Tractable approximation algorithms for the NP-hard problem of growing linear consensus networks

In this paper, we investigate a network synthesis problem that aims to improve the performance of noisy linear consensus networks by establishing a few new interconnection links throughout the network. This network synthesis problem can be equivalently formulated as an optimization problem over a se...

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Bibliographic Details
Published in:Proceedings of the American Control Conference pp. 6429 - 6434
Main Authors: Siami, Milad, Motee, Nader
Format: Conference Proceeding Journal Article
Language:English
Published: American Automatic Control Council (AACC) 01.07.2016
Subjects:
Approximation
Approximation algorithms
Couplings
Eigenvalues and eigenfunctions
Exact solutions
Interconnection
Laplace equations
Links
Mathematical analysis
Network synthesis
Networks
Noise measurement
Optimization
ISSN:2378-5861
Online Access:Get full text
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Summary:In this paper, we investigate a network synthesis problem that aims to improve the performance of noisy linear consensus networks by establishing a few new interconnection links throughout the network. This network synthesis problem can be equivalently formulated as an optimization problem over a set of candidate graphs, which is inherently combinatorial and NP-hard. We propose an exact solution for this problem when only one new link needs to be established. In this case, a closed form expression is calculated for the optimal value of the systemic performance measure of the augmented network. When it is required to establish more than one interconnection link, we propose two tractable approximate methods with computable performance bounds. Moreover, in order to be able to calculate sub-optimality gaps of our proposed approximate algorithms, we quantify the best achievable performance bounds for the network synthesis problem.
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ISSN:2378-5861
DOI:10.1109/ACC.2016.7526681