Rather than asking "is there any existing algorithm that does X?", rather, I suggest you ask how to do X. That gives you two ways to win. One way is that someone points to a standard algorithm in the literature to do X. Another way is that someone comes up with their own algorithm to do X. Either way, you obtain a way to solve your problem.
I anticipate that will generally be acceptable. Algorithms are on-topic here.
In many cases, a helpful way to specify the task "X" is to describe what is the input to the algorithm, and what is the desired output (e.g., what properties the output must satisfy, to count as a correct output).
I would be wary of a question that asks for an algorithm to "do X without Y". That might depend on what "Y" is. If you ask that kind of question, I encourage you to make sure you are stating the actual requirement, and ideally provide motivation for that requirement.
For instance, asking how to compute shortest paths without using Dijkstra's algorithm would generally not be a good question, because it doesn't explain why you have rejected Dijkstra's algorithm, and consequently it will be hard to know whether any proposed algorithm will be acceptable to you (perhaps you will reject other proposals as well for the same reason you rejected Dijkstra's algorith, but since you haven't specified what are the positive requirements you need satisfied, it will be impossible to tell in advance). Also, there are many ways to craft an algorithm that superficially doesn't look like it is Dijkstra's algorithm but secretly, "under the covers" is related to Dijkstra's algorithm. A better question would be "how do I compute shortest paths, when some edges might be negative? I can't use Dijkstra's algorithm because it doesn't handle negative edges". That is better, because it specifies the positive requirement (must handle arbitrary graphs, even with negative edges).