Finding the smallest string that contains a given set of substrings

Question

The algorithm I am looking for has the following requirements: Input is a set of strings. You are looking for a string containing all input strings. The resulting string should be as short as possible. At least shorter than just concatenating all input strings if possible.

Examples:

Input: a ab bc
Output: abc

Input: abcd bcde ef
Output: abcdef

Is there a name for this problem with which it is better to search for solutions?