Abstract
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 the Lyndon factorization, we in this paper make a first attempt to obtain similar results for the V-order factorization. Indeed, we show that the results describing the connection between suffix arrays and the Lyndon factorization are matched by analogous V-order processing. We then apply the V-BWT to implement pattern matching in V-order after suitably modifying the FM-index.
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Acknowledgements
The third and fifth authors were funded by NSERC Grant Number: 10536797. The fourth author was partially supported by a grant from Pubali Bank Ltd., Bangladesh. The second author was part-funded by the European Regional Development Fund through the Welsh Government, Grant Number 80761-AU-137 (West):
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Alatabbi, A., Daykin, J.W., Mhaskar, N., Rahman, M.S., Smyth, W.F. (2019). Applications of V-Order: Suffix Arrays, the Burrows-Wheeler Transform & the FM-index. In: Das, G., Mandal, P., Mukhopadhyaya, K., Nakano, Si. (eds) WALCOM: Algorithms and Computation. WALCOM 2019. Lecture Notes in Computer Science(), vol 11355. Springer, Cham. https://doi.org/10.1007/978-3-030-10564-8_26
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DOI: https://doi.org/10.1007/978-3-030-10564-8_26
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