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• W2963299914 abstract "Burrows-Wheeler transform (BWT) is an invertible text transformation that, given a text $T$ of length $n$, permutes its symbols according to the lexicographic order of suffixes of $T$. BWT is one of the most heavily studied algorithms in data compression with numerous applications in indexing, sequence analysis, and bioinformatics. Its construction is a bottleneck in many scenarios, and settling the complexity of this task is one of the most important unsolved problems in sequence analysis that has remained open for 25 years. Given a binary string of length $n$, occupying $O(n/log n)$ machine words, the BWT construction algorithm due to Hon et al. (SIAM J. Comput., 2009) runs in $O(n)$ time and $O(n/log n)$ space. Recent advancements (Belazzougui, STOC 2014, and Munro et al., SODA 2017) focus on removing the alphabet-size dependency in the time complexity, but they still require $Omega(n)$ time. In this paper, we propose the first algorithm that breaks the $O(n)$-time barrier for BWT construction. Given a binary string of length $n$, our procedure builds the Burrows-Wheeler transform in $O(n/sqrt{log n})$ time and $O(n/log n)$ space. We complement this result with a conditional lower bound proving that any further progress in the time complexity of BWT construction would yield faster algorithms for the very well studied problem of counting inversions: it would improve the state-of-the-art $O(msqrt{log m})$-time solution by Chan and Pv{a}trac{s}cu (SODA 2010). Our algorithm is based on a novel concept of string synchronizing sets, which is of independent interest. As one of the applications, we show that this technique lets us design a data structure of the optimal size $O(n/log n)$ that answers Longest Common Extension queries (LCE queries) in $O(1)$ time and, furthermore, can be deterministically constructed in the optimal $O(n/log n)$ time." @default.
• W2963299914 created "2019-07-30" @default.
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• W2963299914 date "2019-06-23" @default.
• W2963299914 modified "2023-10-01" @default.
• W2963299914 title "String synchronizing sets: sublinear-time BWT construction and optimal LCE data structure" @default.
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• W2963299914 doi "https://doi.org/10.1145/3313276.3316368" @default.
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