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Decentralized computation of effective resistances and acceleration of consensus algorithms | IEEE Conference Publication | IEEE Xplore

Decentralized computation of effective resistances and acceleration of consensus algorithms


Abstract:

The effective resistance between a pair of nodes in a weighted undirected graph is defined as the potential difference induced between them when a unit current is injecte...Show More

Abstract:

The effective resistance between a pair of nodes in a weighted undirected graph is defined as the potential difference induced between them when a unit current is injected at the first node and extracted at the second node, treating edge weights as the conductance values of edges. The effective resistance is a key quantity of interest in many applications and fields including solving linear systems, Markov Chains and continuous-time averaging networks. We develop an efficient linearly convergent distributed algorithm for computing effective resistances and demonstrate its performance through numerical studies. We also apply our algorithm to the consensus problem where the aim is to compute the average of node values in a distributed manner. We show that the distributed algorithm we developed for effective resistances can be used to accelerate the convergence of the classical consensus iterations considerably by a factor depending on the network structure.
Date of Conference: 14-16 November 2017
Date Added to IEEE Xplore: 08 March 2018
ISBN Information:
Conference Location: Montreal, QC, Canada

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