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 | |
| State | Published - 2014 |
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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
Cite this
On the properties of optimal weak links in consensus networks. / Fardad, Makan; Zhang, Xi; Lin, Fu; Jovanovic, Mihailo R.
In: Unknown Journal, Vol. 2015-February, No. February, 7039712, 2014, p. 2124-2129.Research output: Contribution to journal › Article
}
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
VL - 2015-February
SP - 2124
EP - 2129
JO - Nuclear Physics A
JF - Nuclear Physics A
SN - 0375-9474
IS - February
M1 - 7039712
ER -