Talk:Shortest path problem

message: Shouldn't there be a section where various practical adaptions and optimizations can be discussed? For instance, finding the shortest path between a pair of vertex by using two dijkstras (forward and backward) simultaneously?
rasmusdf 08:30, 14 June 2007 (UTC)
thread_title:  2007-2002 in approximately random order 

message: “It turns out that there are no algorithms for solving the single-pair problem that are asymptotically faster than algorithms that solve the single-source problem.” 
Has that been proven, or do they just imply no-one has invented such an algorithm? Roman V. Odaisky 17:39, 24 May 2007 (UTC)
replies: text: The wording seems to vaguely imply a proof ("it turns out" is a phrase rigorous mathematics people often use, and it doesn't use the word "known"), but I'll be damned if I have a source handy. Dcoetzee 07:59, 25 May 2007 (UTC)
thread_title:  single-pair vs. single-source 

message: I reverted back from this wording "[TSP] is not able to be perfectly solved on large graphs in a reasonable time" to the earlier wording "[TSP] is not known to be efficiently solvable."  This version is more correct as it has the uncertainty, and I think the wording is cleaner.  Also, I'm not sure we want to get into detail about all the caveats here—approximations and small instances and "reasonable time", plus special cases that are easier, or the average case time, etc.... Leave that all to the articles on the topic.  But in the spirit of the revision I reverted, I added another wikilink that will hopefully fill in those details. --Nethgirb 20:21, 9 July 2007 (UTC)
thread_title:  TSP wording 

message: "A graph with 6 vertices and 7 edges"  But the graph actually has 14 edges since the distance between two vertices need not be commutative.  Is this nit worth picking?  Dmforcier (talk) 18:22, 8 August 2010 (UTC)
replies: text: I don't understand your objection.  The graph pictured has 7 edges.  Counting the number of edges in a graph doesn't really have anything to do with distance.  Are you talking about directed graphs?  Meaning that a single undirected edge is really two directed edges?  All of the graph theory books and papers I've ever read would count the number of edges in that graph as 7.  —Preceding unsigned comment added by 131.136.242.1 (talk) 18:42, 26 August 2010 (UTC)
thread_title:  Caption on the pic 

message: the following recent addition removed from the article. 
:Actually, there isn't an algorithm to directly solve the single-pair shortest path problem on general graph. Finding single-pair shortest path would be done by solving single-source shortest path problem. However, there are algorithms to solve single-pair shortest path on special graphs, such as tree, linear graph and cycle graph.
It has several issues. 
*The corrected first statement would be something like this: "All known algorithms for single-pair shortest path in general graphs are in fact algorithms for single-source shortest path problem, which can be stopped once the destination vertex is reached."
*The correct second statement might be: However there are dedicated single-pair algorithms for some special graph classes, such as such as trees, linear graphs and cycle graphs.
As you maight have noticed, these staements reqire citaitions. Please provide them and re-add accoringly into the article. - Altenmann >t 05:01, 18 November 2012 (UTC)
replies: text: The first statement is not true. See e.g. bidirectional search. Perhaps what is meant is that there is no known single-pair shortest path algorithm whose worst case running time is better than that of the known single-source shortest path algorithms. —David Eppstein (talk) 07:27, 18 November 2012 (UTC)
replies: text: Well, it is not exactly not true. While I admit I forgot to mention  the runtime issue, the bidirrectional search is nothing but a heuristic in which two searches stop a bit earlier. Here again, which bidir search will be worst-case better than the Dijkstra-based one? - Altenmann >t 05:18, 19 November 2012 (UTC)

text: The references in the Shortest path problem#Directed graphs with nonnegative weights table are not in the article; clicking on them seeks an anchor that is not on the page. I added Bellman with ref=harv, so clicking Bellman 1958 now works. Is that your concern? Glrx (talk) 16:25, 20 November 2012 (UTC)
thread_title:  sloppy addition 

message: Under the "Algorithms" section, perturbation theory is listed and it links to the Wiki article on perturbation theory.  However, the wiki page on perturbation theory has absolutely no mention of perturbation theory on graphs for shortest path algorithms, and is devoted to the standard applications of perturbation theory only.  Therefore, I am adding a "citation needed", even though the article links to the Wiki page, and I am also questioning whether the link to the Wiki page is even appropriate (but leaving it for now) until someone adds to that article "perturbation theory on graphs" or some other section that is relevant to the shortest path problem.
99.116.177.3 (talk) 08:29, 7 January 2013 (UTC)
thread_title:  Edit Made to "Perturbation Theory" Section Under Algorithms 

message: I've made an animation to show the difference between algorithms: Bellman–Ford and Dijkstra.
Do you have any comments for animation? Do you have any objections not to include animation to article?
Artyom Kalinin (talk) 06:32, 10 December 2013 (UTC)
replies: text: I find it hard to understand. Basically I think you have to already know the algorithms pretty well just to be able to figure out which of the two is which. In addition: What does a vertex being blue represent, in Bellman-Ford, since that algorithm does not have a concept of a vertex being finished? Why are you illustrating two algorithms neither of which is the best choice for the type of graph you use as an example? (It's a directed acyclic graph, for which a linear time algorithm is possible.) Why does your animation of Bellman-Ford only make one pass through the graph, and why do you think an input for which it gets the correct answer after only one pass is illustrative of how the algorithm works? —David Eppstein (talk) 07:00, 10 December 2013 (UTC)
replies: text: Thanks for the answer. I studied this topic again and agree with you, that this animation is not suitable for Bellman-Ford algorithm.Artyom Kalinin (talk) 16:58, 16 December 2013 (UTC)
thread_title:  Gif animation 

message: I should note here that Jungnickel's 4th ed. (2013) also covers the algebraic path problem (p. 97-102) although he uses rather quaint terminology from an algebraic perspective and still adds some restrictions that aren't really needed since Mohri's paper. So I'm not sure I want to cite/recommend Jungnickel's book as source for this particular topic. JMP EAX (talk) 22:31, 18 August 2014 (UTC)
thread_title:  algebraic path problem 

message: Faster all-pairs shortest paths via circuit complexity <http://arxiv.org/abs/1312.6680>
Probably not but perhaps of interest to someone 92.25.12.77 (talk) 19:01, 16 November 2015 (UTC)
replies: text: It's a theoretical rather than practical advance, but probably worth mentioning in the article (in the tables of results for all pairs, both undirected and directed). —David Eppstein (talk) 19:23, 16 November 2015 (UTC)
thread_title:  Not my area, however is this useful or relevant 

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thread_title:  External links modified 

message: The Shortest Path node diagram provided seems to have a scale issue that is misleading in it's purpose when first looking at the objective of the article. The node distances for paths "10" and "11" are clearly not to scale to those marked "3" and "4".  This throws off the reader in general, since the first initial observer's solution looking at the shortest distance path, is A-B-D-F, just based on relative scale alone.  I think this detracts from the overall objective of the diagram - to demonstrate the optimal shortest path.  SquashEngineer (talk) 13:20, 18 April 2019 (UTC)
thread_title:  Diagram Scale 

message: The square roots have the wrong format in sections like
https://en.wikipedia.org/wiki/Shortest_path_problem#Directed_graphs_with_arbitrary_weights_with_negative_cycles
I think \sqrt should be used instead. Otherwise, the square roots will look off in other themes. Comeza (talk) 12:24, 1 June 2022 (UTC)
thread_title:  Display of square roots