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Note on optimal gossiping in some weak-connected graphs

1994
*
Theoretical Computer Science
*

Introduction

doi:10.1016/0304-3975(94)90049-3
fatcat:3oqbdbnaj5c2vecaxkqdz4zfgq
*In*this paper we shall investigate the problem of dissemination of information*in**some**weak*-*connected**graphs*. ...*In*this way we obtain*optimal**gossip*algorithms for*some*families of*graphs*which have at least*one*bridge or at least*one*cycle which is edge-disjoint from all other cycles*in*the*graph*. ...##
###
Page 562 of Mathematical Reviews Vol. , Issue 95a
[page]

1995
*
Mathematical Reviews
*

*weak*-

*connected*

*graphs*. ... A direct consequence of these lower bounds is the construction of

*optimal*

*gossip*algorithms for

*some*families of

*weak*-

*connected*

*graphs*. ...

##
###
Order Optimal Information Spreading Using Algebraic Gossip
[article]

2011
*
arXiv
*
pre-print

*In*turn, this leads to the

*optimally*of TAG

*on*these

*graphs*for k=Ω(polylog(n)). ... The second uses a sophisticated, recent

*gossip*protocol to build a fast spanning tree

*on*

*graphs*with large

*weak*conductance. ... for broadcast

*on*

*graphs*with large

*weak*conductance. ...

##
###
Consensus and Products of Random Stochastic Matrices: Exact Rate for Convergence in Probability

2013
*
IEEE Transactions on Signal Processing
*

Finally, we apply our results to

doi:10.1109/tsp.2013.2248003
fatcat:fbsn2btcb5cubcoyljnbcanwby
*optimally*allocate the sensors' transmission power*in*consensus+innovations distributed detection. ... Further, for commonly used random models like with*gossip*and link failure, we show that the rate I is found by solving a min-cut problem and, hence, easily computable. ...*In*the*gossip*algorithm, only*one*link is active at a time. Let be the probability of occurrence of link . We*note*that . Lemma 16: Consider a*gossip*model*on*a*graph*with link probabilities . ...##
###
Randomized gossiping with unreliable communication: Dependent or independent node updates

2012
*
2012 IEEE 51st IEEE Conference on Decision and Control (CDC)
*

*Weak*

*connectivity*is required when the communication is perfectly dependent, while double

*connectivity*is required when the communication is independent. ... These results indicate the fundamental role the node interactions have

*in*randomized

*gossip*algorithms. ... (

*Weak*

*Connectivity*) The underlying

*graph*G 0 is weakly

*connected*. ...

##
###
Optimal algorithms for dissemination of information in generalized communication modes
[chapter]

1992
*
Lecture Notes in Computer Science
*

*Some*generalized communication modes enabling the dissemination of information among processors of interconnection networks via vertex-disjoint or edge-disjoint paths

*in*

*one*communication step will be ... For those networks

*in*which a Hamiltonian path exists (hypercubes, cube

*connected*cycles, butterflies, shuffle exchange, etc.)

*optimal*algorithms can be obtained quite easily, but for complete binary trees ... An interesting fact proved here is that also for the

*weak*

*connected*

*graphs*(

*graphs*which can be partitioned into two or more components be removing a constant number of edges), the

*optimal*

*gossip*algorithm ...

##
###
Optimal algorithms for dissemination of information in generalized communication modes

1994
*
Discrete Applied Mathematics
*

*Some*generalized communication modes enabling the dissemination of information among processors of interconnection networks via vertex-disjoint or edge-disjoint paths

*in*

*one*communication step will be ... For those networks

*in*which a Hamiltonian path exists (hypercubes, cube

*connected*cycles, butterflies, shuffle exchange, etc.)

*optimal*algorithms can be obtained quite easily, but for complete binary trees ... An interesting fact proved here is that also for the

*weak*

*connected*

*graphs*(

*graphs*which can be partitioned into two or more components be removing a constant number of edges), the

*optimal*

*gossip*algorithm ...

##
###
Author Index Volume 127 (1994)

1994
*
Theoretical Computer Science
*

Monien,

doi:10.1016/0304-3975(94)90050-7
fatcat:zyznrn7m4nhgfofcltok6asss4
*Note**on**optimal**gossiping**in**some**weak*-*connected**graphs*(*Note*) Ikeda, Y., see C. Hosono Iliopoulos, C.S., see J.W. Daykin Inoue, K., A. Ito and I. ... Takanami,*On*l-inkdot alternating Turing machines with small space (*Note*) Ito, A., see K. Inoue Jain, S. and A. Sharma, Program size restrictions*in*computational learning Jantzen. M. and H. ...##
###
Weighted Gossip: Distributed Averaging using non-doubly stochastic matrices

