El algoritmo de Dijkstra desde el álgebra tropical

Abstract

This work presents a formulation and algorithmic implementation of the shortest path problem in directed graphs using the tropical algebra framework, starting with a theoretical description of tropical semirings and their application to optimization problems, followed by the construction of a symbolic algorithm capable of operating on tropical graph representations; the methodology is validated through its application to a road network in the city of Bogotá, represented as a graph derived from real geographic data, and through symbolic evaluations and optimal path visualizations, it is demonstrated that the tropical approach is not only mathematically sound but also useful and efficient from a computational perspective; the work concludes that tropical algebra enables new ways to model, analyze, and solve classical graph theory problems.