Dynamic graph research is an essential subject in Computer Science. The shortest path problem is still the central in this field; moreover there is a variety of applications in practical projects. In this paper, we select the transportation activity as a paradigm to study. Of course there exists the most clear and appealing practical application over the intelligent navigation, also which is an important part in intelligent transportation system (ITS). Totally speaking, this activity is fairly simple and well-behavior under our consideration, for which, there is a lot of sophisticated theories and techniques to motivate our researches although this problem relates to interdisciplinary; so that we can be dedicated to computing aspect. Below, a host of practical problems will by the way be discussed in theory and empiricism including correctness, sampling, accuracy, compatibility, quick query and the application into other research; therein some have been scarcely argued intentionally or not in literatures before. Through these contents, we are able to have a smart system built which easy to incorporate other modules to realize a sophisticated industrial system.
Abstract The shortest route problems so far analyzed fall seriously short of reality in that they assume that the time required between any two vertices (nodes) is constant, an assumption which is certainly not true in many physical and biological applications. This analysis demonstrates how to perform a shortest route iteration in the more realistic case where internodal time requirements are time-variable. In the paper a modified form of Bellman's iteration scheme [1] for finding the shortest route between any two vertices in a network is developed for application to our generalized case. It converges to the shortest path between any two vertices in a finite number of iterations, and for any initial starting time, provided that certain initial conditions are satisfied. One of the main points of this treatment has been to arrange the work so that when computing a new iterate one does not have to recompute previous iterates at more advanced time points.