# Triangle Extension: Efficient Localizability Detection in Wireless Sensor Networks

## TL;DR

This paper introduces a distributed algorithm for localizability detection in wireless sensor networks that is efficient, accurate, and scalable, outperforming existing methods in simulations and real-world tests.

## Contribution

It presents a novel distributed approach with proven correctness that detects more localizable nodes using fewer known locations, with linear time complexity.

## Key findings

- Outperforms existing algorithms in latency and accuracy
- Detects more localizable nodes with fewer known locations
- Operates with linear time complexity

## Abstract

Determining whether nodes can be localized, called localizability detection, is essential for wireless sensor networks (WSNs). This step is required for localizing nodes, achieving low-cost deployments, and identifying prerequisites in location-based applications. Centralized graph algorithms are inapplicable to a resource-limited WSN because of their high computation and communication costs, whereas distributed approaches may miss a large number of theoretically localizable nodes in a resource-limited WSN. In this paper, we propose an efficient and effective distributed approach in order to address this problem. Furthermore, we prove the correctness of our algorithm and analyze the reasons our algorithm can find more localizable nodes while requiring fewer known location nodes than existing algorithms, under the same network configurations. The time complexity of our algorithm is linear with respect to the number of nodes in a network. We conduct both simulations and real-world WSN experiments to evaluate our algorithm under various network settings. The results show that our algorithm significantly outperforms the existing algorithms in terms of both the latency and the accuracy of localizability detection.