Fast Information Spreading in Graphs with Large Weak Conductance

Censor-Hillel, Keren; Shachnai, Hadas

doi:10.1137/110845380

Cited by 23 publications

(39 citation statements)

References 16 publications

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“…Certainly, the most striking aspect of Theorem 1.1 is that it constitutes the first deterministic gossip algorithm for the broadcast setting studied here and in [4,3]. We feel that this is an interesting and surprising result given the general intuition and the results from [7,16,19,15] that at least some randomness is needed to enable an efficient gossip algorithm.…”

Section: Our Resultsmentioning

confidence: 72%

“…We emphasize that our result does not stem from unusual model assumptions. Exactly as in, e.g., [4,3] we only assume that (1) each node only knows the IDs of its neighbors and (2) two nodes involved in a call can exchange all rumors known to them.…”

Section: Our Resultsmentioning

confidence: 99%

“…In [4] a rumor spreading algorithm was provided which works well for any graph with good weak expansion. This includes some graphs with (few) bottlenecks.…”

Section: Related Workmentioning

confidence: 99%

“…More precisely, the main result is a tight bound of O( log n Φ ) rounds, where Φ is the conductance of the network. More recently, non-uniform random gossip schemes were devised to allow efficient rumor spreading in arbitrary networks [4,3]. The local broadcast problem, that asks each node to exchange rumors locally with all its neighbors, has been a crucial abstraction to obtain results independent from any conductance-type measure.…”

Section: Introductionmentioning

confidence: 99%

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Simple, Fast and Deterministic Gossip and Rumor Spreading

Haeupler

2015

J. ACM

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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 line of work was that uniform gossip completes in O( log n Φ ) rounds where Φ is the conductance of the network. More recently, non-uniform random gossip schemes were devised to allow efficient rumor spreading in networks with bottlenecks. In particular, STOC'12] gave an O(log 3 n) algorithm to solve the 1-local broadcast problem in which each node wants to exchange rumors locally with its 1-neighborhood. 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 k-local broadcast problem in 2(k + log n) log n rounds 1 . 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 its randomized pendant and guarantees success with certainty instead of with high probability. Its analysis is furthermore simple, self-contained, and fundamentally different from prior works. * The conference version of this paper was published in the ACM-SIAM Symposium for Discrete Algorithms [18] where it won a best student paper award.1 Throughout this paper log x denotes log 2 x , that is, the rounded up binary logarithm.

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Section: Our Resultsmentioning

confidence: 72%

Section: Our Resultsmentioning

confidence: 99%

“…In [4] a rumor spreading algorithm was provided which works well for any graph with good weak expansion. This includes some graphs with (few) bottlenecks.…”

Section: Related Workmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Simple, Fast and Deterministic Gossip and Rumor Spreading

Haeupler

2015

J. ACM

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“…This does not yet conclude the proof, for the following reason. The analysis of the synchronous protocol goes through in this simulation except for one argument [5,Claim 1], which bounds the size of the deterministic list of subset of neighbors that is maintained by a node v. This size is bounded by the number of steps taken by v. On one hand, we need the number of steps taken by v in each O(n log (n)) time slots to be at least one to argue the simulation, but on the other hand, it may be that a node takes a larger number of steps. This would imply that its list is larger than in the corresponding synchronous case.…”

Section: Proof Of Theoremmentioning

confidence: 99%

Order optimal information spreading using algebraic gossip

Avin

Borokhovich

Censor-Hillel

et al. 2011

Proceedings of the 30th Annual ACM SIGACT-SIGOPS Symposium on Principles of Distributed Computing

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In this paper we study gossip based information spreading with bounded message sizes. We use algebraic gossip to disseminate k distinct messages to all n nodes in a network. For arbitrary networks we provide a new upper bound for uniform algebraic gossip of O((k + log n + 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).To eliminate the factor of ∆ from the upper bound we propose a non-uniform gossip protocol, TAG, which is based on algebraic gossip and an arbitrary spanning tree protocol S. The stopping time of TAG is O(k + log n + 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.

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Rumor Spreading with Bounded In-Degree

Daum

Kühn

2016

Structural Information and Communication Complexity

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We consider a variant of the well-studied gossip-based model of communication for disseminating information in a network, usually represented by a graph. Classically, in each time unit, every node u is allowed to contact a single random neighbor v. If u knows the data (rumor) to be disseminated, node v learns it (known as push) and if node v knows the rumor, u learns it (known as pull). While in the classic gossip model, each node is only allowed to contact a single neighbor in each time unit, each node can possibly be contacted by many neighboring nodes. If, for example, several nodes pull from the same common neighbor v, v manages to inform all these nodes in a single time unit.In the present paper, we consider a restricted model where at each node only one incoming request can be served in one time unit. As long as only a single piece of information needs to be disseminated, this does not make a difference for push requests. It however has a significant effect on pull requests. If several nodes try to pull the information from the same common neighbor, only one of the requests can be served. In the paper, we therefore concentrate on this weaker pull version, which we call restricted pull.We distinguish two versions of the restricted pull protocol depending on whether the request to be served among a set of pull requests at a given node is chosen adversarially or uniformly at random. As a first result, we prove an exponential separation between the two variants. We show that there are instances where if an adversary picks the request to be served, the restricted pull protocol requires a polynomial number of rounds whereas if the winning request is chosen uniformly at random, the restricted pull protocol only requires a polylogarithmic number of rounds to inform the whole network. Further, as the main technical contribution, we show that if the request to be served is chosen randomly, the slowdown of using restricted pull versus using the classic pull protocol can w.h.p. be upper bounded by O(∆/δ · log n), where ∆ and δ are the largest and smallest degree of the network.

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Fast Information Spreading in Graphs with Large Weak Conductance

Cited by 23 publications

References 16 publications

Simple, Fast and Deterministic Gossip and Rumor Spreading

Simple, Fast and Deterministic Gossip and Rumor Spreading

Order optimal information spreading using algebraic gossip

Rumor Spreading with Bounded In-Degree

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