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The Power of Local Information in Social Networks
, 2012
"... We study the power of local information algorithms for optimization problems on social and technological networks. We focus on sequential algorithms for which the network topology is initially unknown and is revealed only within a local neighborhood of vertices that have been irrevocably added to th ..."
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We study the power of local information algorithms for optimization problems on social and technological networks. We focus on sequential algorithms for which the network topology is initially unknown and is revealed only within a local neighborhood of vertices that have been irrevocably added to the output set. The distinguishing feature of this setting is that locality is necessitated by constraints on the network information visible to the algorithm, rather than being desirable for reasons of efficiency or parallelizability. In this sense, changes to the level of network visibility can have a significant impact on algorithm design. This framework captures situations in which the optimizer is an external agent that does not have direct access to the network data, but rather learns about the graph structure only via (costly) queries. For instance, a user may wish to strategically find, and form connections to, highdegree nodes in an online social network. An appropriatealgorithm for this search problem must take into account the fact that the structure of the graph is not known in advance, and is only revealed locally as nodes are added to the user’s set of connections. Given this limited network visibility, how should the user choose which connections to form? This question is
Rumor Spreading in Random Evolving Graphs
"... In this paper, we aim at analyzing the classical information spreading Push protocol in dynamic networks. We consider the edgeMarkovian evolving graph model which captures natural temporal dependencies between the structure of the network at time t, and the one at time t + 1. Precisely, a nonedg ..."
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In this paper, we aim at analyzing the classical information spreading Push protocol in dynamic networks. We consider the edgeMarkovian evolving graph model which captures natural temporal dependencies between the structure of the network at time t, and the one at time t + 1. Precisely, a nonedge appears with probability p, while an existing edge dies with probability q. In order to fit with realworld traces, we mostly concentrate our study on the case where p = Ω ( 1 n) and q is constant. We prove that, in this realistic scenario, the Push protocol does perform well, completing information spreading in O(log n) time steps, w.h.p., even when the network is, w.h.p., disconnected at every log n n time step (e.g., when p ≪). The bound is tight. We also address other ranges of parameters p and q (e.g., p+q = 1 with arbitrary p and q, and p = Θ () 1 with arbitrary q). Although they do not precisely fit with n the measures performed on realworld traces, they can be of independent interest for other settings. The results in these cases confirm the positive impact of dynamism.
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
Breathe Before Speaking: Efficient Information Dissemination Despite Noisy, Limited and Anonymous Communication
 In Proc. of the ACM Symp. on Principles of Distributed Computing (PODC ’14
, 2014
"... ar ..."
RandomnessEfficient Rumor Spreading
, 1304
"... We study the classical rumor spreading problem, which is used to spread information in an unknown network with n nodes. We present the first protocol for any expander graph G with n nodes and minimum degree Θ(n) such that, the protocol informs every node in O(logn) rounds with high probability, and ..."
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We study the classical rumor spreading problem, which is used to spread information in an unknown network with n nodes. We present the first protocol for any expander graph G with n nodes and minimum degree Θ(n) such that, the protocol informs every node in O(logn) rounds with high probability, and uses O(lognloglogn) random bits in total. The runtime of our protocol is tight, and the randomness requirement of O(lognloglogn) random bits almost matches the lower bound of Ω(logn) random bits. We further study rumor spreading protocols for more general graphs, and for several graph topologies our protocols are as fast as the classical protocol and use Õ(logn) random bits in total, in contrast to O(nlog 2 n) random bits used in the wellknown rumor spreading push protocol. These results together give us almost full understanding of the randomness requirement for this basic epidemic process. Ourprotocolsrelyonanovelreductionbetweenrumorspreadingprocessesandbranching programs, and this reduction provides a general framework to derandomize these complex and distributed epidemic processes. Interestingly, one cannot simply apply PRGs for branching programs as rumor spreading process is not characterized by smallspace computation. Our protocols require the composition of several pseudorandom objects, e.g. pseudorandom generators, and pairwise independent generators. Besides designing rumor spreading protocols, the techniques developed here may have applications in studying the randomness complexity of distributed algorithms.
Branching Random Walks on Graphs
"... We study a new distributed randomized information propagation mechanism in networks that we call a branching random walk (BRW). BRW is a generalization of the wellstudied “standard ” random walk which is a fundamental primitive useful in a wide variety of network applications ranging from token man ..."
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We study a new distributed randomized information propagation mechanism in networks that we call a branching random walk (BRW). BRW is a generalization of the wellstudied “standard ” random walk which is a fundamental primitive useful in a wide variety of network applications ranging from token management and load balancing to search, routing, information propagation and gossip. BRW is parameterized by a branching factor k. The process starts from an arbitrary node, which is labeled active for step 1. For instance, this could be a node that has a piece of data, rumor, or a virus. In a BRW, in any step, each active node chooses k random neighbors to become active for the next step. A node is active for step t + 1 only if it is chosen by an active node in step t. This results in a branching type process in the underlying network which has interesting properties that are strikingly different from the standard random walk, which is equivalent to BRW with branching factor k = 1. Similar to the standard random walk, we focus on the cover time, which is the the number of steps for the walk to reach all the nodes and the partial cover time, which is the number of steps needed for the walk to reach at least a constant fraction of the nodes. We derive almosttight bounds on cover time and partial cover time in expander graphs, an important
Associate Team acronym: RADCON Principal investigator (Inria):
"... Over recent years, computing systems have seen a massive increase in parallelism and interconnectivity. Peertopeer systems, adhoc networks, sensor networks, or the “cloud ” are based on highly connected and volatile networks. Individual nodes such as cell phones, desktop computers or high perfor ..."
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Over recent years, computing systems have seen a massive increase in parallelism and interconnectivity. Peertopeer systems, adhoc networks, sensor networks, or the “cloud ” are based on highly connected and volatile networks. Individual nodes such as cell phones, desktop computers or high performance computing systems rely on parallel processing power achieved through multiple processing units. To exploit the power of massive networks or multiple processors, algorithms must cope with the scale and asynchrony of these systems, and their inherent instability, e.g., due to node, link, or processor failures. In this research project we explore randomized algorithms for largescale networks of distributed systems, and for shared memory multiprocessor systems. For largescale networks, decentralized gossip protocols have emerged as a standard approach to achieving faulttolerant communication between nodes with simple and scalable algorithms. We will devise new gossip protocols for various complex distributed tasks, and we will explore the power and limits of gossip protocols in various settings. For shared memory systems, randomized algorithms have proved extremely useful to deal with asynchrony and failures. Sometimes probabilistic algorithms provide the only solution to a problem; sometimes they are more efficient; sometimes they are simply easier to implement. We will devise efficient algorithms for some of the fundamental problems of shared memory computing, such as mutual exclusion, renaming, and consensus.