Talk:Dijkstra's algorithm: Difference between revisions

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== The explanation makes no sense ==

== Is the algorithm description incorrect? ==

Under Algorithm 2: <br>

"Assign to every node a distance from start value: for the starting node, it is zero, and for all other nodes, it is infinity, since initially no path is known to these nodes. During execution of the algorithm, the distance of a node N is the length of the shortest path discovered so far between the starting node and N.[17]" <br>

You just assigned INFINITE to ALL. How is the shortest going to be find? <br><br>

Under 3:<br>

"From the unvisited set, select the current node to be the one with the smallest finite distance; initially, this will be the starting node, which has distance zero. If the unvisited set is empty, or contains only nodes with infinite distance (which are unreachable)"<br>

Again, you assigned infinite to all nodes ... <br><br>

AI newstopped gifreading withit no values inside the nodes should be createdhere. <!-- Template:Unsigned IP --><small class="autosigned">—&nbsp;Preceding [[Wikipedia:Signatures|unsigned]] comment added by [[Special:Contributions/2A02:ED0:33B2:6C00:F5D1:308E:202D:179C115.70.29.185|2A02:ED0:33B2:6C00:F5D1:308E:202D:179C115.70.29.185]] ([[User talk:2A02:ED0:33B2:6C00:F5D1:308E:202D:179C115.70.29.185#top|talk]]) 0908:1449, 1022 SeptemberOctober 20202024 (UTC)</small> <!--Autosigned by SineBot-->

Step six of the algorithm section is:

== Add A Fact: "Dijkstra's algorithm proven universally optimal" ==

"6. Otherwise, select the unvisited node that is marked with the smallest tentative distance, set it as the new "current node", and go back to step 3."

I found a fact that might belong in this article. See the quote below

I don't believe that's correct. Shouldn't the "tentative" be removed? Since this is an important article I wanted to be sure I was correct before editing it, but if it is incorrect [https://www.youtube.com/watch?v=gdmfOwyQlcI&t=20s we've already hit citogenesis].

<blockquote>

Dijkstra’s algorithm was long thought to be the most efficient way to find a graph’s best routes. Researchers have now proved that it’s “universally optimal.”

</blockquote>

The fact comes from the following source:

: https://www.quantamagazine.org/computer-scientists-establish-the-best-way-to-traverse-a-graph-20241025/

Here is a wikitext snippet to use as a reference:

[[User:Botlord|Botlord]] ([[User talk:Botlord|talk]]) 06:04, 21 February 2018 (UTC)

<nowiki> {{Cite web |title=Computer Scientists Establish the Best Way to Traverse a Graph |url=https://www.quantamagazine.org/computer-scientists-establish-the-best-way-to-traverse-a-graph-20241025/ |website=Quanta Magazine |date=2024-10-25 |access-date=2024-11-17 |language=en |first=Ben |last=Brubaker |quote=Dijkstra’s algorithm was long thought to be the most efficient way to find a graph’s best routes. Researchers have now proved that it’s “universally optimal.”}} </nowiki>

Perhaps it should also be noted in:

: It is the smallest among all the "tentative distances". While it is true that for the node with the smallest one, it is also the real distance, it is probably not so for the others, and even for that one it requires a proof, which will only be given after the algorithm has been described. --[[User:Alexey Muranov|Alexey Muranov]] ([[User talk:Alexey Muranov|talk]]) 06:25, 21 February 2018 (UTC)

https://en.wikipedia.org/wiki/Shortest_path_problem

This post was generated using the [[:meta:Future_Audiences/Experiment:Add_a_Fact|Add A Fact]] browser extension.

== Is there a typo in the "Invariant hyphothesis" sentence? ==

It says: "This assumption is only considered if a path not exists," but should it be "This assumption is only considered if a path exists," ?

[[User:BotlordDKEdwards|BotlordDKEdwards]] ([[User talk:BotlordDKEdwards|talk]]) 0618:0437, 2117 FebruaryNovember 20182024 (UTC)

== Animation incorrect/misleading? ==

:What it actually means is that if

:#what you really want is the sorted order of vertices by distance from the source and not just the distances and paths,

:#you know ahead of time what graph you're going to run it on but not the weights, and

:#you can only access the weights by pairwise comparisons,

:then a specific version of Dijkstra (with a special priority queue) will get a number of comparisons within a constant factor of optimal. It's a nice result, and probably should be mentioned in this article ([[Dijkstra's algorithm]]) but I question the relevance to [[shortest path problem]] because it's about sorting rather than shortest paths per se. It may have been a bit oversold by Quanta. —[[User:David Eppstein|David Eppstein]] ([[User talk:David Eppstein|talk]]) 21:14, 17 November 2024 (UTC)

