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Rumor spreading and vertex expansion
 In SODA
, 2012
"... 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 nnode graph wit ..."
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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 nnode graph with vertex expansion α, we show that this protocol spreads a rumor from a single node to all other nodes in O(α −1 log 2 n √ log n) rounds with high probability. Further, we construct graphs for which Ω(α −1 log 2 n) rounds are needed. Our results complement a long series of works that relate rumor spreading to edgebased notions of expansion, resolving one of the most natural questions on the connection between rumor spreading and expansion. 1
Global Computation in a Poorly Connected World: Fast Rumor Spreading with No Dependence on Conductance
, 2012
"... In this paper, we study the question of how efficiently a collection of interconnected nodes can perform a global computation in the GOSSIP model of communication. In this model, nodes do not know the global topology of the network, and they may only initiate contact with a single neighbor in each r ..."
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Cited by 12 (3 self)
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In this paper, we study the question of how efficiently a collection of interconnected nodes can perform a global computation in the GOSSIP model of communication. In this model, nodes do not know the global topology of the network, and they may only initiate contact with a single neighbor in each round. This model contrasts with the much less restrictive LOCAL model, where a node may simultaneously communicate with all of its neighbors in a single round. A basic question in this setting is how many rounds of communication are required for the information dissemination problem, in which each node has some piece of information and is required to collect all others. In the LOCAL model, this is quite simple: each node broadcasts all of its information in each round, and the number of rounds required will be equal to the diameter of the underlying communication graph. In the GOSSIP model, each node must independently choose a single neighbor to contact, and the lack of global information makes it difficult to make any sort of principled choice. As such, researchers have focused on the uniform gossip algorithm, in which each node independently selects a neighbor uniformly at random. When the graph is wellconnected, this works quite well. In a string of beautiful papers, researchers proved a sequence of successively stronger bounds on the number of rounds required in terms of the conductance φ and graph size n, culminating in a bound of O(φ −1 log n). In this paper, we show that a fairly simple modification of the protocol gives an algorithm that solves the information dissemination problem in at most O(D + polylog(n)) rounds in a network of diameter D, with no dependence on the conductance. This is
Order Optimal Information Spreading Using Algebraic Gossip
, 2011
"... In this paper we study gossip based information spreading with bounded message sizes. We use algebraicgossip to disseminate k distinct messagesto all n nodes in a network. For arbitrary networks we provide a new upper bound for uniform algebraic gossip of O((k + logn + D)∆) rounds with high probabil ..."
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Cited by 10 (3 self)
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In this paper we study gossip based information spreading with bounded message sizes. We use algebraicgossip to disseminate k distinct messagesto all n nodes in a network. For arbitrary networks we provide a new upper bound for uniform algebraic gossip of O((k + logn + D)∆) rounds with high probability, where D and ∆ are the diameter and the maximum degree in the network, respectively. For many topologies and selections of k this bound improves previous results, in particular, for graphs with a constant maximum degree it implies that uniform gossip is order optimal and the stopping time is Θ(k +D). Toeliminate the factorof∆from the upperbound we proposeanonuniform gossipprotocol, TAG,whichisbasedonalgebraicgossipandanarbitraryspanningtreeprotocolS. Thestopping time of TAG is O(k+logn+d(S)+t(S)), where t(S) is the stopping time of the spanning tree protocol, and d(S) is the diameter of the spanning tree. We provide two general cases in which this bound leads to an order optimal protocol. The first is for k = Ω(n), where, using a simple gossip broadcast protocol that creates a spanning tree in at most linear time, we show that TAG finishes after Θ(n) rounds for any graph. The second uses a sophisticated, recent gossip protocol to build a fast spanning tree on graphs with large weak conductance. In turn, this leads to the optimally of TAG on these graphs for k = Ω(polylog(n)). The technique used in our proofs relies on queuing theory, which is an interesting approach that can be useful in future gossip analysis. Michael Borokhovich is a fulltime student at Ben Gurion University and is principally responsible for the paper’s contributions.
Experimental Analysis of Rumor Spreading in Social Networks
"... Abstract Randomized rumor spreading was recently shown to be a very efficient mechanism to spread information in preferential attachment networks. Most interesting from the algorithm design point of view was the observation that the asymptotic runtime drops when memory is used to avoid recontactin ..."
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Cited by 3 (0 self)
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Abstract Randomized rumor spreading was recently shown to be a very efficient mechanism to spread information in preferential attachment networks. Most interesting from the algorithm design point of view was the observation that the asymptotic runtime drops when memory is used to avoid recontacting neighbors within a small number of rounds. In this experimental investigation, we confirm that a small amount of memory indeed reduces the runtime of the protocol even for small network sizes. We observe that one memory cell per node suffices to reduce the runtime significantly; more memory helps comparably little. Aside from extremely sparse graphs, preferential attachment graphs perform faster than all other graph classes examined. This holds independent of the amount of memory, but preferential attachment graphs benefit the most from the use of memory. We also analyze the influence of the network density and the size of the memory. For the asynchronous version of the rumor spreading protocol, we observe that the theoretically predicted asymptotic advantage of preferential attachment graphs is smaller than expected. There are other topologies which benefit even more from asynchrony. We complement our findings on artificial network models by the corresponding experiments on crawls of popular online social networks, where again we observe extremely rapid information dissemination and a sizable benefit from using memory and asynchrony. 1
Simple, Fast and Deterministic Gossip and Rumor Spreading
"... We study gossip algorithms for the rumor spreading problem which asks each node to deliver a rumor to all nodes in an unknown network. Gossip algorithms allow nodes only to call one neighbor per round and have recently attracted attention as message efficient, simple and robust solutions to the rumo ..."
