IMF: Iterative Max-Flow for Node Localizability Detection in Barycentric Linear Localization

TL;DR

This paper introduces an efficient iterative max-flow algorithm to detect localizable nodes in barycentric linear localization, addressing a gap in existing localizability theories for this emerging schema.

Contribution

It proposes necessary and sufficient conditions for node localizability in barycentric linear localization and develops an iterative max-flow algorithm to identify such nodes.

Findings

The IMF algorithm accurately detects localizable nodes.

Theoretical analysis confirms the algorithm's correctness.

Experimental results demonstrate efficiency and effectiveness.

Abstract

Determining whether nodes can be uniquely localized, called localizability detection, is a concomitant problem of network localization. Localizability under traditional Non-Linear Localization (NLL) schema has been well explored, whereas localizability under the emerging Barycentric coordinate-based Linear Localization (BLL) schema has not been well touched. In this paper, we investigate the deficiency of existing localizability theories and algorithms in BLL, and then propose a necessary condition and a sufficient condition for BLL node localizability. Based on these two conditions, an efficient iterative maximum flow (IMF) algorithm is designed to identify BLL localizable nodes. Finally, our algorithms are validated by both theoretical analysis and experimental evaluations.