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Unformatted text preview: 1 Lecture 6 Critical Path Method Acyclic directed graphs So far we computed shortest paths in undirected graphs with nonnegative edge costs. Let’s look at acyclic directed graphs. directed path not a directed path directed cycle not a directed cycle Acyclic directed graphs have no directed cycles. 2 Acyclic directed graphs Problem: Given an acyclic directed graph, find the length of shortest path from one node to all others. 1 4 3 2 7 6 5 8 4 1 2 2 5 13 1 11 8 1 6 7 9 3 Note: In acyclic directed graphs we can number the nodes 1,2,...,n such that implies i<j. Acyclic directed graphs i j Why? 1) there must be a node with no incoming arc (why?) 2) Label this with number 1, and delete all outgoing edges. Then, 1) applies again – number this node with the next higher number. Etc... 1 4 3 2 7 6 5 8 4 1 2 2 5 13 1 11 8 1 6 7 9 3 1 4 1 2 2 5 13 1 11 8 1 6 7 9 3 1 4 1 2 2 5 13 1 11 8 1 6 7 9 3 2 1 4 1 2 2 5 13 1 11 8 1 6 7 9 3 2 3 1 2 3 4 5 6 7 8 4 1 2 2 5 13 1 11 8 1 6 7 9 3 3 1 2 3 4 5 6...
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 Spring '05
 TROTTER
 Graph Theory, Shortest path problem, acyclic, acyclic directed graph

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