Dijkstra's and A-Star in Finding the Shortest Path: a Tutorial

Abstract

As one form of the greedy algorithm, Dijkstra's can handle the shortest path search with optimum result in longer search time. Dijkstra's is contrary to A-Star, a best-first search algorithm, which can handle the shortest path search with a faster time but not always optimum. By looking at the advantages and disadvantages of Dijkstra's and A-Star, this tutorial discusses the implementation of the two algorithms in finding the shortest path in routes selection between 24 SPBU (gas stations). The routes are located in Medan City and represented in a directed graph. Moreover, the authors compare Dijkstra's and A-star based on the complexity of Big-Theta (Θ) and running time. The results show that the shortest path search between SPBU can be solved with Dijkstra's and A-Star, where in some cases, the routes produced by the two algorithms are different so that the total distance generated is also different. In this case, the running time of A-Star is proven to be faster than Dijkstra's, and it is following A-Star principle which selects the location point based on the best heuristic value while Dijkstra's does not. For the complexity, Dijkstra's is $\Theta(\mathrm{n}^{2})$ and A-Star is $\Theta(\mathrm{m}\ast \mathrm{n})$, where $0\leq \mathrm{m}\leq \mathrm{n}$.