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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 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 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)

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)

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)