# Optimal Routing in Urban Road Networks: A Graph-Based Approach Using [PERSON]'s Algorithm
## 2 Literature Review  
Through an extensive review of the literature on the shortest path in urban traffic networks, the authors conclude that a large number of specialists and researchers have studied this demanding and comprehensive problem. Despite the papers published so far, there is still a significant gap that can be filled with new research in the field of determining the shortest path in urban traffic networks. The following provides a critical analysis of the existing shortest path algorithms, as well as a comparative analysis of different shortest path algorithms. In the paper by [PERSON] et al., 2023, the authors address the problem of route analysis in modern urban transportation service systems and provide appropriate passenger transport plans. The paper proposes an improved A* algorithm to solve optimal path analysis for constrained networks, aiming to provide reasonable solutions for public transportation travel, specifically the combination of metro, bus, ferry, and other modes of transport within the urban public transportation network [6]. [PERSON] and others, in their 2021 paper, propose a new method for calculating statistical parameters based on a unidirectional road network model that is more aligned with the real world, as well as an algorithm for path planning in dynamically constrained search areas. In their work, they use [PERSON]'s algorithm and also emphasize that, despite the methods for shortest path calculation developed so far, there is still significant room for further research to fill the gaps in this area. In this context, they suggest that future proposed shortest path algorithms should incorporate the delay time at signalized intersections [7]. In their 2021 study, [PERSON] and others investigate a method for finding the shortest path in a road network using the example of the city of Cartagena. The core concept of this paper lies in considering the city's topology and, consequently, the development of the transportation network through the topology of the terrain throughout history. A limitation of this algorithm is that it uses the simplest model, without considering the characteristic factors that influence the formation of the transportation network, such as waiting times at signalized intersections, traffic flow density, agent movement speed, and the peak hours during the day for determining the shortest route [8]. [PERSON] and others, in their 2023 paper, studied four algorithms for finding the shortest path in a graph, of which two actually find the optimal path: the A* algorithm and [PERSON]'s algorithm. [PERSON]'s algorithm always finds optimal paths, but it can be concluded from the test results that it may potentially explore many nodes before reaching the target. On the other hand, A* uses heuristics to determine which nodes are better to explore next, giving it a \"direction\" toward the target node. The study is presented with a limited number of nodes. In future research, the developed simulator should be improved by adding more nodes and edges [9]. In their 2023 paper, [PERSON] and others present an improved discrete Jaya algorithm for solving the shortest path problem. The time complexity of the Jaya algorithm is analyzed. This solution adds a term that can randomly generate neighboring nodes to improve the quality of the shortest path solution. Further research is focused on enhancing the algorithm for large traffic networks [10]. In their 2024 paper, [PERSON] and others propose three methods for the shortest path problem. The dynamic interval (DI) graph models the uncertainty of curve costs in the graph, showing great potential for application in planning and managing unstable road transportation. Despite the updated data, the dynamic robust shortest path (DRSP) model is not better than the dynamic greedy robust shortest path (DGRSP) and dynamic mean shortest path (DMSP) models in many cases. The models have limitations. The DRSP model does not perform well in complex traffic networks.