Single-Pair Shortest-Path using Dijkstra

Suppose we have a graphG in which the number of vertices distance d away from any given vertex is roughly b (in other words, our graph has a branching factor of b). An example of a graph like this is the Rubik’s cube state graph. If we have n total vertices in this graph, then we can roughly estimate the diameter of the graph to be logb n if we assume that the last layer outwards dominates the number of nodes. In these highly branching situations, bidirectional search can be used to speed up the DIJKSTRA modification to solve the singlepair shortest-path problem. Notice that the speedup does not change worst-case behavior, but reduces the number of visited vertices in practice.