When is a new method publishable? In computer Science, let us assume that we have three different methods, A, B and C, to solve the problem X. 


All three methods have been proposed by more or less the same group of authors 
A improves B that improves C, and all the methods are optimal in their results (for example method A converges faster than B, so it needs a smaller sample to perform the same task and produces more stable results).
All three methods have been presented in a top conference of the field.


Assume now that an author (myself in this case) has a fourth method D, which solves the problem X in a more general setting (a setting that was of no interest for the authors of method A, B and C) but is not optimal (while methods A, B and C are optimal) and has performances between method A and B (on real data).

In this setting, what are the possibilities of being published for method D, and should the author go on investing time on method D? 

How much space is there in scientific literature for methods solving the same problem?
In general, for any scientific paper, the key question for being able to publish in a reputable venue is: "Do we learn something new and interesting?"

In this case, I think the key questions to ask in this regard are:


Is there a set of real-world (or otherwise interesting) problems that fit the more general case of algorithm D, and for which A/B/C are not applicable (or perform badly)?
Does algorithm D also out-perform even-more-general algorithms (e.g., some of the foundational algorithms), or do they not apply for some reason?


If the answer to both question is yes, then you've probably got a nicely publishable result.  If the answer to either one is no, then you've probably got something new but not particularly interesting: that may still be publishable in some venue, but probably not well and probably won't have an impact.