Navigatingdensely connected networks can be complex due to the different connection structures present within a network. No explicit algorithms are designed specifically for this navigation, so heuristic approaches and existing network systems are often employed. However, this task can become computationally asymmetrical, as the complexity of creating a representation of the city is lower than the complexity involved in identifying a set of feasible paths in a combinatorial order. This paper extends the applicability of morphological approaches to compute the shortest path in smart cities, driven by the complexity and size of the vital communication infrastructure. As is well known, this communication infrastructure changes dynamically, particularly with the evolving connection paths due to continuous population growth. Consequently, efficient communication trajectories can quickly become obsolete. The challenge of computing the best trajectories to respond more quickly to the growing population comes with high computational complexity. This paper presents an application that uses a discrete algorithm designed to compute the shortest path through a morphological approach. Specifically, it seeks to identify the best trajectory within a densely populated city based on a complex density graph. By incorporating morphological approaches into path-search algorithms, we can define a new family of methods that operate in discrete spaces with a morphological representation, resulting in approaches that have lower computational requirements. Other well-known applications in this context include the delivery of resources, such as managing electrical power consumption or minimizing time delays in resource delivery. This task is essential but classified as an NP problem, making it an appropriate scenario for applying the proposed algorithm to navigate a dense graph. The paper highlights the well-known problem of finding the shortest path as one of the potential applications of the introduced algorithm. The algorithm aims to identify the optimal path trajectory within a graph representing a dense city’s real scenario. This discussion compares and contrasts the proposal with other established approaches, highlighting the advantages and characteristics of the proposed method.
Read full abstract