::[[User:Lfstevens]]: when adding this material, it would have been helpful for you to have read this thread. Your version of what they did is far too vague and hypey. I have edited it to more accurately reflect the claims of the new paper. —[[User:David Eppstein|David Eppstein]] ([[User talk:David Eppstein|talk]]) 08:01, 9 December 2024 (UTC)

:::Thanks for noticing and fixing my mush. It was pretty much a pull from the Quanta piece. [[User:Lfstevens|Lfstevens]] ([[User talk:Lfstevens|talk]]) 21:43, 9 December 2024 (UTC)

::::''Quanta'' is often mush. —[[User:David Eppstein|David Eppstein]] ([[User talk:David Eppstein|talk]]) 21:49, 9 December 2024 (UTC)

==Pseudocode==

The main animation is very confusing. It purports to minimize distance, but in the triangle formed by nodes 1-3-6, the distance between nodes 1 and 6 is labelled as 14, while the distance from node 1 to 3 to 6 sums to 11, which is geometrically imnpossible by the nature of triangles. Visually, the path 1-6-5 is obviously the shortest distance. Either the labels of the distances between nodes should be changed (and therefore the optimal path changed) or the description should be changed to not refer to distance and make clear that the labels do not reference distance between nodes. Am I seeing this correctly? [[User:Voyaging|<span style="color:darkblue">'''''Voyaging'''''</span>]][[User talk:Voyaging|^{<span style="color:darkred">'''talk'''</span>}]] 14:44, 11 July 2019 (UTC)

The pseudocode seems to fail into an endless loop unless all vertices are connected. [[User:Kkddkkdd|Kkddkkdd]] ([[User talk:Kkddkkdd|talk]]) 17:32, 23 November 2024 (UTC)

:The pseudocode removes a vertex from Q in every iteration, starting with all vertices. It cannot get into an endless loop. If the graph is not connected then some vertices will have priority infinity when they are removed, but that is not a problem for the algorithm. —[[User:David Eppstein|David Eppstein]] ([[User talk:David Eppstein|talk]]) 17:28, 24 November 2024 (UTC)

== Practical optimizations and infinite graphs ==

== Formatting of pseudocodes broken ==

The pseudocode is a sort of Breadth-First Search, not Uniform-Cost Search, as it does not consider edge weight.[[User:Ehasl|Elias]] ([[User talk:Ehasl|talk]]) 10:49, 9 January 2020 (UTC)

The change from @[[User:Lfstevens|Lfstevens]] on 8 December 2024, at 10:36 PM broke the formatting of the pseudocodes.<br>

== GIF is confusing ==

This also causes the pseudocode to be wrong since the nested loop is not recognizable (as nested) anymore.

Last good version:<br>

The gif of Dijkstra's implementation gives irrelevant information which is misleading and confusing - the values inside the nodes are pointless and contribute nothing to the understanding of the algorithm, while the excessive amount of information is confusing.

https://en.wikipedia.org/w/index.php?title=Dijkstra%27s_algorithm&oldid=1261954063 [[Special:Contributions/82.218.89.72|82.218.89.72]] ([[User talk:82.218.89.72|talk]]) 07:06, 16 December 2024 (UTC)

A new gif with no values inside the nodes should be created. <!-- Template:Unsigned IP --><small class="autosigned">—&nbsp;Preceding [[Wikipedia:Signatures|unsigned]] comment added by [[Special:Contributions/2A02:ED0:33B2:6C00:F5D1:308E:202D:179C|2A02:ED0:33B2:6C00:F5D1:308E:202D:179C]] ([[User talk:2A02:ED0:33B2:6C00:F5D1:308E:202D:179C#top|talk]]) 09:14, 10 September 2020 (UTC)</small> <!--Autosigned by SineBot-->

== An interesting paper questioning optimality ==

This paper "Breaking the Sorting Barrier for Directed Single-Source Shortest Paths":

https://arxiv.org/abs/2504.17033

claims better-than-Dijkstra asymptotic performance in some edge cases.

The abstract reads as follows: "We give a deterministic <math>O(m\log^{2/3}n)</math>-time algorithm for single-source shortest paths (SSSP) on directed graphs with real non-negative edge weights in the comparison-addition model. This is the first result to break the <math>O(m+n\log n)</math> time bound of Dijkstra’s algorithm on sparse graphs, showing that Dijkstra’s algorithm is not optimal for SSSP."

They cite the earlier work on proof of universal optimality, and state that Dijkstra's algorithm is still optimal ''if you want to know the order of the points in the path''; their algorithm does not produce this ordering.

It will be interesting to see if this gets out of pre-print status into [[WP:RS]].

&mdash; [[User:The Anome|The Anome]] ([[User talk:The Anome|talk]]) 12:43, 1 June 2025 (UTC)