String indexing for patterns with wildcards. Theory Comput

Abstract. We consider the problem of indexing a string t of length n to report the occurrences of a query pattern p containing m characters and j wildcards. Let occ be the number of occurrences of p in t, and σ the size of the alphabet. We obtain the following results. – A linear space index with query time O(m+σj log logn+ occ). This significantly improves the previously best known linear space index by Lam et al. [ISAAC 2007], which requires query time Θ(jn) in the worst case. – An index with query timeO(m+j+occ) using spaceO(σk 2 n logk logn), where k is the maximum number of wildcards allowed in the pattern. This is the first non-trivial bound with this query time. – A time-space trade-off, generalizing the index by Cole et al. [STOC 2004]. Our results are obtained using a novel combination of well-known and new techniques, which could be of independent interest.