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    Low Space External Memory Construction of the Succinct Permuted Longest Common Prefix Array

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    The longest common prefix (LCP) array is a versatile auxiliary data structure in indexed string matching. It can be used to speed up searching using the suffix array (SA) and provides an implicit representation of the topology of an underlying suffix tree. The LCP array of a string of length nn can be represented as an array of length nn words, or, in the presence of the SA, as a bit vector of 2n2n bits plus asymptotically negligible support data structures. External memory construction algorithms for the LCP array have been proposed, but those proposed so far have a space requirement of O(n)O(n) words (i.e. O(nlogn)O(n \log n) bits) in external memory. This space requirement is in some practical cases prohibitively expensive. We present an external memory algorithm for constructing the 2n2n bit version of the LCP array which uses O(nlogσ)O(n \log \sigma) bits of additional space in external memory when given a (compressed) BWT with alphabet size σ\sigma and a sampled inverse suffix array at sampling rate O(logn)O(\log n). This is often a significant space gain in practice where σ\sigma is usually much smaller than nn or even constant. We also consider the case of computing succinct LCP arrays for circular strings
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