Application of Binary Programming and Graph Theory for Optimal Camera Allocation in the Santa Elena Urbanization

Abstract

This research addressed the optimization of video surveillance camera placement using binary programming and graph theory in the Santa Elena neighborhood. In this context, the main objective of this project was to design a mathematical model to determine the optimal placement of video surveillance cameras, in order to maximize coverage of critical points and, consequently, strengthen citizen security. To achieve this, binary integer programming was applied, which allowed for the optimal selection of resources, and graph theory was also used to represent the connections and relationships between vulnerable areas. Furthermore, the research followed a quantitative approach with a non-experimental design, supported by the collection of data on crime rates and the spatial distribution of the neighborhood. As a result, it was evident that the proposal significantly reduced unmonitored areas and optimized resources compared to a traditional scheme, thus ensuring greater strategic coverage with fewer cameras. In summary, it is concluded that the integration of advanced mathematical tools constitutes an effective alternative for planning urban security systems, contributing to both crime prevention and improving the perception of security among the residents of Santa Elena. It is also applicable to other communities with similar problems.