Gen-FW: A Generalization of the Fermat-Weber Problem with Applications to Data Processing

Abstract

The project "Gen-FW: A Generalization of the Fermat-Weber Problem with Applications to Data Processing" was a project affiliated with the Vicerrectoría de Investigación y Extensión (VIE) of the Instituto Tecnológico de Costa Rica during the years 2020-2022. This project proposes a generalization of the well-known Fermat-Weber problem, or simply the FW problem, in addition to studying computational aspects and applications in image processing. The FW problem calculates a vector that minimizes the sum of weighted distances with respect to other given vectors in a vector space, where the vector to be optimized is represented by a linear transformation. The FW problem has garnered growing interest due to its valuable applications in various engineering fields, such as in navigation algorithm design and establishing connectivity in mobile networks with wireless sensors, among other relevant applications.

In this article, we will provide a concise yet comprehensive overview of the contributions obtained during the development of this project. The Gen-FW project offers a new perspective in the field of data processing and represents a significant advancement in solving complex problems with practical applications in various engineering areas.