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Spatial gossip and resource location protocols
, 2001
"... 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 d ..."
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Cited by 141 (7 self)
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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 distancebased 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
Protocols and impossibility results for gossipbased communication mechanisms
, 2002
"... In recent years, gossipbased 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 ..."
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Cited by 55 (3 self)
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In recent years, gossipbased 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 lowlevel gossip mechanism — the means by which communication partners are chosen — affect one’s ability to design efficient highlevel gossipbased 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 nearestresource location problems. In contrast, very efficient protocols for this problem can be designed using a nonuniform 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 gossipbased 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.
Connectivity and Inference Problems for Temporal Networks
 J. Comput. Syst. Sci
, 2000
"... 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. ..."
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Cited by 51 (3 self)
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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 timerespecting if the time labels on its edges are nondecreasing. 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 timerespecting paths in place of arbitrary paths, many of these problems acquire a character that is different from the
Kernels of Minimum Size Gossip Schemes
 Discr. Math
, 1995
"... The main part of gossip schemes are the kernels of their minimal orders. We give a complete characterization of all kernels that may appear in gossip schemes on simple graphs with a minimum number of calls. As consequences we prove several results on gossip schemes, e.g. the minimum number of rounds ..."
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Cited by 1 (0 self)
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The main part of gossip schemes are the kernels of their minimal orders. We give a complete characterization of all kernels that may appear in gossip schemes on simple graphs with a minimum number of calls. As consequences we prove several results on gossip schemes, e.g. the minimum number of rounds of a gossip scheme with a minimum number of calls is computed. Moreover, in the new context we give proofs of known results, e.g. the wellknown FourCycleTheorem. In the last part, we deal with order theoretic questions for such kernel posets. After describing all pgridkernels in terms of permutations and subsets, isomorphism is investigated and they are enumerated. Then we compute the order dimension and the jump number of all possible kernels, and finally, we show how to determine the numbers of their linear extensions. Research supported by a special grant of the AlexandervonHumboldt foundation, and SFB 303 (DFG), Institute of Discrete Mathematics/ Operations Research, University...
Representations of Gossip Schemes
, 1994
"... . Formalisms for representing gossip problems are surveyed. A new method "calling schemes" is presented which generalizes existing methods. This survey is intended to serve primarily as a basis for future work. 1 Introduction In the gossip problem [6], each of a number of people (or processing elem ..."
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. Formalisms for representing gossip problems are surveyed. A new method "calling schemes" is presented which generalizes existing methods. This survey is intended to serve primarily as a basis for future work. 1 Introduction In the gossip problem [6], each of a number of people (or processing elements) has an item of gossip to share with the others through a sequence of communication events called calls. In general we can have fullduplex or twoway calls ("gossiping by telephone"), halfduplex or oneway calls ("gossiping by telegraph"), multiway or conference calls, and we may have limits on the number of calls a person can participate in simultaneously (usually just one). One can study gossiping in terms of the time it takes, the number of calls, the "cost," the structure of communication patterns, and so on. This paper presents and compares several formalisms that can represent these problems, and it introduces a new formalism "calling schemes" which is seen to be a generalizatio...