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We study gossip algorithms for the rumor spreading problem which asks each node to deliver a rumor to all nodes in an unknown network. Gossip algorithms allow nodes only to call one neighbor per round and have recently attracted attention as message efficient, simple and robust solutions to the rumor spreading problem. A long series of papers analyzed the performance of uniform random gossip in which nodes repeatedly call a random neighbor to exchange all rumors with. A main result of this investigation was that uniform gossip comlog n pletes in O( Φ) rounds where Φ is the conductance of the network. More recently, nonuniform random gossip schemes were devised to allow efficient rumor spreading in networks with bottlenecks. In particular, [CensorHillel et al., STOC’12] gave an O(log 3 n) algorithm to solve the 1local broadcast problem in which each node wants to exchange rumors locally with its 1neighborhood. By repeatedly applying this protocol one can solve the global rumor spreading quickly for all networks with small diameter, independently of the conductance. All these algorithms are inherently randomized in their design and analysis. A parallel research direction has been to reduce and determine the amount of randomness needed for efficient rumor spreading. This has been done via lower bounds for restricted models and by designing gossip algorithms with a reduced need for randomness, e.g., by using pseudorandom generators with short random seeds. The general intuition and consensus of these results has been that randomization plays a important role in effectively spreading rumors and that at least a polylogarithmic number of random bit are crucially needed. In this paper we improves over this state of the art in several ways by presenting a deterministic gossip algorithm that solves the the klocal broadcast problem in 2(k + log n) log n rounds1. Besides being the first efficient deterministic solution to the rumor spreading problem this algorithm is interesting in many aspects: It is simpler, more natural, more robust and faster than
On the influence of graph density on randomized gossiping
 Proceedings of the 29th IEEE International Parallel & Distributed Processing Symposium (IPDPS
"... Information dissemination is a fundamental problem in parallel and distributed computing. In its simplest variant, known as the broadcasting problem, a single message has to be spread among all nodes of a graph. A prominent communication protocol for this problem is based on the socalled random pho ..."
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Information dissemination is a fundamental problem in parallel and distributed computing. In its simplest variant, known as the broadcasting problem, a single message has to be spread among all nodes of a graph. A prominent communication protocol for this problem is based on the socalled random phone call model (Karp et al., FOCS 2000). In each step, every node opens a communication channel to a randomly chosen neighbor, which can then be used for bidirectional communication. In recent years, several efficient algorithms have been developed to solve the broadcasting problem in this model. Motivated by replicated databases and peertopeer networks, Berenbrink et al., ICALP 2010, considered the socalled gossiping problem in the random phone call model. There, each node starts with its own message and all messages have to be disseminated to all nodes in the network. They showed that any O(log n)time algorithm in complete graphs requires Ω(log n) message transmissions per node to complete gossiping, with high probability, while it is known that in the case of
Distributed Computation of Sparse Cuts
, 2013
"... Finding sparse cuts is an important tool in analyzing largescale distributed networks such as the Internet and PeertoPeer networks, as well as largescale graphs such as the web graph, online social communities, and VLSI circuits. Sparse cuts are useful in graph clustering and partitioning among ..."
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Finding sparse cuts is an important tool in analyzing largescale distributed networks such as the Internet and PeertoPeer networks, as well as largescale graphs such as the web graph, online social communities, and VLSI circuits. Sparse cuts are useful in graph clustering and partitioning among numerous other applications. In distributed communication networks, they are useful for topology maintenance and for designing better search and routing algorithms. In this paper, we focus on developing fast distributed algorithms for computing sparse cuts in networks. Given an undirected nnode network G with conductance φ, the goal is to find a cut set whose conductance is close to φ. We present two distributed algorithms that find a cut set with sparsity Õ( φ) (O ̃ hides polylog n factors). Both our algorithms work in the CONGEST distributed computing model and output a cut of conductance at most Õ( φ) with high probability, in Õ(1b ( 1
How to Optimally Allocate Your Budget of Attention in Social Networks
"... Abstract—We consider the performance of information propagation through social networks in a scenario where each user has a budget of attention, that is, a constraint on the frequency with which he pulls content from neighbors. In this context we ask the question “when users make selfish decisions o ..."
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Abstract—We consider the performance of information propagation through social networks in a scenario where each user has a budget of attention, that is, a constraint on the frequency with which he pulls content from neighbors. In this context we ask the question “when users make selfish decisions on how to allocate their limited access frequency among neighbors, does information propagate efficiently? ” For the metric of average propagation delay, we provide characterizations of the optimal social cost and the social cost under selfish user optimizations for various topologies of interest. Three situations may arise: wellconnected topologies where delay is small even under selfish optimization; treelike topologies where selfish optimization performs poorly while optimal social cost is low; and “stretched ” topologies where even optimal social cost is high. We propose a mechanism for incentivizing users to modify their selfish behaviour, and observe its efficiency in the family of treelike topologies mentioned above. I.
Author manuscript, published in "Social Network Systems (SNS 2012) (2012)" On The Impact of Users Availability In OSNs
, 2012
"... Availability of computing resources has been extensively studied in literature with respect to uptime, session lengths and interarrival times of hardware devices or software applications. Interestingly enough, information related to the presence of users in online applications has attracted less at ..."
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Availability of computing resources has been extensively studied in literature with respect to uptime, session lengths and interarrival times of hardware devices or software applications. Interestingly enough, information related to the presence of users in online applications has attracted less attention. Consequently, only a few attempts have been made to leverage user availability pattern to improve such applications. Based on an availability trace collected from MySpace, we show in this paper that the online presence of users tends to be correlated to those of their friends. We then show that user availability plays an important role in some algorithms and focus on information spreading. In fact, identifying central users i.e. those located in central positions in a network, is key to achieve a fast dissemination and the importance of users in a social graph precisely vary depending on their availability.