1. Depth-First Search D B A C E Depth-First Search Depth-First Search
2/19/2019 6:58 AM
Depth-First Search D B A C E
Depth-First Search

2. Depth-First Search
Depth-first search (DFS) is a general technique for traversing a graph
Similar to Pre-order traversal of a tree
“children” -> neighbors
level -> number of edges away from starting vertex
Not to visit the same vertex more than once
Depth-First Search

3. Depth-first Search Algorithm DFS(G, v) visit v setLabel(v, VISITED)
neighbors  getAdjacentVertices(G, v)
for each w  neighbors if getLabel(w) != VISITED // “children”
DFS(G, w)
Depth-First Search

4. Depth-first Search The book uses an iterative algorithm same as BFS
Algorithm DFS(G, v)
visit v
setLabel(v, VISITED)
neighbors  getAdjacentVertices(G, v)
for each w  neighbors if getLabel(w) != VISITED // “children”
DFS(G, w)
The book uses
an iterative algorithm same as BFS
the DFS alg. uses a stack instead of a queue as the container C
With recursion, we don’t need to manipulate a stack.
Depth-First Search

5. Example unexplored vertex visited vertex unexplored edgeB A C E A A
visited vertex
unexplored edge
discovery edge
back edge D B A C E D B A C E
Depth-First Search

6. Example (cont.) D B A C E D B A C E D B A C E D B A C E
Depth-First Search

7. Analysis of DFS Setting/getting a vertex/edge label takes O(1) time
Each vertex is labeled twice
once as UNEXPLORED
once as VISITED
O(n)
getAdjacentVertices() is called once for each vertex
Each edge in the graph is used as most twice
Each edge has two vertices
O(m)
DFS runs in O(n + m) time provided the graph is represented by the adjacency list structure
[less precisely, since m is O(n2), BFS is also O(n2)]
Depth-First Search

8. Properties of DFS Property 1 Property 2
DFS(G, v) visits all the vertices and edges in the connected component of v
Property 2
The discovery edges labeled by DFS(G, v) form a spanning tree of the connected component of v D B A C E
Depth-First Search