We consider the problem of computing a shortest solid cover of an
indeterminate string. An indeterminate string may contain non-solid symbols,
each of which specifies a subset of the alphabet that could be present at the
corresponding position. We also consider covering partial words, which are a
special case of indeterminate strings where each non-solid symbol is a don't
care symbol. We prove that indeterminate string covering problem and partial
word covering problem are NP-complete for binary alphabet and show that both
problems are fixed-parameter tractable with respect to k, the number of
non-solid symbols. For the indeterminate string covering problem we obtain a
2O(klogk)+nkO(1)-time algorithm. For the partial word covering
problem we obtain a 2O(klogk)+nkO(1)-time algorithm. We
prove that, unless the Exponential Time Hypothesis is false, no
2o(k)nO(1)-time solution exists for either problem, which shows
that our algorithm for this case is close to optimal. We also present an
algorithm for both problems which is feasible in practice.Comment: full version (simplified and corrected); preliminary version appeared
at ISAAC 2014; 14 pages, 4 figure