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DAG Shortest Path

Summarized notes on Introduction to Algorithms, Chapter 24

  • If DAG contains path from u to v then u precedes v in topological sort
  • Make just one pass over vertices and relax edges that leave the vertex
  • critical path is the longest path through the DAG
    → to find critical path, negate edge weights then run DAG-Shortest-Paths

Pseudo code implementation

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Dag-shortest-paths(G, w, s)
    topologically sort vertices of G
    Initialize-single-source(G, s)
    for each vertex u, taken in topologically sorted order
        for each vertex v in G.Adj[u]
            Relax(u, v, w)

Complexity

Running Time
Θ(V+E) DAG-shortest-path