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I am planning to write a journal article about real-world algorithms solving a practical problem for an IEEE Computer Society transactions journal. The section outline currently is as follows:

  1. Introduction
  2. Related work
  3. Problem definition
  4. Simple algorithm for a simpler problem that cannot be scaled up to the real problem but is very interesting from mathematical viewpoint
  5. Several mathematical observations from the simple algorithm
  6. Simple algorithm that can be scaled up
  7. Good, slow algorithm, as used in literature
  8. Implementation details of our version of the good, slow algorithm
  9. Another good algorithm from the literature and some improvements to it
  10. Even more improved version of the Section 9 algorithm
  11. How to deploy Section 6 algorithm for worldwide use
  12. How to deploy Section 9/10 algorithm for worldwide use
  13. Results and discussion
  14. Discussion about one important point that could be claimed to invalidate the results but in reality doesn't
  15. Conclusions

So, there are 15 sections. In IEEE double column style, the text is now 7 pages + references + biographies, but I expect it to grow to 10 pages + references + biographies because some of the sections are empty currently, their text not being written yet.

Now, my question is: do I have too many sections? I have intentionally kept the sections concise, not being too wordy. So they explain things just once and expect the reader to understand. So, the paper is not overly long.

The paper is quite conclusive because it explores 4 different algorithms and manages to optimize one of them to be fast enough to be used in practice. I don't want to remove any content because it would make the paper less conclusive. The results are important as well: the best algorithm as optimized by me runs over 60 000 times faster than equivalent prior art algorithm in the Section 3 problem.

I don't see any simple yet good reorganization into subsections: for example, Section 5 really has to be immediately after Section 4 so that the reader doesn't forget the important things from Section 4 when reading Section 5. So I can't combine Sections 4-10 into subsections of an algorithm section, because in the middle there would be a mathematical observation section unrelated to algorithms. In theory, Sections 11-12 could be combined to be subsections of a deployment section, but that would save just one section number. Another way to save one section number would be to do this:

  1. Results and discussion
    • 13.1. Results
    • 13.2. Discussion
    • 13.3. Discussion about one important point that could be claimed to invalidate the results but in reality doesn't

After really hard work, I came up with the following barely acceptable outline having less sections:

  1. Introduction
  2. Related work
  3. Problem definition
  4. Simple algorithm for a simpler problem that cannot be scaled up to the real problem but is very interesting from mathematical viewpoint
  5. Several mathematical observations from the simple algorithm
  6. Scalable algorithms
    • 6.1. Simple algorithm that can be scaled up
    • 6.2. Good, slow algorithm, as used in literature
    • 6.3. Implementation details of our version of the good, slow algorithm
    • 6.4. Another good algorithm from the literature and some improvements to it
    • 6.5. Even more improved version of the Section 6.4 algorithm
  7. Deployment
    • 7.1. How to deploy Section 6.1 algorithm for worldwide use
    • 7.2. How to deploy Section 6.4/6.5 algorithm for worldwide use
  8. Results and discussion
    • 8.1. Results
    • 8.2. Discussion
    • 8.3. Discussion about one important point that could be claimed to invalidate the results but in reality doesn't
  9. Conclusions

Is this 9 section outline better?

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    The 9 section outline is much better, since it has a cleaner structure. Why do you say "barely acceptable"? If anything, in my subfield, the "Deployment" section wouldn't be an own section, but probably a part of the discussion in 8.2. Also, consider merging 4 and 5. – lighthouse keeper Mar 28 '18 at 20:24
  • I would combine 1 and 2. It's normal to describe work and problems related to the one you are working on in the introduction – DSVA Mar 29 '18 at 10:10
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Yes, you improved it a lot with the 9-section outline, because:

  • It is much easier to communicate the tiered the structure of the paper to the reader, which makes readers and reviewers much happier.

    • It is easier for readers to scan through and understand the main outline of the paper, instead of having to figure out for themselves which points are more closely related.

    • It is easier for your to preview the shorter outline in words near the beginning, than if you're thinking of it as 15 sections.

  • It may slightly save you space, because subheadings likely take up less room than main headings.

Here are two additional potential revisions to further streamline:

  • Change point 5 into a subpoint under point 4. It's still about that simple algorithm. (As I just saw, lighthouse keeper also advises this.)
  • Shorten the title for 8.3. (Obviously, you're giving a generic version, but it could be done briefly by saying "Addressing Entropy Concern," replacing "Entropy" with a reference to whatever issue thoughtful reviewers may anticipate as a problem.)

Someone in your field may have better comments about whether the information you want to pack in here is all too much to effectively demonstrate in a 10-page paper. In particular, the simple, unscalable, mathematically interesting algorithm might not be as related to the rest, if you must cut something.

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    Agree -- in fact, I would put 5 under 4 (as @cactus_pardner suggests) and then put both under 6 -- then, 6 is just "algorithms." (One could argue that 5 really belongs under 8, but I assume understanding 5 will help understand 6 so you can't postpone it until 8). – cag51 Mar 28 '18 at 21:04
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The nine-point list is certainly much better than the fifteen-point list, but it should still be reduced further, with some sections being incorporated into others. For an article this short (7-10 pages) it would probably be excessive to have sub-headings, and you could easily deal with these matters under the main section headings. The section names should be short and clear; you should avoid excessively long descriptive titles. It is okay to incorporate multiple results under a single generic section without giving sub-headings for each particular item of discussion. For an article with only 7-10 pages, I would suggest that it is reasonable to encapsulate this in five or six sections. If you want to get it down to its bare bones, I would suggest something like the following:

  1. Introduction and literature

    • Introduce the problem
    • Set out relevant literature and related work
  2. Problem definition and scalability issues

    • Define the problem
    • Introduce your simplified algorithm and discuss scalability
    • Differentiate this algorithm from your problem to discuss the difficulty of the problem
  3. Scalable algorithms

    • Discuss each of the scalable algorithms
    • Compare these as they are discussed
    • Discuss deployment of these algorithms
  4. Results and discussion

  5. Conclusions

You mention in your post that one of your difficulties is that you introduce mathematical results that are important to the problem but unrelated to the algorithms. If this is the case, that stuff should be introduced in the section on the problem definition, in order to elucidate the problem. If you are concerned that the mathematical parts could interrupt the flow of the paper, you could consider framing some of these a "Remark" (often presented like a theorem, in its own little paragraph).

Ultimately, what you seem to want to do is to present a problem with a simplified algorithm and some math results to elucidate it, and then discuss four more complex algorithms in greater details. The should be able to be achieve in something like the above structure.

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