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Note on optimal gossiping in some weak-connected graphs

Juraj Hromkovič, Claus-Dieter Jeschke, Burkhard Monien
1994 Theoretical Computer Science  
Introduction 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.  ... 
doi:10.1016/0304-3975(94)90049-3 fatcat:3oqbdbnaj5c2vecaxkqdz4zfgq

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]

Chen Avin, Michael Borokhovich, Keren Censor-Hillel, Zvi Lotker
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.  ... 
arXiv:1101.4372v1 fatcat:pdvivppj5bchjhaaan3hlktzp4

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

Dragana Bajovic, ao Xavier, eM. F. Moura, Bruno Sinopoli
2013 IEEE Transactions on Signal Processing  
Finally, we apply our results to 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 .  ... 
doi:10.1109/tsp.2013.2248003 fatcat:fbsn2btcb5cubcoyljnbcanwby

Randomized gossiping with unreliable communication: Dependent or independent node updates

Guodong Shi, Mikael Johansson, Karl Henrik Johansson
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.  ... 
doi:10.1109/cdc.2012.6426729 dblp:conf/cdc/ShiJJ12 fatcat:i6ksmqd7inb7vme5svpgaii324

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

R. Feldmann, J. Hromkovic, S. Madhavapeddy, B. Monien, P. Mysliwietz
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  ... 
doi:10.1007/3-540-55599-4_84 fatcat:64zeze37ivaj5d67tzedqqpysu

Optimal algorithms for dissemination of information in generalized communication modes

R. Feldmann, J. Hromkovič, S. Madhavapeddy, B. Monien, P. Mysliwietz
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  ... 
doi:10.1016/0166-218x(94)90179-1 fatcat:yic5npkmdnbyfir27f3cslumzm

Author Index Volume 127 (1994)

1994 Theoretical Computer Science  
Monien, 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.  ... 
doi:10.1016/0304-3975(94)90050-7 fatcat:zyznrn7m4nhgfofcltok6asss4

Weighted Gossip: Distributed Averaging using non-doubly stochastic matrices

Florence Benezit, Vincent Blondel, Patrick Thiran, John Tsitsiklis, Martin Vetterli
2010 2010 IEEE International Symposium on Information Theory  
While Uniform 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] .  ... 
doi:10.1109/isit.2010.5513273 dblp:conf/isit/BenezitBTTV10 fatcat:v6vvtiheafcl3c7d3catrwma2u

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]

Keren Censor-Hillel, Bernhard Haeupler, Jonathan A. Kelner, Petar Maymounkov
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] .  ... 
arXiv:1104.2944v1 fatcat:t7ipiqb6bjdtzckvygdowmuo7a

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

Shaochuan Wu, Jiayan Zhang, Yuguan Hou, Xu Bai
2014 Mathematical Problems in Engineering  
By nonnegative matrix theory and ergodicity coefficient theory, we prove 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  ... 
doi:10.1155/2014/836584 fatcat:ivwve523vfazpgwva3cn4ym3cm

Accelerated Gossip in Networks of Given Dimension using Jacobi Polynomial Iterations [article]

Raphaël Berthier, Pierre Gaillard
2019 arXiv   pre-print
The 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.  ... 
arXiv:1805.08531v4 fatcat:yubf6p77ojdupaif4lg5wvzlxi

A gossip algorithm for convex consensus optimization over networks

Jie Lu, Choon Yik Tang, P R Regier, T D Bow
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  ... 
doi:10.1109/acc.2010.5530844 fatcat:v676sd3tsfejfalxiiiot5nwba

Global computation in a poorly connected world

Keren Censor-Hillel, Bernhard Haeupler, Jonathan Kelner, Petar Maymounkov
2012 Proceedings of the 44th symposium on Theory of Computing - STOC '12  
As such, researchers have focused 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.  ... 
doi:10.1145/2213977.2214064 dblp:conf/stoc/Censor-HillelHKM12 fatcat:hizel6da6rckrpzjxgdzqgeydm
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