Dijkstra’s shortest path algorithm is currently the most commonly used shortest path algorithms used in GIS systems today.  Not only is it a popular shortest path algorithm in GIS systems, but also is also widely used in programs made for network modeling.  The biggest drawback to Dijkstras algorithm is that it does not work with negative lengths.  Edsger Dijkstra, who is currently a professor at the University of Texas, discovered the algorithm.  It turns out that one can find the shortest paths from a given source to all points in a graph in the same time, hence this problem is sometimes called the single-source shortest path problem.  It tends to be relatively fast and efficient compared to other algorithms solving the same problem.

Another shortest path algorithm is Floyd’s Algorithm.  In the algorithm’s process it looks for the best yet path to find a final path that is better than all others.  Depending on the size of the graph this algorithm may take more time than Dijkstras algorithm but has the potential to find a solution as good as or better than Dijkstras algorithm.  The Bellman Ford algorithm can be applied to a more general case problem than that of Dijkstras algorithm, but may not produce as good of a result.  Another way of finding the shortest path is by using the Topological Ordering algorithm.  This algorithm can find a shortest path in linear time but may not find the best-case path.  The A-Star (A*) algorithm is also a commonly used algorithm for shortest path problems.  When implemented, the A* algorithm can find a solution as good a Dijkstras with less of a burden on memory.  The main reason why it is not used as much as Dijkstras algorithm is because it tends to be much more difficult to implement when used to solve a shortest path problem.