Abstract
The suffix array is one of the most prevalent data structures for string indexing; it stores the lexicographically sorted list of suffixes of a given string. Its practical advantage compared to the suffix tree is space efficiency. In Property Indexing, we are given a string x of length n and a property \(\varPi \), i.e. a set of \(\varPi \)-valid intervals over x. A suffix-tree-like index over these valid prefixes of suffixes of x can be built in time and space \(\mathcal {O}(n)\). We show here how to directly build a suffix-array-like index, the Property Suffix Array (PSA), in time and space \(\mathcal {O}(n)\). We mainly draw our motivation from weighted (probabilistic) sequences: sequences of probability distributions over a given alphabet. Given a probability threshold \(\frac{1}{z}\), we say that a string p of length m matches a weighted sequence X of length n at starting position i if the product of probabilities of the letters of p at positions \(i,\ldots ,i+m-1\) in X is at least \(\frac{1}{z}\). Our algorithm for building the PSA can be directly applied to build an \(\mathcal {O}(nz)\)-sized suffix-array-like index over X in time and space \(\mathcal {O}(nz)\).
P. Charalampopoulos—Supported by the Graduate Teaching Scholarship scheme of the Department of Informatics at King’s College London and by the A.G. Leventis Foundation.
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Charalampopoulos, P., Iliopoulos, C.S., Liu, C., Pissis, S.P. (2018). Property Suffix Array with Applications. In: Bender, M., Farach-Colton, M., Mosteiro, M. (eds) LATIN 2018: Theoretical Informatics. LATIN 2018. Lecture Notes in Computer Science(), vol 10807. Springer, Cham. https://doi.org/10.1007/978-3-319-77404-6_22
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