Find the shortest string that is not a sub-string of a set of strings
Here's one possible solution, similar to the linked question: Algorithm Request: “Shortest non-existing substring over given alphabet”

Use a sliding window over each input string to build your trie. 


For n=1 to n=max(length(s)) where s is an input string, do:
For each s, construct window of size n, slide window over s adding each window (substring of size n) to the trie, then
Visit each parent of the leaf set of the trie. If there exists a parent node whose set of child nodes is smaller than the size of the alphabet, then you can form your desired string from this parent by appending a character from the alphabet that does not result in a string identical to one of the leaf nodes
If no such parent node exists, continue to next larger n