Run Dijkstra to compute the Shortest Path Spanning Tree (SPST) for each vertex used as source. Note that the array of predecessors completely specifies the SPST.

Single Source Shortest Paths: Given G = (V; E); w and a source vertex S, nd (S; V ) [and the best path] from S to each v 2 V . Data structures: d[v]

All-Pairs Shortest Paths: Earlier, we saw that Dijkstra’s algorithm and the Bellman-Ford al-gorithm both solved the problem of computing shortest paths in graphs from a single source vertex. Suppose that …

Shortest Paths: Today we consider the problem of computing shortest paths in a directed graph. We are given a digraph G = (V, E) and a source vertex s ∈ V , and we want to compute the shortest path …

Problem. Given a directed graph G = (V, E ) with positive edge weights: that is, each edge e ∈ E has a positive weight w(e) and vertices s and t , find the shortest path from s to t . The shortest path from s …

In this chapter, we concern exclusively with shortest path problems in directed networks. If all arc lengths are positive, then an undirected network can be converted to a directed one with each arc …

T is a shortest-path tree from v to the nodes in T, and ˆd(u) = d(u) for every u ∈ T.