# Dynamic Median Consensus Over Random Networks

arXiv: https://arxiv.org/abs/2110.05317 · HTML: https://mlsanity.com/paper/2110.05317/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 11 Oct 2021.

## Built on by (most cited first, 1 of 1)

- [Distributed Maximum Consensus over Noisy Links](https://mlsanity.com/paper/2403.18509/) (2024)

## Abstract (arXiv)

This paper studies the problem of finding the median of N distinct numbers distributed across networked agents. Each agent updates its estimate for the median from noisy local observations of one of the N numbers and information from neighbors. We consider an undirected random network that is connected on average, and a noisy observation sequence that has finite variance and almost surely decaying bias. We present a consensus+innovations algorithm with clipped innovations. Under some regularity assumptions on the network and observation model, we show that each agent's local estimate converges to the set of median(s) almost surely at an asymptotic sublinear rate. Numerical experiments demonstrate the effectiveness of the presented algorithm.