Manufacturing consent

Author

Borkar, Vivek S. ; Nair, Jayakrishnan ; Sanketh, Nalli

Author_Institution

Sch. of Technol. & Comput. Eng., Tata Inst. of Fundamental Res., Mumbai, India

fYear

2010

fDate

Sept. 29 2010-Oct. 1 2010

Firstpage

1550

Lastpage

1555

Abstract

A scheme for consensus formation is considered wherein the value of a certain variable associated with the nodes of a network is fixed a priori for a prescribed set of K nodes, and allowed to propagate throughout the network through an averaging process that mimics a gossip algorithm. The objective is to find the best choice of these K nodes that will achieve the fastest convergence to consensus. This objective is captured by the Perron-Frobenius eigenvalue of the resultant sub-stochastic matrix, which then is the quantity one seeks to minimize. We propose an algorithm for this optimization problem, as well as a greedy scheme with some performance guarantees for a variant of the problem that seeks to minimize a simpler objective. Some other related formulations are also considered.

Keywords

convergence; eigenvalues and eigenfunctions; greedy algorithms; matrix algebra; minimisation; network theory (graphs); social sciences; stochastic processes; K nodes; Perron-Frobenius eigenvalue; averaging process; consensus formation; gossip algorithm; greedy scheme; optimization problem; substochastic matrix; Convergence; Dynamic programming; Eigenvalues and eigenfunctions; Greedy algorithms; Heuristic algorithms; Markov processes; Optimization;

fLanguage

English

Publisher

ieee

Conference_Titel

Communication, Control, and Computing (Allerton), 2010 48th Annual Allerton Conference on

Conference_Location

Allerton, IL

Print_ISBN

978-1-4244-8215-3

Type

conf

DOI

10.1109/ALLERTON.2010.5707097

Filename

5707097