The Contraction Coefficient of a Complete Gossip Sequence,

Liu, J.; Morse, A. Stephen; Anderson, Brian D. O.; Yu, Changbin

doi:10.1007/978-3-642-11278-2_19

Cited by 8 publications

(4 citation statements)

References 11 publications

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“…It is an interesting research question to determine sufficient and necessary conditions that characterize digraphs that are doubly stochasticable via weight assignments that can have some zero entries and still preserve the graph connectivity. Regarding Proposition 3.11, note that even if connectivity is preserved, fewer edges lead to smaller algebraic connectivity [38], which in turn affects negatively the rate of convergence of the consensus, optimization, and gossip algorithms executed over doubly stochastic digraphs, see e.g., [5,8,13,21].…”

Section: Corollary 38 (Necessary and Sufficient Condition For Doublymentioning

confidence: 99%

“…Examples include distributed averaging [6,28,32,39] and distributed convex optimization [19,25,40]. Convergence in gossip algorithms also relies on the structure of doubly stochastic digraphs, see [5,21].…”

mentioning

confidence: 99%

“…Our focus in this paper is on nonzero weight assignments. In addition to its theoretical interest, the consideration of nonzero weight assignments is also relevant from a practical perspective, as the use of the maximum number of edges leads to higher algebraic connectivity [38], which in turn affects positively the rate of convergence [5,8,13,21] of the algorithms typically executed over doubly stochastic digraphs. Alternative versions of the problem, where some edge weights are allowed to be zero, are also worth exploring, although we do not consider them here.…”

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confidence: 99%

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Distributed Strategies for Generating Weight-Balanced and Doubly Stochastic Digraphs

Gharesifard

Cortés

2012

European Journal of Control

146

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This paper deals with the design and analysis of dynamical systems on directed graphs (digraphs) that achieve weight-balanced and doubly stochastic assignments. Weight-balanced and doubly stochastic digraphs are two classes of digraphs that play an essential role in a variety of coordination problems, including formation control, agreement, and distributed optimization. We refer to a digraph as doubly stochasticable (weight-balanceable) if it admits a doubly stochastic (weightbalanced) adjacency matrix. This paper studies the characterization of both classes of digraphs, and introduces distributed dynamical systems to compute the appropriate set of weights in each case. It is known that semiconnectedness is a necessary and sufficient condition for a digraph to be weightbalanceable. The first main contribution is a characterization of doubly-stochasticable digraphs. As a by-product, we unveil the connection of this class of digraphs with weight-balanceable digraphs. The second main contribution is the synthesis of a distributed strategy running synchronously on a directed communication network that allows individual agents to balance their in-and out-degrees. We show that a variation of our distributed procedure over the mirror graph has a much smaller time complexity than the currently available centralized algorithm based on the computation of the graph cycles. The final main contribution is the design of two cooperative strategies for finding a doubly stochastic weight assignment. One algorithm works under the assumption that individual agents are allowed to add self-loops. For the case when this assumption does not hold, we introduce an algorithm distributed over the mirror digraph which allows the agents to compute a doubly stochastic weight assignment if the digraph is doubly stochasticable and announce otherwise if it is not. Various examples illustrate the results.

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Section: Corollary 38 (Necessary and Sufficient Condition For Doublymentioning

confidence: 99%

mentioning

confidence: 99%

mentioning

confidence: 99%

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Distributed Strategies for Generating Weight-Balanced and Doubly Stochastic Digraphs

Gharesifard

Cortés

2012

European Journal of Control

146

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“…6. We invented new tools for analyzing convergence rates for consensus and gossiping algorithms [7,12,15].…”

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confidence: 99%

Intelligent Distributed Control

Morse¹

2012

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When does a digraph admit a doubly stochastic adjacency matrix?

Gharesifard

Cortés

2010

Proceedings of the 2010 American Control Conference

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The Contraction Coefficient of a Complete Gossip Sequence,

Cited by 8 publications

References 11 publications

Distributed Strategies for Generating Weight-Balanced and Doubly Stochastic Digraphs

Distributed Strategies for Generating Weight-Balanced and Doubly Stochastic Digraphs

Intelligent Distributed Control

When does a digraph admit a doubly stochastic adjacency matrix?

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