# Optimal Routing in Urban Road Networks: A Graph-Based Approach Using [PERSON]'s Algorithm
## 2 Literature Review
The development of new RTSP models, as well as the application of the developed methods in practical applications, are future research directions [11]. In their 2022 paper, [PERSON] and others model a road network system using the concept of a semi-directed graph and determine the shortest paths. In the semi-directed graph, the concepts of directed and undirected edges are introduced together into the graph. Therefore, in this paper, a modified Floyd-Warshall algorithm is proposed. The proposed algorithm is executed in two phases. The first phase of the algorithm is capable of converting all undirected edges into directed edges. Then, all undirected edges of the semi-directed graph are converted into directed edges, and the semi-directed graph is transformed into a directed graph. The second phase of the proposed algorithm is able to identify the shortest path using the Floyd-Warshall algorithm. Future research suggests evaluating the congestion of undirected edges [12]. In their 2021 paper, [PERSON] and others propose a new model of situational road networks, based on situational information, applied to the emergency route planning framework on an equally spaced network for finding the shortest path. A heuristic search methodology for the situational network is proposed, which can be used for detecting vehicles passing through congestion networks and finding the fastest route to the destination. The route planning methodology includes a search strategy inspired by the network, based on a quaternion function [13]. In their 2024 paper, [PERSON] and others develop an integrated traffic management system taking into account user preferences in order to optimize the performance of each user. Connected vehicles are introduced into the system to assess traffic conditions and costs associated with different user preferences. Microscopic simulations were conducted to evaluate the effectiveness of the transportation system in alleviating road congestion, reducing fuel consumption, and limiting turns [14]. In the paper by [PERSON] et al. (2023), a technique is proposed for calculating the shortest path based on the costs of the most optimal paths and nodes using instances of road graphs in different time intervals to reduce traffic congestion for real drivers in urban areas. The proposed method is effective when traffic congestion in urban environments is lower. It is suggested that the model be applied to other cities as well. The application of the method in two different cities yielded varying accuracy, primarily due to the model being trained on a larger or smaller dataset of taxi trajectories from the cities, which resulted in more accurate or less accurate outcomes [15]. [PERSON] (2023) proposes a collaborative intelligent algorithm for traffic planning based on artificial intelligence, which uses traffic sensors to determine traffic congestion and the optimal driving path for vehicles. This traffic flow planning algorithm takes into account both local and global traffic flow modules, and based on this, it estimates the timely arrival of vehicles or their delays [16]. In the work by [PERSON] et al. (2025), they expand the applicability of morphological approaches for calculating the shortest path in smart cities, driven by the complexity and size of vital communication infrastructure. The applied algorithm aims to identify the optimal path within a graph that represents the real scenario of a dense city [17]. Analyzing the shortest path algorithm through the literature, it can be concluded that the contribution was made by [PERSON] and [PERSON] in 1988. This paper presents eight algorithms that solve the shortest path problem on directed graphs, and the main emphasis in this paper is on the implementation of different data structures that are used in algorithms [18]. The study by [PERSON] et al. (1993) does not provide a single code for all classes of shortest path problems but proposes two algorithms, one for networks with negative arcs and one for networks without negative arcs.