# Using Quantization to Deploy Heterogeneous Nodes in Two-Tier Wireless Sensor Networks

## TL;DR

This paper models the deployment of heterogeneous access points and fusion centers in a two-tier wireless sensor network as a quantization problem, optimizing for minimal power consumption through a novel Lloyd algorithm.

## Contribution

It introduces a new optimal cell partition based on a variation of Voronoi diagrams and proposes a Lloyd algorithm for efficient node deployment in heterogeneous networks.

## Key findings

- The proposed algorithm outperforms existing clustering methods in simulations.
- Optimal AP placement is between connected FCs and the cell's geometric center.
- A variation of Voronoi diagrams is used for optimal cell partitioning.

## Abstract

We study a heterogeneous two-tier wireless sensor network in which N heterogeneous access points (APs) collect sensing data from densely distributed sensors and then forward the data to M heterogeneous fusion centers (FCs). This heterogeneous node deployment problem is modeled as a quantization problem with distortion defined as the total power consumption of the network. The necessary conditions of the optimal AP and FC node deployment are explored in this paper. We provide a variation of Voronoi Diagram as the optimal cell partition for this network, and show that each AP should be placed between its connected FC and the geometric center of its cell partition. In addition, we propose a heterogeneous two-tier Lloyd algorithm to optimize the node deployment. Simulation results show that our proposed algorithm outperforms the existing clustering methods like Minimum Energy Routing, Agglomerative Clustering, and Divisive Clustering, on average.