State-Space Graphs with Weighted Edges
Let S be space of possible states.
Let (si, sj) be an edge representing a move from si to sj.
w(si, sj) is the weight or cost associated with moving from si to sj.
The cost of a path [ (s1, s2), (s2, s3), . . ., (sn-1, sn) ] is the sum of the weights of its edges.
A minimum-cost path P from s1 to sn has the property that for any other path P’ from s1 to sn, cost(P) ? cost(P’).