2010
*
2010 IEEE International Symposium on Information Theory
*

While Uniform

doi:10.1109/isit.2010.5513273
dblp:conf/isit/BenezitBTTV10
fatcat:v6vvtiheafcl3c7d3catrwma2u
*Gossip*works synchronously*on*complete*graphs*, weighted*gossip*algorithms allow asynchronous rounds and converge*on*any*connected*, directed or undirected*graph*. ... Double-stochasticity being very restrictive*in*a distributed setting [7], this novel degree of freedom is essential and it opens the perspective of designing a large number of new*gossip*-based algorithms ...*On*random geometric*graphs*, Pairwise*Gossip*requires Θ(n 2 ) messages whereas Path Averaging requires only Θ(n log n) messages under*some*conditions [5] . ...##
###
Page 4619 of Mathematical Reviews Vol. , Issue 97G
[page]

1997
*
Mathematical Reviews
*

.; Laskar, Renu (1-CLEM; Clemson, SC)
Cyclic

*gossiping*times for*some*classes of*graphs*. (English summary ) Networks 28 (1996), no. 3, 135-141. ... We give upper bounds*on*the forwarding index*in*k-*connected*digraphs and*in*digraphs with half-degrees at least k. Related conjectures are proposed.” ...##
###
Global Computation in a Poorly Connected World: Fast Rumor Spreading with No Dependence on Conductance
[article]

2011
*
arXiv
*
pre-print

*In*this paper, we give an algorithm that solves the information dissemination problem

*in*at most O(D+polylog(n)) rounds

*in*a network of diameter D, withno dependence

*on*the conductance. ...

*In*fact, we prove that something stronger is true: any algorithm that requires T rounds

*in*the LOCAL model can be simulated

*in*O(T +polylog(n)) rounds

*in*the

*GOSSIP*model. ... The uniform

*gossip*mixes well

*on*well-

*connected*

*graphs*, and good bounds for its convergence

*in*terms of the

*graph*conductance have been given [4, 13, 23] . ...

##
###
Convergence of Gossip Algorithms for Consensus in Wireless Sensor Networks with Intermittent Links and Mobile Nodes

2014
*
Mathematical Problems in Engineering
*

By nonnegative matrix theory and ergodicity coefficient theory, we prove

doi:10.1155/2014/836584
fatcat:ivwve523vfazpgwva3cn4ym3cm
*gossip*algorithms surely converge as long as the*graph*is partitionally weakly*connected*which,*in*comparison with existing analysis ... Furthermore,*on*the condition that the*graph*is partitionally strongly*connected*, the rate of convergence is proved to be exponential and governed by the second largest eigenvalue of expected coefficient ...*In*addition, we define the partitionally*weak**connection*and partitionally strong*connection*as the elementary assumption for subsequent discussion*on*convergence and the rate of convergence, respectively ...##
###
Accelerated Gossip in Networks of Given Dimension using Jacobi Polynomial Iterations
[article]

2019
*
arXiv
*
pre-print

The

arXiv:1805.08531v4
fatcat:yubf6p77ojdupaif4lg5wvzlxi
*gossip*problem consists*in*estimating the average of the values diffused*in*the network*in*a distributed manner. ... We develop a method solving the*gossip*problem that depends only*on*the spectral dimension of the network, that is,*in*the communication network set-up, the dimension of the space*in*which the agents live ... ∼ w, that is v and w are*connected**in*the*graph*. ...##
###
A gossip algorithm for convex consensus optimization over networks

2010
*
Proceedings of the 2010 American Control Conference
*

*In*many applications, nodes

*in*a network wish to achieve not only a consensus, but an

*optimal*

*one*. ... Moreover, we show that PE admits a common Lyapunov function and reduces to the well-studied Pairwise Averaging and Randomized

*Gossip*Algorithm

*in*a special case. ...

*Note*that if the

*graph*(V, ∪ M ℓ=1 E ℓ ) is not

*connected*, it means that the set V of nodes can be partitioned into two nonempty subsets V 1 and V 2 , such that after

*some*finite time, the nodes

*in*V 1 ...

##
###
Global computation in a poorly connected world

2012
*
Proceedings of the 44th symposium on Theory of Computing - STOC '12
*

As such, researchers have focused

doi:10.1145/2213977.2214064
dblp:conf/stoc/Censor-HillelHKM12
fatcat:hizel6da6rckrpzjxgdzqgeydm
*on*the uniform*gossip*algorithm,*in*which each node independently selects a neighbor uniformly at random. When the*graph*is well-*connected*, 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 ...*weak*conductance of the*graph*, a measure of*connectivity*of subsets*in*the*graph*. ...
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