Invariant Properties and Bounds on a Finite Time Consensus Algorithm

Toulouse, Michel; Minh, Bùi Quang; Minh, Quang Tran

doi:10.1007/978-3-662-58808-6_2

Cited by 4 publications

(4 citation statements)

References 33 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…In addition to the probabilistic upper-bound result on the number of time-steps for (general) distributed function computation via linear iterative schemes with random weight-matrix, Sundaram and Hadjicostis [11,12] employ observability theory of linear systems to study the linear-functional case for distributed computation (of linear functions), and achieve an upper bound via the minimal polynomial of the underlying weight-matrix. Toulouse and Minh [15] study the linear functional case with prescribed time-invariant network-topology over random weight-matrices, and obtain various empirical upper-bound results.…”

Section: Resultsmentioning

confidence: 99%

See 1 more Smart Citation

Lower-Bound Study for Function Computation in Distributed Networks via Vertex-Eccentricity

Dai

Toulouse

2019

SN COMPUT. SCI.

View full text Add to dashboard Cite

Distributed computing network-systems are modeled as graphs with vertices representing compute elements and adjacencyedges capturing their uni-or bi-directional communication. Distributed function computation has a wide spectrum of major applications in distributed systems. Distributed computation over a network-system proceeds in a sequence of time-steps in which vertices update and/or exchange their values based on the underlying algorithm constrained by the time-(in)variant network-topology. For finite convergence of distributed information dissemination and function computation in the model, we present a lower bound on the number of time-steps for vertices to receive (initial) vertex-values of all vertices regardless of underlying protocol or algorithmics in time-invariant networks via the notion of vertex-eccentricity in a graph-theoretic framework. We also address lower bounds on vertex-eccentricity and its maximum version in terms of common graphparameters such as maximum degree, and order and size.

show abstract

Section: Resultsmentioning

confidence: 99%

“…Toulouse and Minh [15] refute the conjecture via the notion of rank-step sequences for linear iterative schemes over connected network with an explicit counter-example in Fig. 1.…”

Section: Motivation Of Our Studymentioning

confidence: 86%

Lower-Bound Study for Function Computation in Distributed Networks via Vertex-Eccentricity

Dai

Toulouse

2019

SN COMPUT. SCI.

View full text Add to dashboard Cite

show abstract

“…Toulouse and Minh [18] refute the conjecture via the notion of rank-step sequences for linear iterative schemes over a small-scale (explicit) connected network. We extend the explicit counter-example in Fig.…”

Section: Our Recent Studies On Distributed Function Computationmentioning

confidence: 95%

“…Toulouse and Minh [18] study the linear functional case with prescribed time-invariant network-topology over random weight-matrices, and obtain various empirical upperbound results.…”

Section: Related Work In Literaturementioning

confidence: 99%

Extremal Problem with Network-Diameter and -Minimum-Degree for Distributed Function Computation

Dai

Toulouse

2020

SN COMPUT. SCI.

View full text Add to dashboard Cite

Distributed function computation has a wide spectrum of major applications in distributed systems. Distributed computation over a network-system proceeds in a sequence of time-steps in which vertices update and/or exchange their values based on the underlying algorithm constrained by the time-(in)variant network-topology. Distributed computing network-systems are modeled as directed/undirected graphs with vertices representing compute elements and adjacency-edges capturing their uni-or bi-directional communication. To quantify an intuitive tradeoff between two graph-parameters: minimum vertexdegree and diameter of the underlying graph, we formulate an extremal problem with the two parameters: for all positive integers n and d, the extremal value ∇(n, d) denotes the least minimum vertex-degree among all connected order-n graphs with diameters of at most d. We prove matching upper and lower bounds on the extremal values of ∇(n, d) for various combinations of n-and d-values.

show abstract

Distributed Finite-Time Termination for Consensus Algorithm in Switching Topologies

Saraswat

Khatana

Patel

et al. 2023

IEEE Trans. Netw. Sci. Eng.

View full text Add to dashboard Cite

Invariant Properties and Bounds on a Finite Time Consensus Algorithm

Cited by 4 publications

References 33 publications

Lower-Bound Study for Function Computation in Distributed Networks via Vertex-Eccentricity

Lower-Bound Study for Function Computation in Distributed Networks via Vertex-Eccentricity

Extremal Problem with Network-Diameter and -Minimum-Degree for Distributed Function Computation

Distributed Finite-Time Termination for Consensus Algorithm in Switching Topologies

Contact Info

Product

Resources

About