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Compressed text indexing with wildcards. (English) Zbl 1280.68305
Summary: Let \(T=T_1\phi^{k_1}T_2\phi^{k_2}\cdots\phi^{k_d}T_{d+1}\) 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, A. Tam et al. [“Succinct text indexing with wildcards”, in: SPIRE 2009, 39–50 (2009)] and C. Thachuk [Lect. Notes Comput. Sci. 6661, 27–40 (2011; Zbl 1339.68339)] 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 of space, where \(H_h\) is the \(h\)th-order empirical entropy \((h=o(\log_\sigma n))\) of \(T\).

MSC:
68W32 Algorithms on strings
68R05 Combinatorics in computer science
68P15 Database theory
68U15 Computing methodologies for text processing; mathematical typography
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