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Building Layers of Connected Vertices using Breadth First Search

Breadth First Search (BFS) is connected to a start node (s) by building layers of vertices connected to s. Create layers of vertices at different distances from s. The BFS tree naturally forms a rooted tree at s, with non-tree edges forming levels.

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Building Layers of Connected Vertices using Breadth First Search

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  1. Breadth First Search (BFS) Is s connected to t? Build layers of vertices connected to s Lj: all nodes at distance j from s L0= {s} Assume L0,..,Ljhave been constructed Lj+1set of vertices not chosen yet but are connected to Lj Stop when new layer is empty

  2. BFS Tree BFS naturally defines a tree rooted at s Add non-tree edges Lj forms the jth “level” in the tree u in Lj+1is child of v in Lj from which it was “discovered” L0 1 7 1 2 3 L1 2 3 8 4 7 8 L2 5 5 4 6 6 L3

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