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The shortest path problem seeks to find the shortest path (a.k.a. graph geodesic) connecting two specific vertices of a directed or undirected graph. The length of the graph geodesic between these points
is called the graph distance between
and
. Common algorithms for solving the shortest path problem include the Bellman-Ford algorithm and Dijkstra's algorithm.
The Wolfram Language function FindShortestPath[g, u, v] can be used to find one (of possibly mutiple) shortest path between vertices and
in a graph
.
The so-called reaching algorithm can solve the shortest path problem on an -edge graph in
steps for an acyclic digraph although it allows edges to be traversed opposite their direction and given a negative length.
Pemmaraju, S. and Skiena, S. Computational Discrete Mathematics: Combinatorics and Graph Theory with Mathematica. Cambridge, England: Cambridge University Press, 2003.
Skiena, S. Implementing Discrete Mathematics: Combinatorics and Graph Theory with Mathematica. Reading, MA: Addison-Wesley, pp. 224-227, 1990.
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