fastest c++ / stl algorithm to find strings in set of pairs

I'm looking for a very fast algorithm to return the values of pairs which are stored in a set like this set<pair<string,string>>

To be more specific I look for all the second-values, where the first-value starts with a string.

Example: I have a set with these pairs:

<"asdf","qwer">,
<"asdfghj", "qwertyui">,
<"lkj","mno">

Then I call my method with "asdf" an I want to get back a set or vector of these strings:

"qwer"
"qwertyui"

Thank you!