Example
As a simple example, suppose you're at a convention of foreign ambassadors, each of which speaks English and also various other languages. You want to make an announcement to a group of them, but because you don't trust them, you don't want them to be able to speak among themselves without you being able to understand them. To ensure this, you will choose a group such that no two ambassadors speak the same language, other than English. On the other hand you also want to give your announcement to as many ambassadors as possible.
In this case, the elements of the set are languages other than English, and the subsets are the sets of languages spoken by a particular ambassador. If two sets are disjoint, those two ambassadors share no languages other than English. A maximum set packing will choose the largest possible number of ambassadors under the desired constraint. Although this problem is hard to solve in general, in this example a good heuristic is to choose ambassadors who only speak unusual languages first, so that not too many others are disqualified.
Read more about this topic: Set Packing
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