#8714: add Bellman-Ford algorithm for shortest paths
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Reporter: mvngu | Owner: jason, ncohen, rlm
Type: enhancement | Status: new
Priority: major | Milestone: sage-4.4
Component: graph theory | Keywords:
Author: | Upstream: N/A
Reviewer: | Merged:
Work_issues: |
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I'm using #698 as a wish list of items to add to the graph theory module
of Sage. The purpose of this ticket is to implement the
[http://en.wikipedia.org/wiki/Bellman%E2%80%93Ford_algorithm Bellman-Ford]
algorithm for finding shortest paths in a weighted graph `G` that may have
negative weights. If `G` doesn't have negative weights, Dijkstra's
algorithm can be used. However, if `G` has negative weights, we fall back
on the Bellman-Ford algorithm. The Bellman-Ford algorithm is able to
handle graphs with negative weights, but not graphs that have negative-
weight cycles. See also the function
[http://reference.wolfram.com/mathematica/Combinatorica/ref/BellmanFord.html
BellmanFord] in Mathematica's
[http://reference.wolfram.com/mathematica/Combinatorica/guide/CombinatoricaPackage.html
Combinatorica] package. See this [http://code.google.com/p/graph-theory-
algorithms-book/ graph theory book] for an algorithmic presentation of the
Bellman-Ford algorithm.
--
Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/8714>
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