### 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.

Original language | English (US) |
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Title of host publication | 2017 IEEE Global Conference on Signal and Information Processing, GlobalSIP 2017 - Proceedings |

Publisher | Institute of Electrical and Electronics Engineers Inc. |

Pages | 538-542 |

Number of pages | 5 |

ISBN (Electronic) | 9781509059904 |

DOIs | |

State | Published - Mar 7 2018 |

Event | 5th IEEE Global Conference on Signal and Information Processing, GlobalSIP 2017 - Montreal, Canada Duration: Nov 14 2017 → Nov 16 2017 |

### Publication series

Name | 2017 IEEE Global Conference on Signal and Information Processing, GlobalSIP 2017 - Proceedings |
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Volume | 2018-January |

### Other

Other | 5th IEEE Global Conference on Signal and Information Processing, GlobalSIP 2017 |
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Country | Canada |

City | Montreal |

Period | 11/14/17 → 11/16/17 |

### Fingerprint

### All Science Journal Classification (ASJC) codes

- Information Systems
- Signal Processing

### Cite this

*2017 IEEE Global Conference on Signal and Information Processing, GlobalSIP 2017 - Proceedings*(pp. 538-542). (2017 IEEE Global Conference on Signal and Information Processing, GlobalSIP 2017 - Proceedings; Vol. 2018-January). Institute of Electrical and Electronics Engineers Inc.. https://doi.org/10.1109/GlobalSIP.2017.8308701

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*2017 IEEE Global Conference on Signal and Information Processing, GlobalSIP 2017 - Proceedings.*2017 IEEE Global Conference on Signal and Information Processing, GlobalSIP 2017 - Proceedings, vol. 2018-January, Institute of Electrical and Electronics Engineers Inc., pp. 538-542, 5th IEEE Global Conference on Signal and Information Processing, GlobalSIP 2017, Montreal, Canada, 11/14/17. https://doi.org/10.1109/GlobalSIP.2017.8308701

**Decentralized computation of effective resistances and acceleration of consensus algorithms.** / Aybat, Necdet S.; Gurbuzbalaban, Mert.

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

TY - GEN

T1 - Decentralized computation of effective resistances and acceleration of consensus algorithms

AU - Aybat, Necdet S.

AU - Gurbuzbalaban, Mert

PY - 2018/3/7

Y1 - 2018/3/7

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=85048130703&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85048130703&partnerID=8YFLogxK

U2 - 10.1109/GlobalSIP.2017.8308701

DO - 10.1109/GlobalSIP.2017.8308701

M3 - Conference contribution

T3 - 2017 IEEE Global Conference on Signal and Information Processing, GlobalSIP 2017 - Proceedings

SP - 538

EP - 542

BT - 2017 IEEE Global Conference on Signal and Information Processing, GlobalSIP 2017 - Proceedings

PB - Institute of Electrical and Electronics Engineers Inc.

ER -