DAG shortest paths


Definition: Solve the single-source shortest-path problem in a weighted directed acyclic graph by 1) doing a topological sort on the vertices by edge so vertices with no incoming edges are first and vertices with only incoming edges are last, 2) assign an infinite distance to every vertex (dist(v)=∞) and a zero distance to the source, and 3) for each vertex v in sorted order, for each outgoing edge e(v,u), if dist(v) + weight(e) < dist(u), set dist(u)=dist(v) + weight(e) and the predecessor of u to v.

See also Dijkstra's algorithm, Bellman-Ford algorithm.

Author: PEB

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Entry modified 19 April 2004.
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Cite this as:
Paul E. Black, "DAG shortest paths", in Dictionary of Algorithms and Data Structures [online], Paul E. Black, ed. 19 April 2004. (accessed TODAY) Available from: