How to make my work publishable if my supervisor isn’t any help?

Question

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.

Answer 1

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 authorship.

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.

Answer 2

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.

Answer 3

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.