Modified Search Problem: Directed Graph

  • Recognize BFS/DFS can be carried on a directed graph.
  • Trace the shortest path algorithm in an unweighted graph by specifying the values in auxiliary data structures.
  • Analyze the running time of the (unweighted) shortest path algorithm, assuming an incidence/adjacency list Graph implementation.

The BFS/DFS algorithm can be carried out on a directed graph. The only adjustment would be to consider each vertex's "outgoing neighbors" during "exploration."

Consider the following directed graph:

Exercise Carry out the BFS algorithm on the graph above starting at vertex $A$. Keep track of previous and distance values for each vertex. Reflect on the complexity of the algorithm.

Solution
  • The algorithm's complexity is the same as the simple BFS algorithm; it runs in $\Omicron(N+M)$.
  • The modified BFS requires more auxiliary space, although it is asymptotically linear (same as plain BFS).