Compressed Text Indexing with Wildcards

Let T = T1φ 1T2φ k2 · · ·φdTd+1 be a text of total length n, where characters of each Ti are chosen from an alphabet Σ of size σ, and φ denotes a wildcard symbol. The text indexing with wildcards problem is to index T such that when we are given a query pattern P , we can locate the occurrences of P in T efficiently. This problem has been applied in indexing genomic sequences that contain single-nucleotide polymorphisms (SNP) because SNP can be modeled as wildcards. Recently Tam et al. (2009) and Thachuk (2011) have proposed succinct indexes for this problem. In this paper, we present the first compressed index for this problem, which takes only nHh + o(n log σ) +O(d logn) bits space, where Hh is the hth-order empirical entropy (h = o(logσ n)) of T .