Question

Given a string s, what is the most efficient way of identifying the shortest supersequence of s from a bag of strings? Also, the last character of s should match the last character of the superstring.

Answer 1

Unless i misunderstood it, this problem is most certainly in P.

A naive approach would be:

1. Take all strings in B ending with same character as s. Call this new bag B’. Can be done in O(|B|)
2. Select all strings that are supersequences of s in the bag B’.
   It can be done in O(|B’|* max(|z|)) for z in B. Testing if a given string s is a subsequence of another string z can be done in O(|z|)
3. Select the shortest one of previously found strings (in O(|B’|))

Where |x| means size of x.

You can combine those steps, but it’s O(|B| * max(|z|)) anyway.