(algorithm)

**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.

HTML page formatted Wed Mar 13 12:42:45 2019.

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: https://www.nist.gov/dads/HTML/dagShortPath.html