String indexing for patterns with wildcards

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 + σ j log log n + 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 time O(m + j + occ) using space , 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. © 2012 Springer-Verlag.