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- W2490681498 abstract "In this paper we address the longest common extension (LCE) problem: to compute the length $ell$ of the longest common prefix between any two suffixes of $Tin Sigma^n$ with $ Sigma = {0, ldots sigma-1} $. We present two fast and space-efficient solutions based on (Karp-Rabin) textit{fingerprinting} and textit{sampling}. Our first data structure exploits properties of Mersenne prime numbers when used as moduli of the Karp-Rabin hash function and takes $nlceil log_2sigmarceil$ bits of space. Our second structure works with any prime modulus and takes $nlceil log_2sigmarceil + n/w + wlog_2 n$ bits of space ($ w $ memory-word size). Both structures support $mathcal Oleft(mlogsigma/w right)$-time extraction of any length-$m$ text substring, $mathcal O(logell)$-time LCE queries with high probability, and can be built in optimal $mathcal O(n)$ time. In the first case, ours is the first result showing that it is possible to answer LCE queries in $o(n)$ time while using only $mathcal O(1)$ words on top of the space required to store the text. Our results improve the state of the art in space usage, query times, and preprocessing times and are extremely practical: we present a C++ implementation that is very fast and space-efficient in practice." @default.
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- W2490681498 date "2016-07-22" @default.
- W2490681498 modified "2023-09-27" @default.
- W2490681498 title "Fast Longest Common Extensions in Small Space." @default.
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