How to select 500 most pertinents tags among 10000?
That is a set cover problem. The documents (universe) are being covered by a set of tags (elements). 

In the case of maximizing the number of documents with a limited number of tags, a greedy approach can be taken. Find the single tag that covers the most documents. Then find the next tag that covers the most documents not already covered. Continue the process until the number of tags has been reached.