Suppose you want to find the shortest path between two intersections on a map, a starting point and a destination. To accomplish this, you could highlight the streets (tracing the streets with a marker) in a certain order, until you have a route highlighted from the starting point to the destination. The order is conceptually simple: at each iteration, create a set of intersections consisting of every unmarked intersection that is directly connected to a marked intersection, this will be your set of considered intersections. From that set of considered intersections, find the closest intersection to the destination (this is the "greedy" part, as described above) and highlight it and mark that street to that intersection, draw an arrow with the direction, then repeat. In each stage mark just one new intersection. When you get to the destination, follow the arrows backwards. There will be only one path back against the arrows, the shortest one.