Graph Searching

I. Graph Searching Terminology

    A. Visited Vertices: Vertices that have already been visited

    B. Fringe Vertices: Vertices adjacent to visited vertices but not yet visited

    C. Unseen Verticies: Vertices that haven't been encountered at all yet

II. Depth-first search: A search of a graph in which fringe vertices are
	visited in LIFO order (last-in, first-out):

    A. Depth-first search requires O(V + E) time if implemented with 
	adjacency lists

    B. Pseudo-Code

       void dfs( Vertex v ) {
           v.visited = true;
	   for each w adjacent to v
	       if ( !w.visited )
	           dfs( w );
       }

III. Breadth-first search: A search of a graph in which fringe vertices are
	visited in FIFO order (first-in, first-out):

    A. Strategy: Remove vertices from the front of a queue and add their
        adjacent vertices to the back of the queue. This strategy ensures
	that while level l vertices are being processed, level l+1 vertices
	are being added to the back of the queue. The level l+1 vertices
	will not be visited until all level l vertices have been exhausted.

    B. Pseudo-Code

        bfs(vertex v) {
	    VtxQueue.queue(v);
	    while (!VtxQueue.empty()) do
	       current_vtx = VtxQueue.dequeue()
	       for each w adjacent to v
	           if ( !w.visited )
		       w.visited = true
		       VtxQueue.queue(w)
        }

    C. Time Complexity

        1. Breadth-first search requires O(V + E) time if implemented with 
	   adjacency lists

	2. Breadth-first search requires O(V2) time if implemented
	   with an adjacency matrix