Compressed Text Indexing with Wildcards

Let T = T-1 phi T-k1(2)phi(k2) ... phi T-kd(d+1) be a text of total length n, where characters of each T-i are chosen from an alphabet Sigma of size sigma, and phi 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 nH(h) + o(n log sigma) + O(d log n) bits space, where H-h is the hth-order empirical entropy (h = o(log(sigma) n)) of T.