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Suppose there is a set of combinations of distinct objects a, b, c... We have already imposed some order on the objects(i.e. a<b<c<...) so that we can always sort the combinations to make them appear in a fixed manner.

The domain of the problem is a set of combinations(a very random subset of all the combinations):{ab, ac, abc, afi, bc, cde, cdg, cho...} Please note that each combination is sorted so that they are in the alphabetic order. Now comes the problem: given some objects, i.e. {a, b, c}, how do we efficiently find all the combinations of the three object that appeared in the domain?(in this case, the result should be [ab,ac,abc,bc] )  Is there any special algorithm designed to deal with it in a sound and complete way? The naive way of implementation is not efficient w.r.t big domain, i.e. try all the combinations of a,b,c and match them in the domain. Please forget about it.

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Please post any thought, many thanks.