Results 1  10
of
20
Quasirandom Rumor Spreading
 In Proc. of SODA’08
, 2008
"... We propose and analyse a quasirandom analogue to the classical push model for disseminating information in networks (“randomized rumor spreading”). In the classical model, in each round each informed node chooses a neighbor at random and informs it. Results of Frieze and Grimmett (Discrete Appl. Mat ..."
Abstract

Cited by 29 (9 self)
 Add to MetaCart
We propose and analyse a quasirandom analogue to the classical push model for disseminating information in networks (“randomized rumor spreading”). In the classical model, in each round each informed node chooses a neighbor at random and informs it. Results of Frieze and Grimmett (Discrete Appl. Math. 1985) show that this simple protocol succeeds in spreading a rumor from one node of a complete graph to all others within O(log n) rounds. For the network being a hypercube or a random graph G(n, p) with p ≥ (1+ε)(log n)/n, also O(log n) rounds suffice (Feige, Peleg, Raghavan, and Upfal, Random Struct. Algorithms 1990). In the quasirandom model, we assume that each node has a (cyclic) list of its neighbors. Once informed, it starts at a random position of the list, but from then on informs its neighbors in the order of the list. Surprisingly, irrespective of the orders of the lists, the above mentioned bounds still hold. In addition, we also show a O(log n) bound for sparsely connected random graphs G(n, p) with p = (log n+f(n))/n, where f(n) → ∞ and f(n) = O(log log n). Here, the classical model needs Θ(log 2 (n)) rounds. Hence the quasirandom model achieves similar or better broadcasting times with a greatly reduced use of random bits.
Quasirandom Rumor Spreading: Expanders, Push vs. Pull, and Robustness
"... Randomized rumor spreading is an efficient protocol to distribute information in networks. Recently, a quasirandom version has been proposed and proven to work equally well on many graphs and better for sparse random graphs. In this work we show three main results for the quasirandom rumor spreading ..."
Abstract

Cited by 21 (6 self)
 Add to MetaCart
(Show Context)
Randomized rumor spreading is an efficient protocol to distribute information in networks. Recently, a quasirandom version has been proposed and proven to work equally well on many graphs and better for sparse random graphs. In this work we show three main results for the quasirandom rumor spreading model. We exhibit a natural expansion property for networks which suffices to make quasirandom rumor spreading inform all nodes of the network in logarithmic time with high probability. This expansion property is satisfied, among others, by many expander graphs, random regular graphs, and ErdősRényi random graphs. For all network topologies, we show that if one of the push or pull model works well, so does the other. We also show that quasirandom rumor spreading is robust against transmission failures. If each message sent out gets lost with probability f, then the runtime increases only by a factor of O(1/(1 − f)).
Tight bounds for rumor spreading in graphs of a given conductance
 In Proc. 28th STACS
, 2011
"... conductance∗ ..."
Broadcasting vs. mixing and information dissemination on Cayley graphs
 In 24th Int. Symp. on Theor. Aspects of Computer Science (STACS
, 2007
"... Abstract. One frequently studied problem in the context of information dissemination in communication networks is the broadcasting problem. In this paper, we study the following randomized broadcasting protocol: At some time t an information r is placed at one of the nodes of a graph G. In the succe ..."
Abstract

Cited by 13 (6 self)
 Add to MetaCart
(Show Context)
Abstract. One frequently studied problem in the context of information dissemination in communication networks is the broadcasting problem. In this paper, we study the following randomized broadcasting protocol: At some time t an information r is placed at one of the nodes of a graph G. In the succeeding steps, each informed node chooses one neighbor, independently and uniformly at random, and informs this neighbor by sending a copy of r to it. First, we consider the relationship between randomized broadcasting and random walks on graphs. In particular, we prove that the runtime of the algorithm described above is upper bounded by the corresponding mixing time, up to a logarithmic factor. One key ingredient of our proofs is the analysis of a continuoustype version of the afore mentioned algorithm, which might be of independent interest. Then, we introduce a general class of Cayley graphs, including (among others) Star graphs, Transposition graphs, and Pancake graphs. We show that randomized broadcasting has optimal runtime on all graphs belonging to this class. Finally, we develop a new proof technique by combining martingale tail estimates with combinatorial methods. Using this approach, we show the optimality of our algorithm on another Cayley graph and obtain new knowledge about the runtime distribution on several Cayley graphs. 1
On the Randomness Requirements of Rumor Spreading
, 2011
"... We investigate the randomness requirements of the classical rumor spreading problem on fully connected graphs with n 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 O((log n) 2) random bits in orde ..."
Abstract

