What do you call the problem of finding a largest possible subset of strings with smallest possible information content? I'm studying a particular instantiation of this problem in a different setting and would like to know about this more abstract problem. In terms of Kolmogorov complexity, this would be the following decision problem.
Given: a finite set of binary strings S and positive integers c and d.
Question: is there a subset S' of S such that |S'| is at least c and the resource-bounded Kolmogorov complexity of S' is at most d?
Edit: consider the complexity measure to be one of the resource-bounded Kolmogorov complexity measures (for example, the length of the shortest program that outputs a given string, with an additive penalty of the logarithm of the running time of the program) to make the problem computable, as suggested in the comments.