The errors can be substitutions, insertions or deletions in fragments. Transpositions are common, but can be treated as composed of insertion and a deletion or two substitutions. Because of this, we should consider both orientations for every fragment. For n fragments, we end up with 2 n combinations. In a true assembly program we do not actually search for 2 n combinations.
Repeats are sequences that appear two or more times in the target molecule.
If the repeats are covered within a single fragment then there is no assembly problem. Here we seek the shortest superstring of a collection of given strings. It contains all fragments in F as substrings. Note that when f strings are provided one has to know the orientation of the strings as well. S should be a perfect superstring an not an approximate one.