Cited by 11 (4 self)
 Add to MetaCart
We investigate the randomness requirements of the classical rumor spreading problem on fully connected graphs with n 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 O((log n) 2) random bits in order to spread the rumor in O(log n) rounds with high probability (w.h.p.). For the simple quasirandom rumor spreading protocol proposed by Doerr, Friedrich, and Sauerwald (2008), ⌈log n ⌉ random bits per node are sufficient. A lower bound by Doerr and Fouz (2009) shows that this is asymptotically tight for a slightly more general class of protocols, the socalled gatemodel. In this paper, we consider general rumor spreading protocols. We provide a simple pushprotocol that requires only a total of O(n log log n) random bits (i.e., on average O(log log n) bits per node) in order to spread the rumor in O(log n) rounds w.h.p. We also investigate the theoretical minimal randomness requirements of efficient rumor spreading. We prove the existence of a (nonuniform) pushprotocol for which a total of 2 log n + log log n + o(log log n) random bits suffice to spread the rumor in log n + ln n + O(1) rounds with probability 1−o(1). This is contrasted by a simple timerandomness tradeoff for the class of all rumor spreading protocols, according to which any protocol that uses log n − log log n − ω(1) random bits requires ω(log n) rounds to spread the rumor.
Quasirandom rumor spreading: An experimental analysis
 In Proceedings of the Workshop on Algorithm Engineering and Experiments (ALENEX
, 2009
"... We empirically analyze two versions of the wellknown “randomized rumor spreading ” protocol to disseminate a piece of information in networks. In the classical model, in each round each informed node informs a random neighbor. At SODA 2008, three of the authors proposed a quasirandom variant. Here, ..."
Abstract

Cited by 6 (4 self)
 Add to MetaCart
(Show Context)
We empirically analyze two versions of the wellknown “randomized rumor spreading ” protocol to disseminate a piece of information in networks. In the classical model, in each round each informed node informs a random neighbor. At SODA 2008, three of the authors proposed a quasirandom variant. Here, each node has a (cyclic) list of its neighbors. Once informed, it starts at a random position of the list, but from then on informs its neighbors in the order of the list. While for sparse random graphs a better performance of the quasirandom model could be proven, all other results show that, independent of the structure of the lists, the same asymptotic performance guarantees hold as for the classical model. In this work, we compare the two models experimentally. This not only shows that the quasirandom model generally is faster (which was expected, though maybe not to this extent), but also that the runtime is more concentrated around the mean value (which is surprising given that much fewer random bits are used in the quasirandom process). These advantages are also observed in a lossy communication model, where each transmission does not reach its target with a certain probability, and in an asynchronous model, where nodes send at random times drawn from an exponential distribution. We also show that the particular structure of the lists has little influence on the efficiency. In particular, there is no problem if all nodes use an identical order to inform their neighbors. 1
Gossip Protocols for Renaming and Sorting
 DISC 27TH INTERNATIONAL SYMPOSIUM ON DISTRIBUTED COMPUTING
, 2013
"... We devise efficient gossipbased protocols for some fundamental distributed tasks. The protocols assume an nnode network supporting pointtopoint communication, and in every round, each node exchanges information of size O(log n) bits with (at most) one other node. We first consider the renaming ..."
Abstract

Cited by 2 (1 self)
 Add to MetaCart
(Show Context)
We devise efficient gossipbased protocols for some fundamental distributed tasks. The protocols assume an nnode network supporting pointtopoint communication, and in every round, each node exchanges information of size O(log n) bits with (at most) one other node. We first consider the renaming problem, that is, to assign distinct IDs from a small ID space to all nodes of the network. We propose a renaming protocol that divides the ID space among nodes using a natural push or pull approach, achieving logarithmic round complexity with ID space {1,..., (1 + ɛ)n}, for any fixed ɛ> 0. A variant of this protocol solves the tight renaming problem, where each node obtains a unique ID in {1,..., n}, in O(log² n) rounds. Next we study the following sorting problem. Nodes have consecutive IDs 1 up to n, and they receive numerical values as inputs. They then have to exchange those inputs so that in the end the input of rank k is located at the node with ID k. Jelasity and Kermarrec [20] suggested a simple and natural protocol, where nodes exchange values with peers chosen uniformly at random, but it is not hard to see that this protocol requires Ω(n) rounds. We prove that the same protocol works in O(log² n) rounds if peers are chosen according to a nonuniform power law distribution.
How Efficient Can Gossip Be? (On the Cost of Resilient Information Exchange)
"... Gossip, also known as epidemic dissemination, is becoming an increasingly popular technique in distributed systems. Yet, it has remained a partially open question: how robust are such protocols? We consider a natural extension of the random phonecall model (introduced by Karp et al. [1]), and we an ..."
Abstract

