Linear Algorithm for Conservative Degenerate Pattern Matching

A degenerate symbol x̃ 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 P̃ and T̃ of total length n containing k non-solid symbols in total, the occurrences of P̃ in T̃ in O(nk) time.