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arXiv · 1508.02968

Space-efficient detection of unusual words

Djamal Belazzougui·Fabio Cunial
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Abstract

Detecting all the strings that occur in a text more frequently or less frequently than expected according to an IID or a Markov model is a basic problem in string mining, yet current algorithms are based on data structures that are either space-inefficient or incur large slowdowns, and current implementations cannot scale to genomes or metagenomes in practice. In this paper we engineer an algorithm based on the suffix tree of a string to use just a small data structure built on the Burrows-Wheeler transform, and a stack of $O(σ^2\log^2 n)$ bits, where $n$ is the length of the string and $σ$ is the size of the alphabet. The size of the stack is $o(n)$ except for very large values of $σ$. We further improve the algorithm by removing its time dependency on $σ$, by reporting only a subset of the maximal repeats and of the minimal rare words of the string, and by detecting and scoring candidate under-represented strings that $\textit{do not occur}$ in the string. Our algorithms are practical and work directly on the BWT, thus they can be immediately applied to a number of existing datasets that are available in this form, returning this string mining problem to a manageable scale.

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Djamal Belazzougui, Fabio Cunial. 2015-08-12. Space-efficient detection of unusual words. https://arxiv.org/abs/1508.02968

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