Single Source Shortest Paths

What is the least-cost solution for getting from point A to point B?

Shortest Paths Problem

Given a weighted, directed graph G = (V, E) with edge weights w and a path definition of p = <v₀, v₁, .., v_k> with weight w(p) = , find the shortest path weight from vertex u to vertex v

$$\delta(u,v) \;=\; \left\{ \begin{array}{ll} min\{w(p): u \st... ...{\rm to} \; v \\ \infty & {\rm otherwise} \end{array} \right.$$

Breadth-First Search worked on unweighted (unit weight) graphs.