Lecture Notes on 19 Apr 2013 For the graph given in class Depth First Search (DFS) Event Stack A A B AB F ABF H ABFH Pop H ABF Pop F AB Pop B A C AC Pop C A D AD G ADG I ADGI Pop I ADG Pop G AD Pop D A E AE Pop E A Pop A - DFS starting at A: ABFHCDGIE Breadth First Search (BFS): Event Queue A B B C BC D BCD E BCDE Deq B CDE F CDEF Deq C DEF Deq D EF G EFG Deq E FG Def F G H GH Deq G H I HI Deq H I Deg I - BFS starting at A: ABCDEFGHI Topological Sort in a Directed Graph Step 0: Create an empty sequence list. Step 1: Find a vertex that has no successors. Step 2: Delete this vertex from the graph and insert this vertex to the beginning of the sequence list. Step 3: Repeat Steps 1 and 2 till there are no more vertices. The sequence list has the vertices in topological order. Minimum Cost Spanning Tree - Kruskal's Algorithm Step 1: Create a list of edges. Step 2: Sort that list in order of increasing weight (cost). Step 3: Keep adding the edges from the sorted list to the minimum cost spanning tree as long as the edge does not form a cycle. When there are no more edges to add, you have the minimum cost spanning tree.