### Abstract

We analyze a class of distributed quantized consensus algorithms for arbitrary networks. In the initial setting, each node in the network has an integer value. Nodes exchange their current estimate of the mean value in the network, and then update their estimate by communicating with their neighbors in a limited capacity channel in an asynchronous clock setting. Eventually, all nodes reach consensus with quantized precision. We start the analysis with a special case of a distributed binary voting algorithm, then proceed to the expected convergence time for the general quantized consensus algorithm proposed by Kashyap et al. We use the theory of electric networks, random walks, and couplings of Markov chains to derive an O(N^{3} log N) upper bound for the expected convergence time on an arbitrary graph of size N, improving on the state of art bound of O(N^{4} log N) for binary consensus and O(N ^{5}) for quantized consensus algorithms. Our result is not dependent on the graph topology. Simulations are performed to validate the analysis.

Original language | English (US) |
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Title of host publication | 2013 Proceedings IEEE INFOCOM 2013 |

Pages | 600-604 |

Number of pages | 5 |

DOIs | |

State | Published - Sep 2 2013 |

Event | 32nd IEEE Conference on Computer Communications, IEEE INFOCOM 2013 - Turin, Italy Duration: Apr 14 2013 → Apr 19 2013 |

### Publication series

Name | Proceedings - IEEE INFOCOM |
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### Other

Other | 32nd IEEE Conference on Computer Communications, IEEE INFOCOM 2013 |
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Country | Italy |

City | Turin |

Period | 4/14/13 → 4/19/13 |

### Fingerprint

### All Science Journal Classification (ASJC) codes

- Electrical and Electronic Engineering
- Computer Science(all)

### Cite this

*2013 Proceedings IEEE INFOCOM 2013*(pp. 600-604). [6566843] (Proceedings - IEEE INFOCOM). https://doi.org/10.1109/INFCOM.2013.6566843

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*2013 Proceedings IEEE INFOCOM 2013.*, 6566843, Proceedings - IEEE INFOCOM, pp. 600-604, 32nd IEEE Conference on Computer Communications, IEEE INFOCOM 2013, Turin, Italy, 4/14/13. https://doi.org/10.1109/INFCOM.2013.6566843

**An upper bound on the convergence time for quantized consensus.** / Shang, Shang; Cuff, Paul; Hui, Pan; Kulkarni, Sanjeev.

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

TY - GEN

T1 - An upper bound on the convergence time for quantized consensus

AU - Shang, Shang

AU - Cuff, Paul

AU - Hui, Pan

AU - Kulkarni, Sanjeev

PY - 2013/9/2

Y1 - 2013/9/2

N2 - We analyze a class of distributed quantized consensus algorithms for arbitrary networks. In the initial setting, each node in the network has an integer value. Nodes exchange their current estimate of the mean value in the network, and then update their estimate by communicating with their neighbors in a limited capacity channel in an asynchronous clock setting. Eventually, all nodes reach consensus with quantized precision. We start the analysis with a special case of a distributed binary voting algorithm, then proceed to the expected convergence time for the general quantized consensus algorithm proposed by Kashyap et al. We use the theory of electric networks, random walks, and couplings of Markov chains to derive an O(N3 log N) upper bound for the expected convergence time on an arbitrary graph of size N, improving on the state of art bound of O(N4 log N) for binary consensus and O(N 5) for quantized consensus algorithms. Our result is not dependent on the graph topology. Simulations are performed to validate the analysis.

AB - We analyze a class of distributed quantized consensus algorithms for arbitrary networks. In the initial setting, each node in the network has an integer value. Nodes exchange their current estimate of the mean value in the network, and then update their estimate by communicating with their neighbors in a limited capacity channel in an asynchronous clock setting. Eventually, all nodes reach consensus with quantized precision. We start the analysis with a special case of a distributed binary voting algorithm, then proceed to the expected convergence time for the general quantized consensus algorithm proposed by Kashyap et al. We use the theory of electric networks, random walks, and couplings of Markov chains to derive an O(N3 log N) upper bound for the expected convergence time on an arbitrary graph of size N, improving on the state of art bound of O(N4 log N) for binary consensus and O(N 5) for quantized consensus algorithms. Our result is not dependent on the graph topology. Simulations are performed to validate the analysis.

UR - http://www.scopus.com/inward/record.url?scp=84883089141&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84883089141&partnerID=8YFLogxK

U2 - https://doi.org/10.1109/INFCOM.2013.6566843

DO - https://doi.org/10.1109/INFCOM.2013.6566843

M3 - Conference contribution

SN - 9781467359467

T3 - Proceedings - IEEE INFOCOM

SP - 600

EP - 604

BT - 2013 Proceedings IEEE INFOCOM 2013

ER -