Results 1 - 10
of
11
Tight bounds for rumor spreading in graphs of a given conductance
- In Proc. 28th STACS
, 2011
"... conductance∗ ..."
Ultra-fast rumor spreading in social networks
- In SODA
, 2012
"... We analyze the popular push-pull protocol for spreading a rumor in networks. Initially, a single node knows of a rumor. In each succeeding round, every node chooses a random neighbor, and the two nodes share the rumor if one of them is already aware of it. We present the first theoretical analysis o ..."
Abstract
-
Cited by 18 (2 self)
- Add to MetaCart
(Show Context)
We analyze the popular push-pull protocol for spreading a rumor in networks. Initially, a single node knows of a rumor. In each succeeding round, every node chooses a random neighbor, and the two nodes share the rumor if one of them is already aware of it. We present the first theoretical analysis of this protocol on random graphs that have a power law degree distribution with an arbitrary exponent β> 2. Our main findings reveal a striking dichotomy in the performance of the protocol that depends on the exponent of the power law. More specifically, we show that if 2 < β < 3, then the rumor spreads to almost all nodes in Θ(log log n) rounds with high probability. On the other hand, if β> 3, then Ω(log n) rounds are necessary. We also investigate the asynchronous version of the push-pull protocol, where the nodes do not operate in rounds, but exchange information according to a Poisson process with rate 1. Surprisingly, we are able to show that, if 2 < β < 3, the rumor spreads even in constant time, which is much smaller than the typical distance of two nodes. To the best of our knowledge, this is the first result that establishes a gap between the synchronous and the asynchronous protocol. 1
Fast Information Spreading in Graphs with Large Weak Conductance
"... Gathering data from nodes in a network is at the heart of many distributed applications, most notably, while performing a global task. We consider information spreading among n nodes of a network, where each node v has a message m(v) which must be received by all other nodes. The time required for i ..."
Abstract
-
Cited by 17 (2 self)
- Add to MetaCart
(Show Context)
Gathering data from nodes in a network is at the heart of many distributed applications, most notably, while performing a global task. We consider information spreading among n nodes of a network, where each node v has a message m(v) which must be received by all other nodes. The time required for information spreading has been previously upper-bounded with an inverse relationship to the conductance of the underlying communication graph. This implies high running times for graphs with small conductance. The main contribution of this paper is an information spreading algorithm which overcomes communication bottlenecks and thus achieves fast information spreading for a wide class of graphs, despite their small conductance. As a key tool in our study we use the recently defined concept of
On the complexity of asynchronous gossip
- In Proceedings of the 27th ACM Symposium on Principles of Distributed Computing (PODC
"... We study the complexity of gossip in an asynchronous, message-passing fault-prone distributed system. We show that an adaptive adversary can significantly hamper the spreading of a rumor, while an oblivious adversary cannot. The algorithmic techniques proposed in this article can be used for improvi ..."
Abstract
-
Cited by 15 (6 self)
- Add to MetaCart
We study the complexity of gossip in an asynchronous, message-passing fault-prone distributed system. We show that an adaptive adversary can significantly hamper the spreading of a rumor, while an oblivious adversary cannot. The algorithmic techniques proposed in this article can be used for improving the message complexity of distributed algorithms that rely on an all-to-all message exchange paradigm and are designed for an asynchronous environment. As an example, we show how to improve the message complexity of asynchronous randomized consensus.
The worst case behavior of randomized gossip
"... This paper considers the quasi-random rumor spreading model introduced by Doerr, Friedrich, and Sauerwald in [SODA 2008], hereafter referred to as the list-based model. Each node is provided with a cyclic list of all its neighbors, chooses a random position in its list, and from then on calls its n ..."
