#8714: add Bellman-Ford algorithm for shortest paths
--------------------------------+-------------------------------------------
Reporter: mvngu | Owner: jason, ncohen, rlm
Type: enhancement | Status: new
Priority: major | Milestone: sage-5.1
Component: graph theory | Resolution:
Keywords: | Work issues:
Report Upstream: N/A | Reviewers:
Authors: | Merged in:
Dependencies: #12806 | Stopgaps:
--------------------------------+-------------------------------------------
Changes (by dcoudert):
* cc: dcoudert (added)
Comment:
Hello,
I have checked the networkx implementation of the Bellman-Ford algorithm
([https://networkx.lanl.gov/trac/browser/networkx/networkx/algorithms/shortest_paths/weighted.py
See here]) and we can propose a better implementation.
This is a first implementation that can certainly be improved. Its
advantage is that in the best case the time complexity is in O(|V|+|E|)
and in the worst case, it is O(|V|.|E|). It uses a set to maintain the set
of active vertices, that is vertices for which a change has been performed
during previous round.
{{{
def bellman_ford(G, s):
"""
some documentation
"""
from sage.rings.infinity import Infinity
P = []
dist = {}
predecessor = {}
V = G.vertices()
N = G.num_verts()
E = G.edges()
for v in V:
if v == s:
dist[v] = 0
else:
dist[v] = Infinity
predecessor[v] = 0
W = {}
for e in E:
W[(e[0],e[1])] = e[2]
W[(e[1],e[0])] = e[2]
A = set([s])
B = set()
cpt = 0
while len(A) > 0 and cpt < N:
while len(A) > 0:
u = A.pop()
for v in G.neighbor_iterator(u):
if dist[u] + W[(u,v)] < dist[v]:
dist[v] = dist[u] + W[u,v]
predecessor[v] = u
B.add(v)
A = B.copy()
B.clear()
cpt += 1
# check for negative-weight cycles
for e in E:
u = e[0]
v = e[1]
wt = e[2]
if dist[u] + wt < dist[v]:
raise ValueError("Graph contains a negative-weight cycle")
return dist, predecessor
}}}
The implementation can be adapted to graphs and digraphs.
Let me know if you think it is a good idea to write this patch.
Best,
D.
--
Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/8714#comment:4>
Sage <http://www.sagemath.org>
Sage: Creating a Viable Open Source Alternative to Magma, Maple, Mathematica,
and MATLAB
--
You received this message because you are subscribed to the Google Groups
"sage-trac" group.
To post to this group, send email to [email protected].
To unsubscribe from this group, send email to
[email protected].
For more options, visit this group at
http://groups.google.com/group/sage-trac?hl=en.
