I'll often find myself with some combinatorial problem that's obviously been studied before. For example, "Find the smallest set(s) of positive integers such that every integer from 1 to n is the sum of at most two elements of the set." Without becoming an expert on combinatorics, is there some way of finding out the name such a problem goes by in the literature, say in some sort of catalog? Googling and related tactics don't seem to be very helpful here, as most questions of this sort just consist of the words "set, smallest, such that, ..." repeatedly -- there's generally no unique word or phrase to latch on to. For instance, when I tried to Google the problem above, I got back the subset sum problem (given a set, determine whether some subset sums to zero) and the knapsack problem (given a set of objects with specific weights and values, find the most valuable subset under a given total weight), neither of which have anything to do with what I was actually looking for.
I'm not looking for the name of the problem above in particular (although it wouldn't hurt if anyone knows it), but rather some clean way of looking such things up for myself. Does such a catalog exist?
EDIT: My basic idea here is that a large number of combinatorial problems fall into some basic, MADLIBS-style patterns, for instance:
Choices of $m$ elements of the set ___, (with|without) repetition, (with|without) ordering, satisfying the additional constraint ____.
(Paths|circuits) through a (directed|undirected), (vertex|edge) weighted graph, which visit each (edge|vertex), such that the total weight is (maximal|minimal), and such that _.
An index that listed things in this manner would be helpful to non-experts.