Graph Theory to Optimize the Coverage Network for Public Educational Institutions in the Southern Province of Sumapaz (Colombia)
Abstract
This article determines the fastest travel routes from the University of Cundinamarca (Fusagasugá campus) to public educational institutions in the southern province of Sumapaz (Colombia) to optimize the planning of extracurricular activities. Graph theory is applied, modeling the region's road network as a weighted graph, with the weight of the edges being the travel times between municipalities, population centers, and villages, obtained from Google Maps. Dijkstra's algorithm is used to calculate the minimum cost paths from the origin node to the most distant destinations, structuring the analysis into four strategic routes, which allows the identification of optimal routes and the quantification of minimum travel times. As a result, the fastest travel time to institutions in Cumaca is 59 minutes, to Bateas is 68 minutes, to Cabrera is 146 minutes, and to the village of Andes is 150 minutes, thus confirming that graph theory, applying Dijkstra's algorithm, is an effective and reliable method for route optimization in complex rural contexts, providing a quantitative basis for logistics planning and efficient resource allocation.
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Copyright (c) 2026 Eva Patricia Vásquez Gómez, Jorge Enrique Quevedo Buitrago, Diego Orlando Méndez Pineda , Ana Esperanza Merchán Hernández , Wilson Daniel Gordillo Ochoa
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