### Abstract

We revisit the quantized consensus problem on undirected connected graphs, and obtain some strong results on expected time to convergence. This is unbiased consensus, because the edges emanating from a node have equal probability of being selected. The paper first develops an approach that bounds the expected convergence time of the underlying discrete-time dynamics. The bounds are tight for some simple networks when there exists some symmetry in the network. Following this, the paper provides a tight expression for the expected convergence time of unbiased quantized consensus over general networks. Finally, the paper shows that the expected convergence time can be expressed in terms of the effective resistances of the associated Cartesian product graph. The approach adopted in the paper uses the theory of harmonic functions for reversible Markov chains.

Original language | English (US) |
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Title of host publication | 2013 IEEE 52nd Annual Conference on Decision and Control, CDC 2013 |

Publisher | Institute of Electrical and Electronics Engineers Inc. |

Pages | 6190-6195 |

Number of pages | 6 |

ISBN (Print) | 9781467357173 |

DOIs | |

State | Published - Jan 1 2013 |

Event | 52nd IEEE Conference on Decision and Control, CDC 2013 - Florence, Italy Duration: Dec 10 2013 → Dec 13 2013 |

### Publication series

Name | Proceedings of the IEEE Conference on Decision and Control |
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ISSN (Print) | 0191-2216 |

### Other

Other | 52nd IEEE Conference on Decision and Control, CDC 2013 |
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Country | Italy |

City | Florence |

Period | 12/10/13 → 12/13/13 |

### ASJC Scopus subject areas

- Control and Systems Engineering
- Modeling and Simulation
- Control and Optimization

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## Cite this

*2013 IEEE 52nd Annual Conference on Decision and Control, CDC 2013*(pp. 6190-6195). [6760867] (Proceedings of the IEEE Conference on Decision and Control). Institute of Electrical and Electronics Engineers Inc.. https://doi.org/10.1109/CDC.2013.6760867