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I just finished a bachelor’s degree in applied maths. The thesis was designed to be a fairly formulaic implementation affair of an (obscure) NP-problem, but I happened to develop a novel heuristic algorithm for it, which had some very interesting properties, both theoretical and computational.

The problem is not a canonical NP-problem, but a rather obscure one. It could be that no one would care at all, but

  • it does seem to outperform all previously published heuristics;
  • it is based on a novel way of utilizing the problem structure that conceivably could be applied to other NP-problems.

“Talk to your supervisor” is good advice, but he didn’t show any interest in the project throughout the semester (despite it being his area of research) and he hasn’t even commented on the report, despite being asked repeatedly. At this point, I am close to certain he will be of no aid if I would want to pursue this further.

I asked the head professor at the department as well – he said he’d read it but hasn’t. I reminded him about it but that looks like a dead end as well.

So what are my options? It’s far from publishable in its current state and I obviously can’t pursue it further on my own.

  • i would wonder a bit more on your situation. It could be totally normal, but two people being very quiet about your work could mean something else. From the questions on this site, I could imagine either they are stealing your work for themselves, or your work is so bad they do not want to tell you and are waiting for you to leave – user-2147482637 Jul 24 '15 at 5:14
  • I changed the question in the title to reflect the question in the body as the latter seems to be the one that’s needs to be addressed first. Please see whether everything still fits your intentions. – Wrzlprmft Jul 24 '15 at 7:43
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    @user1938107: "I could imagine either they are stealing your work for themselves" And if your priest is very quiet during your confession, you could imagine that he is taping it to blackmail you later. You can imagine anything, but it seems a bit irresponsible to plant the worry in someone's mind that an authority figure will do the most unethical thing they could possibly do with no evidence whatsoever. – Pete L. Clark Jul 24 '15 at 14:13
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    @user1938107: I read your entire comment and commented on the part for which I had something to say. "Out of context" doesn't make much sense here: your original comment is visible along with mine. Let's forget the priest. The OP has already completed his degree so has submitted his project to the department and the university as a formal document. At any university I have ever known or been involved with, stealing a student's work would be frowned upon in all circumstances but in this circumstance would be incredibly stupid, since the faculty member would be caught and could be fired. – Pete L. Clark Jul 24 '15 at 17:10
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    Do you have any experience with faculty stealing student work in this way? I would be interested to hear it. – Pete L. Clark Jul 24 '15 at 17:11
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The foremost thing you need is a mentor familiar with the subject to guide you through the process of paper writing and in particular provide feedback to you. Unless you are very good at it, writing a mathematical paper without any feedback is a bad idea, as it’s very difficult to estimate yourself whether your writing is understandable to others. Also, scientific writing is an art of its own that you probably have not mastered yet.

As you already guessed, the canonical choice for such a mentor is your supervisor, but as he is not an option, I would consider the following (in roughly this order):

  • other members (PhD students, postdocs, etc.) of your supervisor’s group who have experience in paper writing;
  • visiting scientists or collaborators of your supervisor;
  • other scientists from your department, with whom you are on friendly terms;
  • scientists from other universities doing related work;
  • look for a mentor on your department’s bulletin board or similar.

To avoid quarrels with potential mentors and because it’s ethical, you should clarify the following:

  • You are not good at estimating the publishability of your work. It may very well be that it turns out to be unpublishable.
  • The essentials of the situation between you and your supervisor.
  • How you will handle authorship: Just mentoring your paper writing does not qualify for authorship by common authorship standards, but it’s not unlikely that your mentor will, e.g., find some extension or improvement of your work that is worthy of authorship. Authorship may be a relevant incentive for mentors. For more information, see .

Together with a mentor it should be much easier to decide on the publishability of your work and what journal is suitable for it.

Finally, some further caveats:

  • Depending on how much your supervisor laid the intellectual foundations for your reasearch, e.g., by giving you detailed ideas on what you should research and how to do it, he may have reasonable authorship claims. Unless he verifiably abandons these claims, this would lead to all sorts of trouble.
  • If you are worried about your work being stolen, you can publish the current state as a preprint, e.g., on the ArXiv. Be aware that there are journals that do not allow for such prior publication, but as far as I know, this is not a problem in mathematics.
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The first question you should address is whether your result is worth being published. In your case this translates into "Is your heuristics new, because you had a good idea, or because the problem is so obscure?". Just saying that your algorithm outperforms published ones is not sufficient, even if they are published by well known scientists. Sometimes good Homer sleeps, and pointing out the failings of (future) colleagues is too petty to be proud of. Also "novel way" can mean anything from a great idea to a minor modification of a well known method. Answering these questions is part of the job of your advisor, if he doesn't fulfill his duty and there is no other expert in your department you have to contact some outside person. You could try to present your work at a conference, which might be difficult because at your stage of career funding for conferences is often hard to get. Or you could contact someone working on this problem.

If your paper is worth being published note that a good paper on an obscure question, which is not very short, is hard to publish in a paper journal. An electronic journal does not care about the number pages your article has, or the number of articles it publishes, so obscurity is a minor issue here. A good electronic journal has the same reputation and dissemination as a paper journal.

What you definitely should avoid is looking for a journal which is bad enough to publish your research. While having one peer-reviewed publication is uncommon for a fresh bachelor and can improve your early career, publishing in bad journals leaves a stain which you have to live with forever.

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    Using the same performance metric, my method got better numbers than the existing methods. I don't think that's particularly petty, that's just progress. – Benjamin Lindqvist Jul 23 '15 at 22:59
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    What you definitely should avoid is looking for a journal which is bad enough to publish your research. – You should specify what you mean by bad here. There is no shame in publishing in a low-tier journal, but publishing with predatory and fake publishers should really be avoided. – Wrzlprmft Jul 24 '15 at 7:44
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    @luegofuego: "Better than existing method" is only progress if the existing methods cannot obviously be improved. Even a great mind can miss a simple improvement, and pointing this out would be petty. Unfortunately it is not obvious what obvious means. That's why you should ask an expert. May be he tells you that your approach is great and encourages you to publish in a good place, or he tells you that your approach is good, but only applicable to your specific problem, or he tells you that it is rather trivial. We cannot judge the quality of your results, or the quality of prior results. – Jan-Christoph Schlage-Puchta Jul 24 '15 at 19:08
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    @Wrzlprmft: By bad I mean journals most people never heard of. If your standards are sufficiently low you get everything published which is not complete nonsense. Vice versa it is common to assume that everything published in a strange place is close to worthless. I know several people who count such publications with the weight -1. Note that this is not my opinion, but a common opinion. While I agree that not publishing is better than publishing a bad paper, I don't believe that the quality of a paper can be judged by looking at the name of the journal it appeared in. – Jan-Christoph Schlage-Puchta Jul 24 '15 at 19:17
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Here some questions and statements that might help in your decision:

  • You must know previous publications on the subject. Where have these been published? There must be some interest in it for some people at least.

  • Since there are people who care about the subject, what can that result contribute to them?

  • Write an abstract. Then write an introduction.

  • "it does seem to outperform all previously published heuristics", but in terms of what? Do you have a rigorous complexity estimate? Do you have an experiment on your laptop?

I hope this is helpful.

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