Linear algorithm for conservative degenerate pattern matching

A degenerate symbol  x˜ over an alphabet Σ is a non-empty subset of Σ, and a sequence of such symbols is a degenerate string. A degenerate string is said to be conservative if its number of non-solid symbols is upper-bounded by a fixed positive constant k  . We consider here the matching problem of conservative degenerate strings and present the first linear-time algorithm that can find, for given degenerate strings P˜ and T˜ of total length n containing k   non-solid symbols in total, the occurrences of P˜ in T˜ in O(nk) time.