Dykstra's Algorithm - Concept
This algorithm was originally developed within the mathematically sphere of knowledge to solve for different puzzles what the shortest path between two points is. The mathematics behind the algorithm can become quite complex so I am only going to summarize in saying that the Dykstra Algorithm is used in OSPF (Open Shortest Path First) during the route determination phase. The algorithm makes some assumptions, including that all paths have a positive cost. It also can handle sevaral paths to the destination and effectively compare them. Of note, when speaking about OSPF, the shortest path is not necessarily the path with the least amount of hops.
More information can be found at many websites on the Internet. One of the better and easier to understand ones is available at theory.stanford.edu. It is an email conversation among several programmers, including some who are just beginning, so the explanations tend to be easier than normal for this topic.