Abstract
-
Cited by 3 (0 self)
- Add to MetaCart
This paper considers the quasi-random rumor spreading model introduced by Doerr, Friedrich, and Sauerwald in [SODA 2008], hereafter referred to as the list-based model. Each node is provided with a cyclic list of all its neighbors, chooses a random position in its list, and from then on calls its neighbors in the order of the list. This model is known to perform asymptotically at least as well as the random phone-call model, for many network classes. Motivated by potential applications of the list-based model to live streaming, we are interested in its worst case behavior. Our first main result is the design of an O(m + n log n)-time algorithm that, given any n-node m-edge network G, and any source-target pair s, t ∈ V (G), computes the maximum number of rounds it may take for a rumor to be broadcast from s to t in G, in the list-based model. This algorithm yields an O(n(m + n log n))-time algorithm that, given any network G, computes the maximum number of rounds it may take for a rumor to be broadcast from any source to any target, in the list-based model. Hence, the list-based model is computationally easy to tackle in its basic version. The situation is radically different when one is considering variants of the model in which nodes are aware of the status of their neighbors, i.e., are aware of whether or not they have already received the rumor, at any point in time. Indeed, our second main result states that, unless P = NP, the worst case behavior of the list-based model with the additional feature that every node is perpetually aware of which of its neighbors have already received the rumor cannot be approximated in polynomial time within a ( 1 n) 1 2 −ɛ multiplicative factor, for any ɛ> 0. As a byproduct of this latter result, we can show that, unless P = NP, there are no PTAS enabling to approximate the worst case behavior of the list-based model, whenever every node perpetually keeps track of the subset of its neighbors which have sent the rumor to it so far.
Aggregation in Dynamic Networks
"... The aggregation problem assumes that every process starts an execution with a unique token (an abstraction for data). The goal is to collect these tokens at a minimum number of processes by the end of the execution. This problem is particularly relevant to mobile networks where peer-to-peer communic ..."
Abstract
-
Cited by 1 (0 self)
- Add to MetaCart
The aggregation problem assumes that every process starts an execution with a unique token (an abstraction for data). The goal is to collect these tokens at a minimum number of processes by the end of the execution. This problem is particularly relevant to mobile networks where peer-to-peer communication is cheap (e.g., using 802.11 or Bluetooth), but uploading data to a central server can be costly (e.g., using 3G/4G). With this in mind, we study this problem in a dynamic network model, in which the communication graph can change arbitrarily from round to round. We start by exploring global bounds. First we prove a negative result that shows that in general dynamic graphs no algorithm can achieve any measure of competitiveness against the optimal offline algorithm. Guided by this impossibility result, we focus our attention to dynamic graphs where every node interacts, at some point in the execution, with at least a p-fraction of the total number of nodes in the graph. We call these graphs p-clusters. We describe a distributed algorithm that in p-clusters aggregates the tokens to O(log n) processes with high probability. We then turn our attention to local bounds. Specifically we ask whether its possible to aggregate to O(log n) processes in parts of the graph that locally form a p-cluster. Here we prove a negative result: this is only possible if the local p-clusters are sufficiently isolated from the rest of the graph. We then match this result with an algorithm that achieves the desired aggregation given (close to) the minimal required p-cluster isolation. Together, these results imply a “paradox of connectivity”: in some graphs, increasing connectivity can lead to inherently worse aggregation performance. We conclude by considering what it seems to be a promising performance metric to circumvent our lower bounds for local aggregation algorithms. However, perhaps surprisingly, we show that no aggregation algorithm can perform well with respect to this metric, even in very well connected and very well isolated clusters. 1
Making Evildoers Pay: Resource-Competitive Broadcast in Sensor Networks
- In Proceedings of the 31th Symposium on Principles of Distributed Computing (PODC
, 2012
"... ar ..."
(Show Context)
Faster rumor spreading with multiple calls
"... We consider the random phone call model introduced by Demers et al.,which is a well-studied model for information dissemination in networks. One basic protocol in this model is the so-called Push protocol that proceeds in synchronous rounds. Starting with a single node which knows of a rumor, every ..."
Abstract
- Add to MetaCart
(Show Context)
We consider the random phone call model introduced by Demers et al.,which is a well-studied model for information dissemination in networks. One basic protocol in this model is the so-called Push protocol that proceeds in synchronous rounds. Starting with a single node which knows of a rumor, every informed node calls in each round a random neighbor and informs it of the rumor. The Push-Pull protocol works similarly, but additionally every uninformed node calls a random neighbor and may learn the rumor from it. It is well-known that both protocols need Θ(log n) rounds to spread a rumor on a complete network with n nodes. Here we are interested in how much the spread can be speeded up by enabling nodes to make more than one call in each round. We propose a new model where the number of calls of a node is chosen independently according to a probability distribution R. We provide both lower and upper bounds on the rumor spreading time depending on statistical properties of R such as the mean or the variance (if they exist). In particular, if R follows
