# Dijkstra's algorithm

(algorithm)

**Definition:**
An algorithm to find the *shortest paths* from a single *source* *vertex* to all other vertices in a *weighted, directed graph*. All weights must be nonnegative.

**Aggregate parent** (I am a part of or used in ...)

*Johnson's algorithm*.

**Aggregate child** (... is a part of or used in me.)

*priority queue*, *greedy algorithm*.

**See also**
*Bellman-Ford algorithm*, *all pairs shortest path*.

*Note:
A naive implementation of the **priority queue* gives a run time complexity *O(V²)*, where V is the number of vertices. Implementing the priority queue with a *Fibonacci heap* makes the time complexity *O(E + V log V)*, where E is the number of *edges*.

*
** After [CLR90, page 527].*

Author: PEB

## Implementation

An analysis with code (C)

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Entry modified 20 September 2006.

HTML page formatted Tue May 6 13:48:55 2014.

Cite this as:

Paul E. Black, "Dijkstra's algorithm", in
*Dictionary of Algorithms and Data Structures* [online], Vreda Pieterse and Paul E. Black, eds. 20 September 2006. (accessed TODAY)
Available from: http://www.nist.gov/dads/HTML/dijkstraalgo.html