Property suffix array with applications

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 Π, i.e. a set of Π -valid intervals over x. A suffix-tree-like index over these valid prefixes of suffixes of x can be built in time and space O(n). We show here how to directly build a suffix-array-like index, the Property Suffix Array (PSA), in time and space O(n). We mainly draw our motivation from weighted (probabilistic) sequences: sequences of probability distributions over a given alphabet. Given a probability threshold 1z, 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, …, i+ m- 1 in X is at least 1z. Our algorithm for building the PSA can be directly applied to build an O(nz) -sized suffix-array-like index over X in time and space O(nz).