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Computation of the suffix array, Burrows-Wheeler transform and FM-index in V-order
Theoretical Computer Science  (IF0.827),  Pub Date : 2021-06-06, DOI: 10.1016/j.tcs.2021.06.004
Jacqueline W. Daykin, Neerja Mhaskar, W.F. Smyth

V-order is a total order on strings that determines an instance of Unique Maximal Factorization Families (UMFFs), a generalization of Lyndon words. The fundamental V-comparison of strings can be done in linear time and constant space. V-order has been proposed as an alternative to lexicographic order (lexorder) in the computation of suffix arrays and in the suffix-sorting induced by the Burrows-Wheeler transform (BWT). In line with the recent interest in the connection between suffix arrays and Lyndon factorization, in this paper we obtain similar results for the V-order factorization. Indeed, we show that the results describing the connection between suffix arrays and Lyndon factorization are matched by analogous V-order processing. We also describe a methodology for efficiently computing the FM-Index in V-order, as well as V-order substring pattern matching using backward search.