whose labels respect the ordering of time, we call a path time-respecting if the time labels on its edges are non-decreasing. The central motivation for our work is the following question: how do the basic combinatorial and algorithmic properties of graphs change when we impose this additional temporal condition? The notion of a path is intrinsic to many of the most fundamental algorithmic problems on graphs; spanning trees, connectivity, flows, and cuts are some examples. When we focus on time-respecting paths in place of arbitrary paths, many of these problems acquire a character that is different from the

We propose and evaluate a model for controlling infection patterns defined over rounds or real time in a gossipbased protocol using adaptive fanout. We model three versions of gossip-based protocols: the Synchronous Protocol, the PseudoSynchronous Protocol and the Asynchronous Protocol. Our objective is to ensure that the members of a group receive a desired message within a bounded latency with very high probability. We argue that the most important parameter that controls the latency of message delivery is the fanout used during gossiping, i.e., the number of gossip targets chosen in a particular instance of gossip. We formally analyze the three protocols and provide expressions for fanout. We introduce the idea of using variable fanouts in different rounds in the Synchronous Protocol. We define fanout as a function of time for the Asynchronous Protocol such that an expected infection pattern is observed with high probability. For a better understanding of the theoretical model, we develop a PseudoSynchronous Protocol to highlight the modelling done in order to derive time dependent fanout. We show that our protocols generate Θ(nlogn) messages, which is optimal for gossip protocols. We aim to use the gossiping mechanism for large-scale group communication with soft real time constraints. This would alleviate the dependence on tree-based deterministic protocols which usually lack scalability. 1.