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If it greatly simplifies the explanation, is it possible to present an algorithm in a paper without a high-level mathematical description but simply with pseudocode and very clear elaboration? Or should a high level mathematical description always be included?

anything
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Jamerson2
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    That probably depends on the requirements of the journal you submit to. A referee may ask for a mathematical description. – astronat supports the strike Mar 25 '21 at 08:25
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    What do you mean by "very clear elaboration"? Would that not include explaining what your algorithm does in detail, including whatever math is needed? – GoodDeeds Mar 25 '21 at 11:41
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    What is the point of writing a paper? Who are your audience? The audience will ask different set of research questions. What is the reason for using a math description? Once you find the corresponding answer(s), then you'll know how to write it. – Prof. Santa Claus Mar 27 '21 at 19:52
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    Make sure you have a reference implementation, of course. Whether you intend to publish it or not. – Buffy Mar 29 '21 at 20:51

2 Answers2

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I would say that it strongly depends on the target conference/journal that you will be submitting to. For instance, if you plan to submit to e.g., Algorithmica I wouldn't say that this would be suggested. But if for instance, you plan to submit on a conference that is not algo-oriented, then a high-level mathematical representation might be replaced with a detailed pseudocode along with the appropriate explanation.

But, even if this is the case, there is still the matter of

  1. Completeness
  2. Converging

I do believe, that you would need at least some mathematical representations in order to convince the reviewers about those two points. And in many cases, those are not THAT hard to prove, but once again, this also depends on your algorithm and your application.

So to answer your question, it is possible that you will be asked during the peer-review at least for the completeness of your approach. So I would put a bit of effort in order to justify this point.

ex1led
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Generally speaking, the purpose of the mathematics is to clarify the algorithm and prove that it works (or at least set up the mathematical problem so that it is clear what you need to prove). In some cases the pseudo-code might be sufficiently clear to describe the algorithm, but it will not set the problem up in a way that allows mathematical analysis. This might be okay for some journals/referees, but others will want a mathematical description.

Some commentators have already noted that the answer here depends on the journal you submit to, and their expectations for the level of detail for an algorithm. I would also add that it will probably also depend on the idiosyncrasies of the particular referee you get --- into that crystal ball none of us can peer. If you have good reason to believe that your textual explanation and pseudo-code set out the algorithm clearly, and little is gained from adding a mathematical description, then you should feel free to submit on that basis and see what the referees come back with.

Ben
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