Urban Transport and Traffic Systems: An Approach to the Shortest Path Problem and Network Flow Through Colored Graphs

Urban transport systems generally present complex topologies and constraints, and consequently model them and propose solutions that are not simple. Because of the importance of proposing solutions that improve urban mobility and the people’s quality of life, in this work, we propose two algorithms applicable to transport network and traffic systems. The first algorithm approaches the shortest path problem in colored graphs. In this case, the graphs’ coloration is used in a different and innovative form: each transport mode is represented by a color (label) and various edges exist between two nodes of the graph (each edge represents a transport mode). The second algorithm, in addition to the coloration used to find the shortest path, considers the multimodal flow network problem by an incremental process. Some examples are presented and the behavior of both algorithms is shown.