CMSC 425 : Lecture 16 Motion Planning : Computing Shortest Paths

Computing Shortest Paths: The problem of computing shortest paths in graphs is very well studied. Recall that a directed graph (or digraph) G = (V,E) is a finite set of nodes (or vertices) V and a set of ordered pairs of nodes, called edges E (see Fig. 1(a)). If (u, v) is an edge, we say that v is adjacent to u (or alternately, that v is a neighbor of u). In most geometric settings, graphs are undirected, since if you get from u to v, you can get from v to u. It is often convenient to use a directed graph representation, however, since it allows you to model the fact that travel in one direction (say up hill) may be more expensive than travel in the reversed direction.