chapter 22 Elementary Graph Algorithms

1. Representation of graphs G=(V,E)

• adjacency lists—sparse graphs; directed, undirected, weighted; memory requiresθ(V+E);
• adjacency matrix—dense graph 

2. Breadth-first search

Analysis

queue operations is O(V), scanning adjacency list is O(E), total running time of BFS is O(V+E).

 

3. Depth-first search

Analysis θ(V+E);

breadth-first search's predecessor subgraph forms a tree

depth-first search's predecessor is composed of several trees

 

a directed graph is acyclic if and only if a depth-first search yields no "back" edges