A new public transportation data model and shortest-path algorithms

By studying the best-path problem for public transportation systems, we found that the nature of transfer is that it requires extra costs from an edge to its adjacent edge. Therefore, we propose the notion of direct/indirect adjacent edges in weighted directed multigraphs and extend the notion of path to the line. We use the direct/indirect adjacent edges weighted directed multigraph as a public transportation data model and improve the storage of an adjacency matrix. We introduce the space storage structure, the matrix VL, in order to store the scattered information of transfer in indirect adjacent edges lists. Thus, we solve the problem of complex network graphs´ storage and design a new shortest path algorithm to solve transit problem based on the data model we propose in this paper. Algorithm analysis exhibits that the data model and the algorithm we propose are prior to a simple graph based on the Dijkstra´s algorithm in terms of time and space.