Path-finding is one of the most popular subjects in the field of computer science. Pathfinding strategies determine a path from a given coordinate to another. The focus of this paper is on finding the optimal path for the bus transportation system based on passenger demand. This study is based on bus stations in Incheon, South Korea, and we show that our modified A* algorithm performs better than other basic pathfinding algorithms such as the Genetic and Dijkstra. Our proposed approach can find the shortest path in real-time even for large amounts of data(points).

Shortest path planning is a fundamental building block in many applications. Hence developing efficient methods for computing shortest paths in e.g. road or grid networks is an important challenge. The most successful techniques for fast query answering rely on preprocessing. But for many of these techniques it is not fully understood why they perform so remarkably well and theoretical justification for the empirical results is missing. An attempt to explain the excellent practical performance of preprocessing based techniques on road networks (as transit nodes, hub labels, or contraction hierarchies) in a sound theoretical way are parametrized analyses, e.g., considering the highway dimension or skeleton dimension of a graph. But these parameters tend to be large (order of Θ(√ n )) when the network contains grid-like substructures — which inarguably is the case for real-world road networks around the globe. In this paper, we use the very intuitive notion of bounded growth graphs to describe road networks and also grid graphs. We show that this model suffices to prove sublinear search spaces for the three above mentioned state-of-the-art shortest path planning techniques. For graphs with a large highway or skeleton dimension, our results turn out to be superior. Furthermore, our preprocessing methods are close to the ones used in practice and only require randomized polynomial time.

TRANSIT is a fast and optimal technique for computing shortest path costs in road networks. It is attractive for its usually modest memory requirements and impressive running times. In this paper we give a first analysis of TRANSIT routing on a set of popular grid-based video-game benchmarks taken from the AI pathfinding literature. We show that in the presence of path symmetries, which are inherent to most grids but normally not road networks, TRANSIT is strongly and negatively impacted, both in terms of performance and memory requirements. We address this problem by developing a new general symmetry breaking technique which adds small random epsilon-values to edges in the search graph, reducing the size of the TRANSIT network by up to 4 times while preserving optimality. Using our enhancements TRANSIT achieves up to four orders of magnitude speed improvement vs. A* search and uses in many cases only a small (<=10MB) or modest (<= 50MB) amount of memory. We also compare TRANSIT with CPDs, a recent and very fast database-driven pathfinding approach. We find the algorithms have complementary strengths but also identify a class of problems for which TRANSIT is up to two orders of magnitude faster than CPDs using a comparable amount of memory.