Lyndon Array Construction during Burrows-Wheeler Inversion

10/27/2017

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by   Felipe A. Louza, et al.

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Universidade de São Paulo

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Università del Piemonte Orientale

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University of Campinas

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McMaster University

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In this paper we present an algorithm to compute the Lyndon array of a string T of length n as a byproduct of the inversion of the Burrows-Wheeler transform of T. Our algorithm runs in linear time using only a stack in addition to the data structures used for Burrows-Wheeler inversion. We compare our algorithm with two other linear-time algorithms for Lyndon array construction and show that computing the Burrows-Wheeler transform and then constructing the Lyndon array is competitive compared to the known approaches. We also propose a new balanced parenthesis representation for the Lyndon array that uses 2n+o(n) bits of space and supports constant time access. This representation can be built in linear time using O(n) words of space, or in O(n n/ n) time using asymptotically the same space as T.