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.
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A linear space index with query time O(m + σ j loglogn + 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.
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An index with query time O(m + j + occ) using space \(O(\sigma^{k^2} n \log^k\log n)\), where k is the maximum number of wildcards allowed in the pattern. This is the first non-trivial bound with this query time.
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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.
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Bille, P., Gørtz, I.L., Vildhøj, H.W., Vind, S. (2012). String Indexing for Patterns with Wildcards. In: Fomin, F.V., Kaski, P. (eds) Algorithm Theory – SWAT 2012. SWAT 2012. Lecture Notes in Computer Science, vol 7357. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-31155-0_25
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