Talk:Bellman–Ford algorithm

proposed answer
for i from 1 to size(vertices) - 1 is correct.

in other other words: you intentionally leave one vertex out. reason: let a shortest path from s to an arbitrary vertex v contain k edges. that means, the path p from s to v can be described as follows: p = (s = v0, v1, ..., vk-1, vk = v). in the worst case the shortest path visits all vertices of the graph. these are size(vertices). but the path between s and v only contains size(vertices) - 1 edges. the algorithm tries to relax all edges for every edge on the shortest path - followingly, only size(vertices) - 1 relax-iterations have to be computed.

As for what u is supposed to be, (u, v) is the entire edge, starting at vertex u and finishing at vertex v. — Preceding unsigned comment added by 125.239.41.100 (talk) 03:46, 24 November 2023 (UTC)

Bellman–Ford algorithm in the informational description of the black hole
Write the text.

Does the shortest path of the informational chunks always result in a mixed state? We want that because a pure state will lead to informational loss. One other option is that informational loss exists, but isn't fundamental, because it is the result of untangling a more fundamental field, and dissipating that infoloss into the same spacetime field as virtual particles. — Preceding unsigned comment added by 2A02:587:4118:7CA3:2891:994B:40B:F97D (talk) 21:15, 7 August 2020 (UTC)
 * Whether this has anything real to do with shortest paths, or is just buzzword salad, I'm not sure, but it doesn't appear to have anything to do with this article, which is about a specific method for finding shortest paths and not on the general topic of shortest paths. And it also appears to be off-topic for this talk page, which is about improvements to the article based on published reliable sources. —David Eppstein (talk) 21:42, 7 August 2020 (UTC)

Animated example
The animated gif in the article, while it is a very good initiative, seems to be either wrong or at least confusing.

First of all, what do the numbers next to the vertices mean? If they're the estimated distances, then iiuc they're not supposed to increase. But they do: v4 changes from 4 to 6 between frame #5 and frame #6, just as v3 does between frame #4 and frame #5.

Also, aren't there supposed to be 5 frames instead of 6? That is, the initial state plus the |V|-1 = 4 steps of the algorithm.

And what do the thick arrows and grey vertices mean? Are they the vertices we already have the final distances of, and the shortest paths leading to them? The problem with this is that the algorithm is not supposed to "know" these at that point - if we stop there, we cannot be sure that we would not get better results (shorter paths) for these vertices in a later step.

Thoughts by another editor
I agree with the confusion. I believe that v3 and v4 incorrectly update. There is no possible path by which the cost to v4 is 4, so there's no way the algorithm should ever update the weight to 4. And like the parent said, the algorithm should never increase the weight, so v3 shouldn't temporarily change to 6 and back to 4. I think the original creator of the gif simply swapped the two values by accident.

It also converges after 3 cycles, which is common for this algorithm. In fact, this algorithm can converge after 1 cycle, if the optimal path is (randomly) selected.

I think removing the bold edges, darkening of the vertexes, and stopping the animation after the 3rd frame would really help this page, but I didn't make the change in case I misunderstand the algorithm.

P.S. First comment. Please don't bite the newcomer. I couldn't find a way to comment on the original post so I added to it.

Lothsahn (talk) 21:47, 31 October 2021 (UTC)


 * Seems that the gif has been updated since then, but I still think it's not correct. On the frame that "t" changes from 6 to 2, shouldn't z change to -2 too instead of happening in the next frame? It suggests that z updates on the next loop after the t update one, but if I'm not mistaken it should be on the same frame since t changes to 2 and then after checking x and y, when it checks for z it should see that t is now -2 and not 6. Atleast that's what I understand should happen after reading the pseudocode. Marco2124 (talk) 20:01, 7 December 2022 (UTC)

New preprint
Seems soon (after peer-review) there finally might be an improvement to this absolutely classical algorithm https://arxiv.org/abs/2311.02520 2A00:20:5:B593:5C8F:D801:68C2:458 (talk) 00:29, 8 November 2023 (UTC)


 * Let's wait until it's at least been accepted to a conference before adding anything here. Anyway, the right place is Shortest path problem, because it's a different algorithm than BF. —David Eppstein (talk) 05:02, 8 November 2023 (UTC)

Pseudocode bug?
The pseudocode in the article states: for i from 1 to size(vertices)-1: I'm pretty sure that it's supposed to be for i from 0 to size(vertices)-1: or, equivalently for i from 1 to size(vertices):

The program I made based on the pseudocode didn't work until I made this change. Can anyone confirm that this is indeed the case (and not just some other bug in my program) and if so, correct the article? --Smallhacker (talk) 15:38, 3 March 2011 (UTC)

One more clarification on the Pseudocode for each edge (u, v) with weight w in edges: in this line what is u ? I beleive u should be changed to i or vice versa. — Preceding unsigned comment added by 49.203.64.216 (talk) 08:38, 25 May 2014 (UTC)
 * If there are n vertices, the algorithm needs to iterate n-1 times (as in the given pseudocode), not n times (as your change would have it). It starts out with one vertex having the correct distance (the starting vertex) and each iteration adds one more, so only n-1 iterations are needed until all are correct. If you implemented it correctly the nth iteration would be useless. Further, the case where exactly n-1 iterations are necessary should be unusual: it only happens when the shortest path runs through all vertices and the order of relaxation within an iteration is backwards for the edges of this path. So I strongly suspect it is some other bug in your program. —David Eppstein (talk) 08:20, 24 November 2023 (UTC)

Proposed Merger: SPFA into Optimizations
Pretty much all in the title. The Moore Optimization has a whole article, which takes its name after that in the Fanding Duan article (1994) which popularized it in China. The relevance of having a whole article for it, since its worst case is the same as Bellman-Ford, does not seem to meet the standard. Wyrdwritere (talk) 03:51, 7 April 2024 (UTC)


 * ✅ —David Eppstein (talk) 01:13, 10 June 2024 (UTC)