Cited by 2 (0 self)
 Add to MetaCart
Gossip, also known as epidemic dissemination, is becoming an increasingly popular technique in distributed systems. Yet, it has remained a partially open question: how robust are such protocols? We consider a natural extension of the random phonecall model (introduced by Karp et al. [1]), and we analyze two different notions of robustness: the ability to tolerate adaptive failures, and the ability to tolerate oblivious failures. For adaptive failures, we present a new gossip protocol, TrickleGossip, which achieves nearoptimal O(n log 3 n) message complexity. To the best of our knowledge, this is the first epidemicstyle protocol that can tolerate adaptive failures. We also show a direct relation between resilience and message complexity, demonstrating that gossip protocols which tolerate a large number of adaptive failures need to use a superlinear number of messages with high probability. For oblivious failures, we present a new gossip protocol, CoordinatedGossip, that achieves optimal O(n) message complexity. This protocol makes novel use of the universe reduction technique to limit the message complexity.
Structure and dynamics of information in networks
 Lecture Notes
, 2011
"... The present notes are derived from a course taught at the University of Southern California. The focus of the course is on the mathematical and algorithmic theory underpinning the connections between networks and information. These connections take two predominant forms: • Network structure itself e ..."
Abstract

Cited by 2 (0 self)
 Add to MetaCart
(Show Context)
The present notes are derived from a course taught at the University of Southern California. The focus of the course is on the mathematical and algorithmic theory underpinning the connections between networks and information. These connections take two predominant forms: • Network structure itself encodes a lot of information. For instance, friendships between individuals let us draw inferences about shared interests or other attributes (location, gender, etc.). Similarly, hyperlinks between documents indicate similar topics, but can also be interested as endorsements, and thus hint at quality. The list of scenarios in which network structure helps us interpret information about individual nodes continues beyond this list, and will be explored in more detail throughout these notes. • Networks also play a crucial role in disseminating or gathering information. This applies both to social networks, in which communication between individuals happens naturally, and computer networks, which are designed explicitly to facilitate the exchange of information and distributed computations. We will draw analogies between the two types of networks, and investigate the mathematical underpinnings of the diffusion of information over networks in the later chapters of these notes. These notes are designed to accompany a onesemester graduatelevel course in computer science. We
Diameter and Broadcast Time of Random Geometric Graphs in Arbitrary Dimensions
 ALGORITHMICA
, 2012
"... A random geometric graph (RGG) is defined by placing n points uniformly at random in [0,n1/d] d, and joining two points by an edge whenever their Euclidean distance is at most some fixed r. We assume that r is larger than the critical value for the emergence of a connected component with Ω(n) nodes ..."
Abstract

Cited by 2 (0 self)
 Add to MetaCart
A random geometric graph (RGG) is defined by placing n points uniformly at random in [0,n1/d] d, and joining two points by an edge whenever their Euclidean distance is at most some fixed r. We assume that r is larger than the critical value for the emergence of a connected component with Ω(n) nodes. We show that, with high probability (w.h.p.), for any two connected nodes with a Euclidean log n distance of ω( rd−1), their graph distance is only a constant factor larger than their Euclidean distance. This implies that the diameter of the largest connected component is Θ(n1/d /r) w.h.p. We also prove that the condition on the Euclidean distance above is essentially tight. We also analyze the following randomized broadcast algorithm on RGGs. At the beginning, only one node from the largest connected component of the RGG is informed. Then, in each round, each informed node chooses a neighbor independently and uniformly at random and informs it. We prove that w.h.p. this algorithm informs every node in the largest connected component of an RGG within Θ(n1/d /r + log n) rounds.