On the properties of optimal weak links in consensus networks

Makan Fardad; Xi Zhang; Fu Lin; Mihailo R. Jovanovic

doi:10.1109/CDC.2014.7039712

On the properties of optimal weak links in consensus networks

Makan Fardad, Xi Zhang, Fu Lin, Mihailo R. Jovanovic

Department of Electrical Engineering & Computer Science

Research output: Contribution to journal › Article › peer-review

5 Scopus citations

Abstract

We study consensus networks in which each node updates its state by taking a weighted average of the states of its neighbors. Our objective is to determine the optimal set of weak links whose addition to the network maximally improves the efficiency of reaching consensus. Allocating a small amount of resources to the entire network with which new links can be created, we employ a perturbation method to cast this problem as a linear program. We demonstrate that the set of optimal weak links is sparse and, based on extensive numerical experiments, conjecture that they are also long-range. Examples are provided to illustrate the utility of our developments.

Original language	English (US)
Article number	7039712
Pages (from-to)	2124-2129
Number of pages	6
Journal	Unknown Journal
Volume	2015-February
Issue number	February
DOIs	https://doi.org/10.1109/CDC.2014.7039712
State	Published - 2014

Keywords

Convex optimization
linear programming
long-range links
opinion dynamics
perturbation analysis
social networks
sparsity

ASJC Scopus subject areas

Control and Systems Engineering
Modeling and Simulation
Control and Optimization

Access to Document

10.1109/CDC.2014.7039712

Fingerprint Dive into the research topics of 'On the properties of optimal weak links in consensus networks'. Together they form a unique fingerprint.

Cite this

@article{f61c0e9ddcbe49b6ab6e9fe049df2c2e,

title = "On the properties of optimal weak links in consensus networks",

abstract = "We study consensus networks in which each node updates its state by taking a weighted average of the states of its neighbors. Our objective is to determine the optimal set of weak links whose addition to the network maximally improves the efficiency of reaching consensus. Allocating a small amount of resources to the entire network with which new links can be created, we employ a perturbation method to cast this problem as a linear program. We demonstrate that the set of optimal weak links is sparse and, based on extensive numerical experiments, conjecture that they are also long-range. Examples are provided to illustrate the utility of our developments.",

keywords = "Convex optimization, linear programming, long-range links, opinion dynamics, perturbation analysis, social networks, sparsity",

author = "Makan Fardad and Xi Zhang and Fu Lin and Jovanovic, {Mihailo R.}",

year = "2014",

doi = "10.1109/CDC.2014.7039712",

language = "English (US)",

volume = "2015-February",

pages = "2124--2129",

journal = "Nuclear Physics A",

issn = "0375-9474",

publisher = "Elsevier",

number = "February",

}

TY - JOUR

T1 - On the properties of optimal weak links in consensus networks

AU - Fardad, Makan

AU - Zhang, Xi

AU - Lin, Fu

AU - Jovanovic, Mihailo R.

PY - 2014

Y1 - 2014

N2 - We study consensus networks in which each node updates its state by taking a weighted average of the states of its neighbors. Our objective is to determine the optimal set of weak links whose addition to the network maximally improves the efficiency of reaching consensus. Allocating a small amount of resources to the entire network with which new links can be created, we employ a perturbation method to cast this problem as a linear program. We demonstrate that the set of optimal weak links is sparse and, based on extensive numerical experiments, conjecture that they are also long-range. Examples are provided to illustrate the utility of our developments.

AB - We study consensus networks in which each node updates its state by taking a weighted average of the states of its neighbors. Our objective is to determine the optimal set of weak links whose addition to the network maximally improves the efficiency of reaching consensus. Allocating a small amount of resources to the entire network with which new links can be created, we employ a perturbation method to cast this problem as a linear program. We demonstrate that the set of optimal weak links is sparse and, based on extensive numerical experiments, conjecture that they are also long-range. Examples are provided to illustrate the utility of our developments.

KW - Convex optimization

KW - linear programming

KW - long-range links

KW - opinion dynamics

KW - perturbation analysis

KW - social networks

KW - sparsity

UR - http://www.scopus.com/inward/record.url?scp=84988044617&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84988044617&partnerID=8YFLogxK

U2 - 10.1109/CDC.2014.7039712

DO - 10.1109/CDC.2014.7039712

M3 - Article

AN - SCOPUS:84988044617

VL - 2015-February

SP - 2124

EP - 2129

JO - Nuclear Physics A

JF - Nuclear Physics A

SN - 0375-9474

IS - February

M1 - 7039712

ER -

On the properties of optimal weak links in consensus networks

Abstract

Keywords

ASJC Scopus subject areas

Access to Document

Other files and links

Cite this