A pattern α is a string of variables and terminal letters. We say that
α matches a word w, consisting only of terminal letters, if w can be
obtained by replacing the variables of α by terminal words. The matching
problem, i.e., deciding whether a given pattern matches a given word, was
heavily investigated: it is NP-complete in general, but can be solved
efficiently for classes of patterns with restricted structure. If we are
interested in what is the minimum Hamming distance between w and any word u
obtained by replacing the variables of α by terminal words (so matching
under Hamming distance), one can devise efficient algorithms and matching
conditional lower bounds for the class of regular patterns (in which no
variable occurs twice), as well as for classes of patterns where we allow
unbounded repetitions of variables, but restrict the structure of the pattern,
i.e., the way the occurrences of different variables can be interleaved.
Moreover, under Hamming distance, if a variable occurs more than once and its
occurrences can be interleaved arbitrarily with those of other variables, even
if each of these occurs just once, the matching problem is intractable. In this
paper, we consider the problem of matching patterns with variables under edit
distance. We still obtain efficient algorithms and matching conditional lower
bounds for the class of regular patterns, but show that the problem becomes, in
this case, intractable already for unary patterns, consisting of repeated
occurrences of a single variable interleaved with terminals