Talk:Dijkstra's algorithm: Difference between revisions

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== The explanation makes no sense ==

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

Under Algorithm 2: <br>

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," ?

"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-->

== Practical optimizations and infinite graphs ==

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

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)

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

== GIF is confusing ==

<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:

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.

<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>

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-->

Perhaps it should also be noted in:

== Dubious ==

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.

In the section "Using a priority queue", we have:

[[User:DKEdwards|DKEdwards]] ([[User talk:DKEdwards|talk]]) 18:37, 17 November 2024 (UTC)

:Yet another alternative is to add nodes unconditionally to the priority queue and to instead check after extraction that no shorter connection was found yet. This can be done by additionally extracting the associated priority p from the queue and only processing further '''if p ≤ dist[u]''' inside the while Q is not empty loop.

: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 improvement ==

https://cs.stackexchange.com/a/118406/ thinks that this is mistaken and should be replaced with '''p = dist[u]'''. Ryoji writes (CC-BY SA 4.0):

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)

:You are right. Checking k < d[u] is not sufficient and updating d[u] on the next line is not necessary.

== Formatting of pseudocodes broken ==

:The check prevents proceeding when the source is picked up from the queue (then k = 0 and d[s] = 0). Also, d[u] (u is fixed) is monotonically decreasing as loop proceeds, so even though it is updated after (u, d[u]) is put on the queue, k >= d[u] holds when (u,k) is picked up from the queue. Moreover, if d[u] is strictly smaller than k , the element should simply be ignored since it cannot be the shortest path to u.

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

:You can change the condition to k == d[u] and remove following update to d[u].

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

Last good version:<br>

Should we replace the condition with k == d[u]? —[[User:Enervation|Enervation]] ([[User talk:Enervation|talk]]) 16:44, 30 December 2020 (UTC)

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)

== An interesting paper questioning optimality ==

== Roads and intersections ==

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

https://arxiv.org/abs/2504.17033

Article says that "Note: For ease of understanding, this discussion uses the terms intersection, road and map – however, in formal terminology these terms are vertex, edge and graph, respectively."

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

This...doesn't make it easier. It actually sounds incredibly patronizing. Who in the right mind would try to learn Dijkstra's algorithm without knowing what a vertex is? [[Special:Contributions/2001:569:57B2:4D00:71E1:A843:C41:841C|2001:569:57B2:4D00:71E1:A843:C41:841C]] ([[User talk:2001:569:57B2:4D00:71E1:A843:C41:841C|talk]]) 16:22, 25 May 2022 (UTC)

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."

== Pseudocode improvement ==

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.

In first pseudocode block, on line 15, dist[u] is checked for not being INFINITY. But if it is INFINITY at this point, the code will continue useless looping, because all remaining vertices will also have dist[u]=INFINITY and not influence the result. Maybe move the INFINITY check to line 11 and break out of while block, it would be more human readable too I think --[[Special:Contributions/78.63.123.129|78.63.123.129]] ([[User talk:78.63.123.129|talk]]) 20:43, 20 August 2022 (UTC)

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)