CS 112a
Fall 2000
Ileana Streinu

Graph Traversal, Depth First Search and Connectivity

• Directed graphs versus undirected graphs. Examples.
• Paths in graphs (directed and undirected). Examples.
• Connected versus not connected graphs. Examples.
• Connected digraphs for which there exists no path from a node A to a node B. Examples.
• Graph traversal algorithm: starts at a node v and "visits" all the nodes that can be reached by directed paths from v.
• Depth-first search (DFS) from node v: from each node, follow a path as far as you can, while visiting only vertices that you have not previously seen. When you reach a previously visited vertex, back up to where you came from and visit the next child of the current node, if any exists. Otherwise back up and repeat this procedure. Stop when you are at v and have backed up from its last child.
• Example of how DFS works.
• Implementation of DFS in pseudo code. Recursion. The C++ implementation is part of the final project assignment.
• Simulation of how the code is executed for a graph given by its adjacency list representation (not C++ code, but rather box-and-arrow notation).
• Application to Connectivity problems:
  • Decide if an undirected graph is connected.
  • Decide if there exists a path from a given node v to another node u in a directed graph.
  • Decide if there exists a node that cannot be reached from a node v, in a directed graph.
  • List all the nodes reachable from a given node v.
  Interpretation for computer networks, road networks, etc.