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We study the connection between the rate at which a rumor spreads throughout a graph and the conductance of the graph—a standard measure of a graph's expansion properties. We show that for any n-node graph with conductance φ, the classical PUSH-PULL algorithm distributes a rumor to all nodes of the graph in O(φ −1 log n) rounds with high probability… (More)

We analyze decentralized routing in small-world networks that combine a wide variation in node degrees with a notion of spatial embedding. Specifically, we consider a variation of Kleinberg's augmented-lattice model (STOC 2000), where the number of long-range contacts for each node is drawn from a power-law distribution. This model is motivated by the… (More)

We study the relation between the rate at which rumors spread throughout a graph and the vertex expansion of the graph. We consider the standard rumor spreading protocol where every node chooses a random neighbor in each round and the two nodes exchange the rumors they know. For any n-node graph with vertex expansion α, we show that this protocol spreads a… (More)

We establish a bound for the classic PUSH-PULL rumor spreading protocol on arbitrary graphs, in terms of the vertex expansion of the graph. We show that O(log 2 (n)/α) rounds suffice with high probability to spread a rumor from a single node to all n nodes, in any graph with vertex expansion at least α. This bound matches the known lower bound, and settles… (More)

Revisiting the "small-world" experiments of the '60s, Kleinberg observed that individuals are very effective at constructing short chains of acquaintances between any two people, and he proposed a mathematical model of this phenomenon. In this model, individuals are the nodes of a <i>base graph</i>, the square grid, capturing the <i>underlying structure</i>… (More)

We present a scheme for evenly partitioning the key space in distributed hash tables among the participating nodes. The scheme is based on the multiple random choices paradigm [3, 19], and handles both node joins and leaves. It achieves, with high probability, a ratio of at most 4 between the loads of the most and least burdened nodes, in the face or… (More)

We study the time and space complexity of randomized Test-And-Set (TAS) implementations from atomic read/write registers in asynchronous shared memory models with <i>n</i> processes. We present an adaptive TAS algorithm with an expected (individual) step complexity of <i>O</i>(log<sup>*</sup> <i>k</i>), for contention <i>k</i>, against the oblivious… (More)

We study the communication complexity of rumor spreading in the random phone-call model. Suppose <i>n</i>players communicate in parallel rounds, where in each round every player calls a randomly selected communication partner. A player <i>u</i> is allowed to exchange messages during a round only with the player that <i>u</i> called, and with all the players… (More)

We investigate the randomness requirements of the classical rumor spreading problem on fully connected graphs with <i>n</i> vertices. In the standard random protocol, where each node that knows the rumor sends it to a randomly chosen neighbor in every round, each node needs <i>O</i>((log <i>n</i>)<sup>2</sup>) random bits in order to spread the rumor in… (More)

Recently, there has been significant research activity in the algorithmic analysis of complex networks, such as social networks, or information networks. A problem of great practical importance is that of network immunization against virus spread. Given a network, a virus-propagation model, and an immunization cost function, we are interested in containing… (More)