Solving the String Statistics Problem in Time O(n log n)

The string statistics problem consists of preprocessing a string of length n such that given a query pattern of length m, the maximum number of non-overlapping occurrences of the query pattern in the string can be reported efficiently. Apostolico and Preparata introduced the minimal augmented suffix tree (MAST) as a data structure for the string statistics problem, and showed how to construct the MAST in time \( \mathcal{O} \) (nlog2 n) and how it supports queries in time \( \mathcal{O} \) (m) for constant sized alphabets. A subsequent theorem by Fraenkel and Simpson stating that a string has at most a linear number of distinct squares implies that the MAST requires space \( \mathcal{O} \) (n). In this paper we improve the construction time for the MAST to \( \mathcal{O} \) (nlogn) by extending the algorithm of Apostolico and Preparata to exploit properties of efficient joining and splitting of search trees together with a refined analysis.

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