13. Traversing A Graph

# 13. Traversing A Graph - Traversal of Graph 1 Traversing a...

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Traversal of Graph 1

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2 Traversing a Graph Traversing a Graph (1) Breadth-first Search (BFS) (2) Depth-first Search (DFS) Breadth-first Search (BFS) The breadth-first search ( BFS ) is a graph search algorithm. • BFS starts at a source node s and explores all the neighboring nodes of s. Then for each of these nodes, it explores their unexplored neighbors and so on. It produces a “breadth-first tree” with root s that contains all reachable vertices. For any vertex v reachable from s, the path in the BFS tree from s to v corresponds to a shortest path from s to v in G. This algorithm works on both directed and undirected graphs.
3 Information Needed to Maintain in BFS Algorithm Information Needed to Maintain in BFS Algorithm Input graph G=(V,E) is represented using adjacency list. Each vertex is colored Each vertex is colored white, gray or black. (1) Vertex with White Color: undiscovered vertex. (2) Vertex with Gray Color: Consider to be discovered. (3) Vertex with Black Color: Adjacent-list of Vertex has been discovered . Additional Data Structures (1) color[u] : Store the color of each vertex u ε V (2) Π[u] : Store the predecessor of u.

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